2306.09896

# Demystifying GPT Self-Repair for Code Generation **Authors**: - Theo X. Olausson (MIT EECS & CSAIL &Jeevana Priya Inala) > Correspondence totheoxo@mit.edu. Work partially done while T.X.O. was at Microsoft Research. \usetikzlibrary positioning Abstract Large Language Models (LLMs) have shown remarkable aptitude in code generation but still struggle on challenging programming tasks. Self-repair—in which the model debugs and fixes mistakes in its own code—has recently become a popular way to boost performance in these settings. However, only very limited studies on how and when self-repair works effectively exist in the literature, and one might wonder to what extent a model is really capable of providing accurate feedback on why the code is wrong when that code was generated by the same model. In this paper, we analyze GPT-3.5 and GPT-4’s ability to perform self-repair on APPS, a challenging dataset consisting of diverse coding challenges. To do so, we first establish a new evaluation strategy dubbed pass@t that measures the pass rate of the tasks against the total number of tokens sampled from the model, enabling a fair comparison to purely sampling-based approaches. With this evaluation strategy, we find that the effectiveness of self-repair is only seen in GPT-4. We also observe that self-repair is bottlenecked by the feedback stage; using GPT-4 to give feedback on the programs generated by GPT-3.5 and using expert human programmers to give feedback on the programs generated by GPT-4, we unlock significant performance gains. 1 Introduction Large language models (LLMs) have proven capable of generating code snippets from natural language specifications, but still struggle on complex coding challenges such as those found in competitions and professional software engineering interviews. Recent work has sought to improve performance by leveraging self-repair [Gupta et al., 2020, Le et al., 2022, Chen et al., 2023b, Zhang et al., 2023], in which the model introspects and corrects mistakes in its own code. Figure 1 shows a typical workflow of a self-repair based approach. First, given a specification, a program is sampled from a code generation model; this program is then executed on a suite of unit tests provided as part of the specification; if the program fails on any unit test, then the error message and the faulty program are given to a feedback generation model, which outputs a short explanation of why the code failed; finally, the feedback is passed to a repair model, which generates a fixed version of the program. On the surface, this is a very attractive idea. It allows the system to overcome mistakes caused by unfortunate samples during decoding; easily incorporates feedback during the repair phase from symbolic systems such as compilers, static analysis tools, and execution engines; and mimics the trial-and-error way in which human software engineers write code. <details> <summary>x1.png Details</summary>  ### Visual Description ## Diagram: Code Model Feedback Loop ### Overview The image illustrates a feedback loop for a code model. It shows a user interacting with a code model, the execution of the model, feedback generation, and the model's subsequent refinement. The process involves assertions to validate the model's output. ### Components/Axes The diagram consists of the following components, arranged horizontally from left to right: 1. **User:** A silhouette of a person. 2. **Code Model (Initial):** A circular representation of a code model, containing interconnected blue nodes. 3. **Execution:** A set of assertions comparing the model's output to expected values. 4. **Feedback Model:** A circular representation of a feedback model, containing interconnected yellow nodes. 5. **Code Model (Refined):** A circular representation of a code model, containing interconnected blue nodes. 6. **Assertions (Final):** A set of assertions comparing the model's output to expected values. The diagram also includes numbered arrows indicating the flow of information: (1), (2), (3), (4), and (5). ### Detailed Analysis * **User:** The user interacts with the initial code model. * **Code Model (Initial):** The model is represented by a circle containing six interconnected blue nodes. * **Execution:** The model's output is evaluated using three assertions: * `assert f(x1) == y1` - Marked with a green checkmark, indicating success. * `assert f(x2) == y2` - Marked with a green checkmark, indicating success. * `assert f(x3) == y3` - Marked with a red "X", indicating failure. * **Feedback Model:** Based on the execution results, a feedback model is generated. It is represented by a circle containing six interconnected yellow nodes. * **Code Model (Refined):** The feedback model is used to refine the initial code model. The refined model is again represented by a circle containing six interconnected blue nodes. * **Assertions (Final):** The refined model's output is evaluated using three assertions: * `assert f(x1) == y1` - Marked with a green checkmark, indicating success. * `assert f(x2) == y2` - Marked with a green checkmark, indicating success. * `assert f(x3) == y3` - Marked with a green checkmark, indicating success. ### Key Observations * The initial code model fails one of the assertions (`assert f(x3) == y3`). * The feedback model is used to refine the code model. * The refined code model passes all three assertions. ### Interpretation The diagram illustrates a process of iterative model refinement using feedback from execution results. The initial model has a flaw, which is identified through assertions. A feedback model is then used to correct this flaw, resulting in a refined model that produces the desired output. This demonstrates a closed-loop system for improving code model accuracy and reliability. The use of assertions provides a clear and objective measure of the model's performance at each stage. </details> [ box/.style=rectangle, draw=black, align=justify, inner sep=3pt, tallbox/.style=box, fill=backcolor!50, shortbox/.style=box, fill=backcolor!50 ] [tallbox, text width=3.6cm, minimum height=3.2cm] (A) Given is a string $s$ representing the day of the week today. $s$ is one of SUN, MON, TUE, WED, THU, FRI, or SAT. After how many days is the next Sunday (tomorrow or later)? ⬇ # UNIT TESTS # (EXECUTABLE) assert f (’ MON ’) == 6 assert f (’ WED ’) == 4 assert f (’ SUN ’) == 7 ; \node [draw=none, left=0.2cm of A.west] (1); [shortbox, right=0.2cm of A.north east, text width=8cm, anchor=north west] (B) ⬇ def f (s): return (7 - [’ SUN ’, ... , ’ FRI ’, ’ SAT ’]. index (s)) %7 ; \node [draw=none, right=0.2cm of B.east] (2); [shortbox, below=0.2cm of B, text width=8cm] (C) Given input ’SUN’, the program returned 0, but the expected output was 7. ; \node [draw=none, right=0.2cm of C.east] (3); [shortbox, below=0.2cm of C, text width=8cm] (D) The code does not account for the case where the input is ’SUN’ and the output should be 7. This can be fixed by removing the modulo operation. ; \node [draw=none, right=0.2cm of D.east] (4); [shortbox, below=0.2cm of D, text width=8cm] (E) ⬇ def f (s): return (7 - [’ SUN ’, ... , ’ FRI ’, ’ SAT ’]. index (s)) # %7 ; \node [draw=none, right=0.2cm of E.east] (5); Figure 1: Self-repair with separate code and feedback models. First, a user gives a specification in the form of text and a suite of unit tests (1). Then, a code model (blue) generates a program (2). The program is checked against the unit tests using a symbolic execution engine, and an error message is returned (3). In order to provide more signal to the code model, textual feedback as to why this happened is provided by a feedback model (yellow; 4). Finally, this feedback is used by the code model to repair the program (5). However, it is important to remember that self-repair requires more invocations of the model, thus increasing the computational cost. In particular, whether self-repair is a winning strategy or not ultimately boils down to whether you would—at an equivalent compute budget—have had a greater chance of success if you had simply drawn more code samples i.i.d. from the model and checked them against the suite of unit tests provided as part of the task. Crucially, the effectiveness of self-repair depends not only on the model’s ability to generate code, which has been studied extensively in the literature, but also on its ability to identify how the code (generated by the model itself) is wrong with respect to the task specification. As far as we are aware, no previous or contemporary work has attempted to study the effect of this stage in detail. In this paper, we study the effectiveness of self-repair with GPT-3.5 [Ouyang et al., 2022, OpenAI, 2022] and GPT-4 [OpenAI, 2023] when solving competition-level code generation tasks. We begin by proposing a new evaluation strategy dubbed pass@t, in which the likelihood of obtaining a correct program (with respect to the given unit tests) is weighed against the total number of tokens sampled from the model. Using this instead of the traditional pass@k [Chen et al., 2021, Kulal et al., 2019] metric (which weighs pass rate against the number of trials), we are able to accurately compare performance gained through self-repair against any additional work done by the model when generating the feedback and carrying out the repair. Using this new evaluation strategy, we then carefully study the dynamics of the self-repair process under a range of hyper-parameters. Finally, given our primary objective of gaining insight into the state-of-the-art code generation models’ ability to reflect upon and debug their own code, we carry out a set of experiments in which we investigate the impact of improving the feedback stage alone. We do so by analyzing the impact of using a stronger feedback generation model than the code generation model (using GPT-4 to generate feedback for GPT-3.5 code model), as well as by carrying out a study in which human participants provide feedback on incorrect programs, in order to compare model-generated self-feedback to that provided by human programmers. From our experiments, we find that: 1. When taking the cost of doing inspection and repair into account, performance gains from self-repair can only be seen with GPT-4; for GPT-3.5, the pass rate with repair is lower than or equal to that of the baseline, no-repair approach at all budgets. 1. Even for the GPT-4 model, performance gains are modest at best ( $66\%→ 71\%$ pass rate with a budget of 7000 tokens, $≈$ the cost of 45 i.i.d. GPT-4 samples) and depend on having sufficient diversity in the initial programs. 1. Replacing GPT-3.5’s explanations of what is wrong with feedback produced by GPT-4 leads to better self-repair performance, even beating the baseline, no-repair GPT-3.5 approach ( $50\%→ 54\%$ at 7000 tokens). 1. Replacing GPT-4’s own explanations with those of a human programmer improves repair significantly, leading to a 57% increase in the number of repaired programs which pass the tests. 2 Related work Program synthesis with large language models. The use of large language models for program synthesis has been studied extensively in the literature [Li et al., 2022, Austin et al., 2021, Chen et al., 2021, Le et al., 2022, Fried et al., 2023, Nijkamp et al., 2023, Chowdhery et al., 2022, Touvron et al., 2023, Li et al., 2023]. This literature has predominantly focused on evaluating models in terms of either raw accuracy or the pass@k metric [Kulal et al., 2019, Chen et al., 2021], often leveraging filtering techniques based on execution [Li et al., 2022, Shi et al., 2022] or ranking [Chen et al., 2021, Inala et al., 2022, Zhang et al., 2022] to reduce the number of samples which are considered for the final answer. In contrast, our work focuses on evaluating the models from the point of view of minimizing the number of samples that need to be drawn from the model in the first place. Our work is also different in that we assume access to the full collection of input-output examples, as is typically done in inductive synthesis [Kitzelmann, 2010, Polozov and Gulwani, 2015, Gulwani et al., 2017, Chen et al., 2019a, Ellis et al., 2021]. In particular, unlike some prior work [Li et al., 2022, Shi et al., 2022], we do not make a distinction between public tests used for filtering and private tests used to determine correctness, since our method does not involve filtering the outputs. Code repair. Statistical and learning-based techniques for code repair have a rich history in both the programming languages and machine learning communities, although they have traditionally been used predominantly to repair human-written code [Long and Rinard, 2016, Bader et al., 2019, Le Goues et al., 2021, Yasunaga and Liang, 2021, Chen et al., 2019b, Mesbah et al., 2019, Wang et al., 2018]. More recently, using repair as a post-processing step to improve code which was itself automatically synthesised has been used in the synthesis of both domain-specific languages [Gupta et al., 2020] and general-purpose code [Le et al., 2022, Yasunaga and Liang, 2021, 2020]. Our contribution differs from most prior work in this literature in the use of textual feedback for repair, which is possible thanks to the above mentioned rise in the use of LLMs for program synthesis. Contemporary work on LLM self-repair. Recognizing that there is much contemporary work seeking to self-repair with LLMs, we now briefly highlight a few such papers which are particularly close to our work. Zhang et al. [2023] explore self-repair without natural language feedback on APPS [Hendrycks et al., 2021] using a diverse range of fine-tuned models. They also experiment with prompt-based repair using Codex [Chen et al., 2021], InCoder [Fried et al., 2023], and CodeGen [Nijkamp et al., 2023]. Notably, their framework does not consider the cost associated with feedback and repair, which presents a significantly different perspective on self-repair. Similarly, Chen et al. [2023b] assess Codex’s ability to self-repair across a variety of tasks, in a framework that closely resembles that which we study in this work. However, their study differs from ours in terms of the models considered, the evaluation strategy, and, most importantly, the research goal, as we specifically aim to investigate the significance of the textual feedback stage. Self-repair, or frameworks with other names that are conceptually very similar to it, has also been used in contexts outside of code generation. Peng et al. [2023] use self-repair to mitigate hallucinations and improve factual grounding in a ChatGPT-based web search assistant, in which the model revises its initial response based on self-generated feedback. Similarly, Madaan et al. [2023] present a framework in which a model iteratively provides feedback on and revises its output until a stopping criterion is reached; they apply this framework to a range of tasks, including dialogue and code optimization. Ultimately, we see our work, in which we use the novel evaluation metric pass@t to investigate the significance of the textual feedback stage in competition-level self-repair, as being complementary to contemporary research which uses traditional metrics to evaluate self-repair in a broader context. We are eager to see what the implications of our results will be in these other domains. 3 Methodology 3.1 Self-Repair Overview As shown in Figure 1, our self-repair approach involves 4 stages: code generation, code execution, feedback generation, and code repair. We now formally define these four stages. Code generation. Given a specification $\psi$ , a programming model $M_{P}$ first generates $n_{p}$ samples i.i.d., which we denote $$ \{p_{i}\}_{i=1}^{n_{p}}\stackrel{{\scriptstyle i.i.d.}}{{\sim}}M_{P}(\psi) $$ Code execution. These $n_{p}$ code samples are then executed against a test bed. Recall from Section 2 that we assume that we have access to the full set of tests in executable form (see Section 5 for a brief discussion on the validity of this assumption in software engineering domains). Thus, we stop if any sample passes all of the tests, since a satisfying program has then been found. Otherwise, we collect the error messages $\{e_{i}\}_{i}$ returned by the execution environment. These error messages either contain the compile/runtime error information or an example input on which the program’s output differs from the expected one. An example is shown in Figure 1 (component 3). Feedback generation. Since the error messages from the execution environment are usually very high-level, they provide little signal for repair. Therefore, as an intermediate step, we use a feedback model to produce a more detailed explanation of what went wrong; Figure 1 (component 4) shows an example. Formally, in this stage, we generate $n_{f}$ feedback strings, $\{f_{ij}\}_{j}$ , for each wrong program, $p_{i}$ , as follows: $$ \{f_{ij}\}_{j=1}^{n_{f}}\stackrel{{\scriptstyle i.i.d.}}{{\sim}}M_{F}(\psi;p_{% i};e_{i}) $$ Having an explicit feedback generation step allows us to ablate this component so that we can study its significance in isolation. Code repair. In the final step, for each initial program $p_{i}$ and feedback $f_{ij}$ , $n_{r}$ candidate repaired programs are sampled from $M_{P}$ We use the same model for both the initial code generation and the code repair, since these are fundamentally similar tasks.: $$ \{r_{ijk}\}_{k=1}^{n_{r}}\stackrel{{\scriptstyle i.i.d.}}{{\sim}}M_{P}(\psi;p_% {i};e_{i};f_{ij}) $$ Repair tree. We call the tree of interleaved text and programs produced by this procedure—rooted in the specification $\psi$ , then branching into initial programs $p_{i}$ , each of which branches into feedback $f_{ij}$ and then repairs $r_{ijk}$ —a repair tree, $T$ (Figure 2). Caveat: jointly sampling feedback and repair. The general framework presented above does not require the programming model and feedback model to be the same, thus allowing for the use of specialized models in the system. However, when $M_{P}=M_{F}$ we jointly generate both the feedback and the repaired program in a single API call, since both GPT-3.5 and GPT-4 have a natural tendency to interleave text and code in their responses. See Appendix E for a detailed look at how the prompt differs between this and the previous setting. Formally, we denote this as $$ \{(f_{ij},r_{ij})\}_{j=1}^{n_{fr}}\stackrel{{\scriptstyle i.i.d.}}{{\sim}}M_{P% }(\psi;p_{i};e_{i}) $$ <details> <summary>x2.png Details</summary>  ### Visual Description ## Diagram: Hierarchical Code Generation and Repair Process ### Overview The image depicts a hierarchical diagram illustrating a code generation and repair process. It shows a tree-like structure with nodes representing different stages or components, connected by arrows indicating the flow of information. The diagram also includes a feedback loop for repair. ### Components/Axes * **Nodes:** The diagram consists of circular nodes labeled with variables and indices. * Top-level node: ψ (Psi) * Second-level nodes: p1, ..., pnp * Third-level nodes: f11, ..., f1nf, fnp1, ..., fnpnf * Fourth-level nodes: r111, ..., r11nr, r1nf1, ..., r1nfnr, rnp11, ..., rnp1nr, rnpnf1, ..., rnpnfnr * **Arrows:** Arrows connect the nodes, indicating the direction of flow. * **Ellipses:** Horizontal ellipses (...) are used to indicate that there are intermediate nodes not explicitly shown. * **Right-side labels:** * "Code Gen" (blue arrow pointing downwards) * "Feedback" (yellow arrow pointing downwards) * "Repair" (blue arrow pointing downwards) ### Detailed Analysis The diagram represents a hierarchical process, starting from the top node ψ. This node branches out to multiple nodes p1 to pnp. Each p node further branches out to f nodes, and each f node branches out to r nodes. * **Top Level:** The process starts with a single node labeled ψ. * **Second Level:** ψ branches into p1, ..., pnp. The number of p nodes is denoted by 'np'. * **Third Level:** Each p node (e.g., p1) branches into f nodes (e.g., f11, ..., f1nf). The number of f nodes for p1 is 'nf'. Similarly, pnp branches into fnp1, ..., fnpnf. * **Fourth Level:** Each f node (e.g., f11) branches into r nodes (e.g., r111, ..., r11nr). The number of r nodes for f11 is 'nr'. Similarly, f1nf branches into r1nf1, ..., r1nfnr, and so on. * **Feedback Loop:** On the right side, "Code Gen" (blue) indicates the initial code generation step. "Feedback" (yellow) suggests a feedback mechanism, and "Repair" (blue) indicates a repair process based on the feedback. The arrows suggest a sequential flow: Code Generation -> Feedback -> Repair. ### Key Observations * The diagram illustrates a multi-level hierarchical structure. * The indices suggest a nested structure, where each level depends on the previous one. * The "Code Gen," "Feedback," and "Repair" labels indicate an iterative process. ### Interpretation The diagram likely represents a code generation and repair system where the initial code (ψ) is refined through multiple stages (p, f, r). The indices suggest that the number of branches at each level can vary. The feedback loop indicates that the generated code is evaluated, and repairs are made based on the feedback, leading to an iterative refinement process. The diagram provides a high-level overview of the system's architecture and workflow. </details> Figure 2: A repair tree begins with a specification $\psi$ (root node), then grows into initial programs, feedback, and repairs. 3.2 pass@t: pass rate vs. token count Since self-repair requires several dependent model invocations of non-uniform cost, this is a setting in which pass@ $k$ —the likelihood of obtaining a correct program in $k$ i.i.d. samples—is not a suitable metric for comparing and evaluating various hyper-parameter choices of self-repair. Instead, we measure the pass rate as a function of the total number of tokens sampled from the model, a metric which we call pass@t. Formally, suppose that you are given a dataset $D=\{\psi_{d}\}_{d}$ and a chosen set of values for the hyper-parameters $(M_{P},M_{F},n_{p},n_{f},n_{r})$ . Let $T_{d}^{i}\sim M(\psi_{d})$ denote a repair tree that is sampled as described in Section 3.1 for the task $\psi_{d}$ ; let $\text{size}(T_{d}^{i})$ denote the total number of program and feedback tokens in the repair tree; and say that $T_{d}^{i}\models\psi_{d}$ is true if, and only if, $T_{d}^{i}$ has at least one leaf program that satisfies the unit tests in the specification $\psi_{d}$ . Then the pass@t metric of this choice of hyper-parameters is defined as the expected pass rate at the number of tokens which you would expect to generate with this choice of hyper-parameters: | | $\displaystyle\texttt{pass@t}\triangleq\mathop{\mathbb{E}}_{\stackrel{{% \scriptstyle\psi_{d}\sim D}}{{T_{d}^{i}\sim M(\psi_{d})}}}\left[T_{d}^{i}% \models\psi_{d}\right]\quad\textbf{at}\quad t=\mathop{\mathbb{E}}_{\stackrel{{% \scriptstyle\psi_{d}\sim D}}{{T_{d}^{i}\sim M(\psi_{d})}}}\left[\text{size}(T_% {d}^{i})\right]$ | | | --- | --- | --- | In our experiments, we plot bootstrapped estimates of these two quantities. To obtain these, we first generate a very large repair tree for each task specification, with: $N_{p}≥ n_{p}$ initial program samples; $N_{f}≥ n_{f}$ feedback strings per wrong program; and $N_{r}≥ n_{r}$ repair candidates per feedback string. Given a setting of $(n_{p},n_{f},n_{r})$ , we then sub-sample (with replacement) $N_{t}$ different repair trees from this frozen dataset. Finally, we compute the sample mean and standard deviation of the pass rate and the tree size over these $N_{t}$ trees. Estimating the pass@t in this way greatly reduces the computational cost of our experiments, since we can reuse the same initial dataset to compute the estimates for all of the various choices of $n_{p},n_{f}$ , and $n_{r}$ . We use $N_{p}=50$ for all experiments, and consider $n_{p}≤ 25$ for the self-repair approaches and $n_{p}≤ 50$ for the baseline, no-repair approach. Similarly, for the feedback strings, we use $N_{f}=25$ and $n_{f}≤ 10$ (except for Section 4.2, in which we only consider $n_{f}=1$ and therefore settle for $N_{f}=10$ instead). For the repair candidates, since we do joint sampling of feedback and repair in most of our experiments, we set $N_{r}=n_{r}=1$ . Finally, we use $N_{t}=1000$ for all settings. 4 Experiments In this section, we carry out experiments to answer the following research questions: (a) In the context of challenging programming puzzles, is self-repair better than i.i.d. sampling without repair for the models we consider? If so, under what hyper-parameters is self-repair most effective? (b) Would a stronger feedback model boost the model’s repair performance? (c) Would keeping a human in the loop to provide feedback unlock better repair performance even for the strongest model? We evaluate these hypotheses on Python programming challenges from the APPS dataset [Hendrycks et al., 2021]. The APPS dataset contains a diverse range of programming challenges paired with a suite of tests, making it a perfect (and challenging) setting to study self-repair in. To keep our experiments tractable, we evaluate on a subset of the APPS test set, consisting of 300 tasks. These tasks are proportionally sampled in accordance with the frequency of the different difficulty levels in the test set: 180 interview-level questions, 60 competition-level questions, and 60 introductory-level questions (listed in Appendix F). We use GPT-3.5 [Ouyang et al., 2022, OpenAI, 2022] and GPT-4 [OpenAI, 2023] as our models of choice, and implement self-repair using templated string concatenation with one-shot prompting; our prompts are given in Appendix E. When appropriate, we compare against a baseline without repair. This baseline, shown with a black line in the plots, is simply i.i.d. sampling from the corresponding model (e.g., GPT-4 when we explore whether GPT-4 is capable of self-repair). Based on preliminary experiments, we set the decoding temperature to $0.8$ for all the models to encourage diverse samples. <details> <summary>x3.png Details</summary>  ### Visual Description ## Chart: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a scatter plot showing the relationship between the mean pass rate and the mean number of tokens generated. The plot includes data for different values of `np` (represented by lines) and `nfr` (represented by scatter points). The x-axis represents the mean number of tokens generated, and the y-axis represents the mean pass rate. ### Components/Axes * **X-axis:** Mean number of tokens generated. Scale ranges from 0 to 10000, with tick marks at 0, 2000, 4000, 6000, 8000, and 10000. * **Y-axis:** Mean pass rate. Scale ranges from 0.0 to 1.0, with tick marks at 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. * **Legend (Top-Left):** * Brown line: `np = 1` * Yellow line: `np = 2` * Teal line: `np = 5` * Light Blue line: `np = 10` * Dark Blue line: `np = 25` * **Legend (Top-Right):** * Gray circle: `nfr = 1` * Gray downward-pointing triangle: `nfr = 3` * Gray square: `nfr = 5` * Gray upward-pointing triangle: `nfr = 10` ### Detailed Analysis **Data Series:** * **np = 1 (Brown Line):** The line starts at approximately (0, 0.25) and increases, gradually leveling off to approximately 0.5 at x = 10000. * **np = 2 (Yellow Line):** The line starts at approximately (0, 0.25) and increases, gradually leveling off to approximately 0.5 at x = 10000. * **np = 5 (Teal Line):** The line starts at approximately (0, 0.25) and increases, gradually leveling off to approximately 0.5 at x = 10000. * **np = 10 (Light Blue Line):** The line starts at approximately (0, 0.25) and increases, gradually leveling off to approximately 0.5 at x = 10000. * **np = 25 (Dark Blue Line):** The line starts at approximately (0, 0.25) and increases, gradually leveling off to approximately 0.5 at x = 10000. **Scatter Points:** * **nfr = 1 (Gray Circle):** Data points are located at approximately (200, 0.27), (4000, 0.48), (10000, 0.52). * **nfr = 3 (Gray Downward-Pointing Triangle):** Data points are located at approximately (1500, 0.31), (3500, 0.45), (6000, 0.42). * **nfr = 5 (Gray Square):** Data points are located at approximately (2000, 0.34), (8000, 0.48). * **nfr = 10 (Gray Upward-Pointing Triangle):** Data points are located at approximately (2500, 0.35), (6000, 0.42). ### Key Observations * All `np` lines start at approximately the same y-value (around 0.25) and converge to a similar y-value (around 0.5) as the mean number of tokens generated increases. * The scatter points for different `nfr` values are scattered around the lines, showing some variability. * The lines representing different `np` values are very close to each other, suggesting that `np` has a minimal impact on the mean pass rate. ### Interpretation The chart suggests that the mean pass rate increases with the mean number of tokens generated, but the rate of increase diminishes as the number of tokens increases. The values of `np` appear to have a negligible effect on the mean pass rate, as the lines for different `np` values are almost overlapping. The scatter of points for different `nfr` values around the lines indicates that `nfr` might have some influence on the mean pass rate, but it is not as significant as the mean number of tokens generated. The data implies that increasing the number of tokens generated leads to a higher pass rate, but there is a point of diminishing returns. </details> (a) Mean pass rate vs. number of tokens generated. Black line is i.i.d. sampling without repair from GPT-3.5. Note that the error bars are often smaller than the markers; all settings have a standard deviation of less than 1.5 absolute points on the y-axis. Results truncated at $t=10,000$ . <details> <summary>x4.png Details</summary>  ### Visual Description ## Heatmap: Performance vs. Number of Feedback Repairs and Initial Programs ### Overview The image is a heatmap visualizing performance (represented by color intensity and numerical values) as a function of two variables: the number of feedback repairs (nfr) and the number of initial programs (np). The heatmap shows how performance changes as these two parameters are varied. "O.O.B." is present in the heatmap, likely indicating "Out of Bounds" or a similar condition where a value is not applicable or available. ### Components/Axes * **Y-axis (Vertical):** "Number of feedback-repairs (nfr)". Values: 1, 3, 5, 10. * **X-axis (Horizontal):** "Number of initial programs (np)". Values: 1, 2, 5, 10, 25. * **Cells:** Each cell in the heatmap represents a combination of nfr and np. The color of the cell indicates the performance value, with darker shades of brown representing lower values and lighter shades of yellow representing higher values. The numerical value is displayed within each cell. * **Color Scale:** The color scale is implicit, with darker browns indicating lower values and lighter yellows indicating higher values. Dark gray indicates "O.O.B." ### Detailed Analysis Here's a breakdown of the values in the heatmap: | nfr \ np | 1 | 2 | 5 | 10 | 25 | | :------- | :--- | :--- | :--- | :--- | :--- | | 10 | 0.78 | 0.86 | O.O.B. | O.O.B. | O.O.B. | | 5 | 0.80 | 0.86 | 0.95 | O.O.B. | O.O.B. | | 3 | 0.81 | 0.87 | 0.94 | 1.00 | O.O.B. | | 1 | 0.87 | 0.92 | 0.96 | 0.99 | O.O.B. | **Observations:** * **Trend with increasing np (for a fixed nfr):** For a fixed number of feedback repairs (nfr), the performance generally increases as the number of initial programs (np) increases, up to a point. After np=10, the values are "O.O.B." * **Trend with increasing nfr (for a fixed np):** For a fixed number of initial programs (np), the performance generally decreases as the number of feedback repairs (nfr) increases. * **"O.O.B." Values:** All values for np = 25 are "O.O.B.". Also, for np = 10, the values are "O.O.B." when nfr is 5 or 10. For np = 5, the value is "O.O.B." when nfr is 10. * **Best Performance:** The highest performance value (1.00) is achieved when nfr = 3 and np = 10. * **Worst Performance:** The lowest performance value (0.78) is achieved when nfr = 10 and np = 1. ### Key Observations * Performance tends to improve with more initial programs (np), but only up to a certain point. * Increasing the number of feedback repairs (nfr) does not always improve performance and can sometimes decrease it. * The "O.O.B." values suggest that certain combinations of nfr and np are not feasible or result in undefined behavior. ### Interpretation The heatmap suggests that there is an optimal balance between the number of feedback repairs and the number of initial programs. Increasing the number of initial programs generally improves performance, likely because it provides a larger search space for finding better solutions. However, increasing the number of feedback repairs can sometimes degrade performance, possibly due to overfitting or getting stuck in local optima. The "O.O.B." values indicate limitations in the experimental setup or algorithm, where certain combinations of parameters are not valid or lead to errors. The best performance is achieved with a moderate number of feedback repairs (nfr = 3) and a relatively high number of initial programs (np = 10). </details> (b) Normalized mean pass rate relative to the (interpolated) baseline at an equivalent budget (number of tokens). Cells for which the number of tokens generated exceeds 50 samples from the GPT-3.5 baseline marked O.O.B. (out of bounds). Figure 3: Pass rate versus number of tokens generated for various settings of $n_{p}$ (number of initial programs) and $n_{fr}$ (number of repairs sampled per program). GPT-3.5 is used for all samples, including the baseline. 4.1 Self-repair requires strong models and diverse initial samples In this subsection, we consider the setup where $M_{P}=M_{F}∈\{\text{GPT-3.5, GPT-4}\}$ , i.e., where one single model is used for both code/repair generation and feedback generation. To evaluate if self-repair leads to better pass@t than a no-repair, i.i.d. sampling-based baseline approach, we vary $n_{p}$ and $n_{fr}$ —that is, the number of initial i.i.d. base samples and joint feedback, repair samples drawn from $M_{P}$ —in the range $(n_{p},n_{fr})∈\{1,2,5,10,25\}×\{1,3,5,10\}$ . Recall that when $M_{P}=M_{F}$ , we jointly sample for $n_{fr}$ pairs of feedback strings and repair programs instead of sampling them one after another (Section 3.1). The results are shown in Figure 3 for GPT-3.5 and Figure 4 for GPT-4. In the left-hand subplots, the color of each dot indicates the number of initial samples ( $n_{p}$ ), while its shape indicates the number of feedback-repair samples ( $n_{fr}$ ). In the right hand plots, we show a heat-map with the two hyper-parameters along the axes, where the value in each cell indicates the mean pass rate with self-repair normalized by the mean pass rate of the baseline, no-repair approach when given the same token budget (i.e., pass@t at the same value of t). When the normalized mean pass rate is 1, this means that self-repair has the same pass rate as the no-repair, baseline approach at that same token budget; a higher value ( $≥ 1$ ) means self-repair performs better than the baseline. From the plots, we can see that for the GPT-3.5 model, the pass@t is lower than or equal to the corresponding baseline (black line) for all settings of $n_{p},n_{fr}$ , clearly showing that self-repair is not an effective strategy for GPT-3.5. On the other hand, for GPT-4, there are several values of $n_{p},n_{fr}$ for which the pass rate with self-repair is significantly better than that of the baseline. For example, with $n_{p}=10,n_{fr}=3$ the pass rate increases from 65% to 70%, and with $n_{p}=25,n_{fr}=1$ it increases from 65% to 71%. Our experiments also show a clear trend with respect to the relationship between the hyper-parameters. Given a fixed number of feedback-repairs ( $n_{fr}$ ), increasing the number of initial programs ( $n_{p}$ ) (i.e., moving right along the x-axis on the heat maps) consistently leads to relative performance gains for both models. On the other hand, fixing $n_{p}$ and increasing $n_{fr}$ (i.e., moving up along the y-axis on the heat maps) does not appear to be worth the additional cost incurred, giving very marginal gains at higher budgets and even decreasing performance at lower budgets. This suggests that, given a fixed budget, the most important factor determining whether self-repair will lead to a correct program or not is the diversity of the base samples that are generated up-front, rather than the diversity of the repairs sampled. Having more initial samples increases the likelihood of there being at least one program which is close to the ideal program and, hence, can be successfully repaired. Since $n_{fr}=1$ is the best choice for the hyper-parameter $n_{fr}$ , we next isolate the effect of the number of initial programs, $n_{p}$ , by exploring a denser set of possible values: $(n_{p},n_{fr})∈\{1,2,....,24,25\}×\{1\}$ . The plots are shown in Figure 6 for both $M_{P}=M_{F}∈\{\text{GPT-3.5},\text{GPT-4}\}$ and the baseline, no-repair approaches. Note that since $n_{fr}$ is fixed, in these plots, there is a direct correlation between $n_{p}$ and the total number of tokens, $t$ . Again, we see that self-repair is not an effective strategy for the GPT-3.5 model, but that it is effective for GPT-4—especially at higher values of $n_{p}$ ( $≥ 5000$ ), where it increases pass rate by over 5 points. <details> <summary>x5.png Details</summary>  ### Visual Description ## Line Chart: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a line chart displaying the relationship between the mean pass rate and the mean number of tokens generated. The chart includes multiple data series, each representing a different configuration of parameters denoted as 'np' and 'nfr'. The x-axis represents the mean number of tokens generated, ranging from 0 to 10000. The y-axis represents the mean pass rate, ranging from 0.0 to 1.0. The chart includes a legend to distinguish between the different data series. ### Components/Axes * **X-axis:** Mean number of tokens generated, ranging from 0 to 10000 in increments of 2000. * **Y-axis:** Mean pass rate, ranging from 0.0 to 1.0 in increments of 0.2. * **Title (Y-axis):** Mean pass rate * **Title (X-axis):** Mean number of tokens generated * **Legend:** Located on the right side of the chart. * `np = 1` (Brown line) * `np = 2` (Yellow line) * `np = 5` (Light Blue line) * `np = 10` (Blue line) * `np = 25` (Dark Blue line) * `nfr = 1` (Dark Gray circle markers) * `nfr = 3` (Dark Gray downward triangle markers) * `nfr = 5` (Dark Gray square markers) * `nfr = 10` (Dark Gray upward triangle markers) ### Detailed Analysis * **np = 1 (Brown line):** The line starts at approximately (0, 0.45) and increases rapidly to approximately (2000, 0.58), then plateaus around 0.65. * **np = 2 (Yellow line):** The line starts at approximately (0, 0.4) and increases rapidly to approximately (2000, 0.60), then plateaus around 0.65. * **np = 5 (Light Blue line):** The line starts at approximately (0, 0.4) and increases rapidly to approximately (2000, 0.62), then plateaus around 0.65. * **np = 10 (Blue line):** The line starts at approximately (0, 0.4) and increases rapidly to approximately (2000, 0.62), then plateaus around 0.65. * **np = 25 (Dark Blue line):** The line starts at approximately (0, 0.4) and increases rapidly to approximately (2000, 0.62), then plateaus around 0.65. * **nfr = 1 (Dark Gray circle markers):** Data points are scattered. Approximate values: (200, 0.46), (6500, 0.72). * **nfr = 3 (Dark Gray downward triangle markers):** Data points are scattered. Approximate values: (1500, 0.55), (5000, 0.70). * **nfr = 5 (Dark Gray square markers):** Data points are scattered. Approximate values: (1500, 0.58), (7500, 0.71). * **nfr = 10 (Dark Gray upward triangle markers):** Data points are scattered. Approximate values: (1500, 0.54), (8000, 0.69). ### Key Observations * The mean pass rate generally increases with the mean number of tokens generated, but the rate of increase diminishes as the number of tokens increases. * The lines for different 'np' values (1, 2, 5, 10, 25) converge to a similar plateau level of mean pass rate. * The scattered data points for 'nfr' values (1, 3, 5, 10) appear to be distributed around the plateau level of the 'np' lines. ### Interpretation The data suggests that increasing the mean number of tokens generated initially leads to a significant improvement in the mean pass rate. However, after a certain point (around 2000 tokens), the improvement becomes marginal, and the pass rate plateaus. The different 'np' configurations seem to have a similar effect on the pass rate, as their lines converge. The 'nfr' values, represented by scattered data points, indicate the variability or distribution of the pass rate around the plateau level achieved by the 'np' configurations. The chart demonstrates that there is a diminishing return in increasing the number of tokens generated beyond a certain threshold, and the 'np' parameter has a limited impact on the final pass rate. </details> (a) Mean pass rate vs. number of tokens generated. Black line is i.i.d. sampling without repair from GPT-4. Note that the error bars are often smaller than the markers; all settings have a standard deviation of less than 1.5 absolute points on the y-axis. Results truncated at $t=10,000$ . <details> <summary>x6.png Details</summary>  ### Visual Description ## Heatmap: Performance vs. Number of Feedback Repairs and Initial Programs ### Overview The image is a heatmap visualizing performance (represented by color intensity) as a function of two variables: the number of feedback repairs (nfr) and the number of initial programs (np). The heatmap displays numerical values within each cell, and some cells are marked "O.O.B." (likely indicating "Out Of Bounds"). ### Components/Axes * **X-axis (Horizontal):** Number of initial programs (np). Values: 1, 2, 5, 10, 25. * **Y-axis (Vertical):** Number of feedback-repairs (nfr). Values: 1, 3, 5, 10. * **Color Scale:** The color intensity represents performance. Darker orange indicates lower values, transitioning to lighter yellow and then green for higher values. Black indicates "O.O.B." * **Cells:** Each cell contains a numerical value (performance) or the label "O.O.B.". ### Detailed Analysis or ### Content Details Here's a breakdown of the values in the heatmap: | nfr \ np | 1 | 2 | 5 | 10 | 25 | | :------- | :--- | :--- | :--- | :--- | :--- | | 10 | 0.90 | 0.98 | 1.05 | O.O.B. | O.O.B. | | 5 | 0.91 | 0.98 | 1.04 | 1.08 | O.O.B. | | 3 | 0.93 | 0.99 | 1.04 | 1.08 | O.O.B. | | 1 | 0.98 | 1.01 | 1.04 | 1.06 | 1.09 | **Observations:** * **nfr = 10:** Performance starts at 0.90 for np = 1, increases to 0.98 for np = 2, then to 1.05 for np = 5. It is "O.O.B." for np = 10 and np = 25. * **nfr = 5:** Performance starts at 0.91 for np = 1, increases to 0.98 for np = 2, then to 1.04 for np = 5, and 1.08 for np = 10. It is "O.O.B." for np = 25. * **nfr = 3:** Performance starts at 0.93 for np = 1, increases to 0.99 for np = 2, then to 1.04 for np = 5, and 1.08 for np = 10. It is "O.O.B." for np = 25. * **nfr = 1:** Performance starts at 0.98 for np = 1, increases to 1.01 for np = 2, then to 1.04 for np = 5, 1.06 for np = 10, and 1.09 for np = 25. **Trends:** * For a fixed number of feedback repairs (nfr), performance generally increases as the number of initial programs (np) increases, up to a point. * For a fixed number of initial programs (np), performance generally decreases as the number of feedback repairs (nfr) increases. * "O.O.B." (Out Of Bounds) occurs more frequently with higher numbers of feedback repairs (nfr) and initial programs (np). ### Key Observations * The highest performance values (1.08 and 1.09) are observed when the number of feedback repairs is low (nfr = 1, 3, 5) and the number of initial programs is relatively high (np = 10, 25). * The lowest performance values (0.90, 0.91, 0.93) are observed when the number of feedback repairs is high (nfr = 10, 5, 3) and the number of initial programs is low (np = 1). * The "O.O.B." values suggest that certain combinations of feedback repairs and initial programs are not feasible or result in invalid outputs. ### Interpretation The heatmap suggests that there is an optimal balance between the number of feedback repairs and the number of initial programs. Too many feedback repairs, especially with a small initial program pool, can lead to lower performance. Conversely, a small number of feedback repairs with a large initial program pool can yield the best performance. The "O.O.B." values indicate constraints or limitations in the system being modeled, where certain parameter combinations are not viable. The data suggests that increasing the number of initial programs generally improves performance, but this effect is limited by the number of feedback repairs. The system likely becomes unstable or encounters errors when both the number of feedback repairs and initial programs are too high. </details> (b) Normalized mean pass rate relative to the (interpolated) baseline at an equivalent budget (number of tokens). Cells for which the number of tokens generated exceeds 50 samples from the GPT-4 baseline marked O.O.B. (out of bounds). Figure 4: Pass rate versus number of tokens generated for various settings of $n_{p}$ (number of initial programs) and $n_{fr}$ (number of repairs per failing program). GPT-4 is used for all samples, including the baseline. 4.2 GPT-4 feedback improves GPT-3.5 repair Next, we conduct an experiment in which we evaluate the impact of using a separate, stronger model to generate the feedback. This is to test the hypothesis that self-repair is held back (especially for GPT-3.5) by the model’s inability to introspect and debug its own code. For this experiment, we set $M_{P}$ = GPT-3.5 and $M_{F}$ = GPT-4 and vary the hyper-parameters as $(n_{p},n_{f},n_{r})∈\{1,2,....,24,25\}×\{1\}×\{1\}$ , similarly to the previous experiment. Note that since we are now operating in a setting in which the feedback and repair stages must be separated, we have three hyper-parameters— $n_{p},n_{f},n_{r}$ —instead of two— $n_{p},n_{fr}$ (Section 3.1). To keep the computational budget tractable, and since the variance was seen to be very low in the previous experiment, we use $N_{f}=10$ instead of $N_{f}=25$ for this experiment (see Section 3.2). The results for this experiment are shown in Figure 6 (bright blue line). We observe that in terms of absolute performance, $M_{P}=$ GPT-3.5, $M_{F}=$ GPT-4 does break through the performance barrier and becomes marginally more efficient than i.i.d. sampling from GPT-3.5. This suggests that the textual feedback stage itself is of crucial importance, and that improving it relieves the bottleneck in GPT-3.5 self-repair. Figure 5: Mean pass rate for each model when $n_{fr}$ (or $n_{f}$ and $n_{r}$ ) = 1. Shaded region is $± 1$ standard deviation. Complete breakdown per difficulty in Appendix A. <details> <summary>x7.png Details</summary>  ### Visual Description ## Line Chart: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a line chart comparing the mean pass rate against the mean number of tokens generated for different GPT models. The chart displays five different configurations, each represented by a distinct colored line, along with shaded regions indicating uncertainty. The x-axis represents the mean number of tokens generated, ranging from 0 to 10000. The y-axis represents the mean pass rate, ranging from 0.0 to 1.0. ### Components/Axes * **X-axis:** "Mean number of tokens generated" with tick marks at 0, 2000, 4000, 6000, 8000, and 10000. * **Y-axis:** "Mean pass rate" with tick marks at 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. * **Legend:** Located in the bottom-right quadrant of the chart, it identifies each line by color and corresponding model configuration: * Dark Blue: *M_P* = GPT-4 (no repair) * Light Green: *M_P* = GPT-4; *M_F* = GPT-4 * Gray: *M_P* = GPT-3.5 (no repair) * Brown: *M_P* = GPT-3.5; *M_F* = GPT-3.5 * Light Blue: *M_P* = GPT-3.5; *M_F* = GPT-4 ### Detailed Analysis * **Dark Blue Line:** *M_P* = GPT-4 (no repair) * Trend: The line starts at approximately 0.4 at 0 tokens and increases rapidly, then plateaus around 0.65 at 6000 tokens, remaining relatively flat until 10000 tokens. * Data Points: (0, 0.4), (2000, 0.6), (6000, 0.65), (10000, 0.65) * **Light Green Line:** *M_P* = GPT-4; *M_F* = GPT-4 * Trend: The line starts at approximately 0.4 at 0 tokens and increases rapidly, then plateaus around 0.7 at 6000 tokens, remaining relatively flat until 10000 tokens. * Data Points: (0, 0.4), (2000, 0.65), (6000, 0.7), (10000, 0.7) * **Gray Line:** *M_P* = GPT-3.5 (no repair) * Trend: The line starts at approximately 0.25 at 0 tokens and increases rapidly, then plateaus around 0.5 at 6000 tokens, remaining relatively flat until 10000 tokens. * Data Points: (0, 0.25), (2000, 0.4), (6000, 0.5), (10000, 0.5) * **Brown Line:** *M_P* = GPT-3.5; *M_F* = GPT-3.5 * Trend: The line starts at approximately 0.25 at 0 tokens and increases rapidly, then plateaus around 0.52 at 6000 tokens, remaining relatively flat until 10000 tokens. * Data Points: (0, 0.25), (2000, 0.42), (6000, 0.52), (10000, 0.52) * **Light Blue Line:** *M_P* = GPT-3.5; *M_F* = GPT-4 * Trend: The line starts at approximately 0.4 at 0 tokens and increases rapidly, then plateaus around 0.55 at 6000 tokens, remaining relatively flat until 10000 tokens. * Data Points: (0, 0.4), (2000, 0.5), (6000, 0.55), (10000, 0.57) ### Key Observations * GPT-4 models (dark blue and light green lines) generally outperform GPT-3.5 models (gray, brown, and light blue lines) in terms of mean pass rate. * The "no repair" GPT-4 model (dark blue) performs slightly worse than the GPT-4 model with repair (light green). * For GPT-3.5 models, using GPT-4 for repair (*M_F* = GPT-4, light blue line) improves the mean pass rate compared to using GPT-3.5 for repair (*M_F* = GPT-3.5, brown line) or no repair (gray line). * All models show a rapid increase in mean pass rate with an increasing number of tokens generated up to around 6000 tokens, after which the rate of increase slows significantly. ### Interpretation The data suggests that the GPT-4 models are more effective at generating correct outputs compared to the GPT-3.5 models, as indicated by their higher mean pass rates. Repair mechanisms, particularly using GPT-4 for repair, can improve the performance of both GPT-4 and GPT-3.5 models. The diminishing returns observed after 6000 tokens suggest that there is a point beyond which generating more tokens does not significantly improve the pass rate. This could be due to the models reaching a saturation point in their ability to correct errors or generate more accurate outputs. </details> | Introductory Interview Competition | 42.64% 19.33% 3.67% | 62.21% 45.67% 14.67% | | --- | --- | --- | | Overall | 33.30% | 52.60% | Figure 5: Mean pass rate for each model when $n_{fr}$ (or $n_{f}$ and $n_{r}$ ) = 1. Shaded region is $± 1$ standard deviation. Complete breakdown per difficulty in Appendix A. Figure 6: Success rate of repair with GPT-4’s explanations vs. with those of our human participants. 4.3 Human feedback significantly improves the success rate of GPT-4 repair For our final experiment, we consider the effect of using an expert human programmer’s feedback when performing repair with stronger models such as GPT-4. The goal of this study is not to do a direct comparison between a human-in-the-loop approach vs. self-repair, since a human-in-the-loop approach imposes more cognitive burden, which we do not study. Instead, our goal is to understand how the model’s ability to identify mistakes in the code compares to that of a human, and how this affects downstream performance in self-repair. We thus conduct both qualitative and quantitative analyses of the impact of human feedback on self-repair. Data collection methodology. We first sample 20 tasks $\{\psi_{i}\}_{i=1}^{20}$ from the APPS test set; to make the data collection process less time-consuming for the participants of the study, we skew the distribution towards easier tasks (14 introductory; 3 interview; 3 competition). For each task $\psi_{i}$ , we then sample two failing GPT-4 completions $p_{i,1},p_{i,2}$ , making for a total of $20· 2=40$ programs to refine. We recruit 16 participants, consisting of 15 graduate students and one professional machine learning engineer. Each participant is provided with five different base programs based on their level of experience with Python and competitive programming. Each program is taken from a distinct task; participants are never showed two different programs belonging to the same task. Participants are then asked to explain, in their own words, what the program is doing wrong. To reduce the cognitive load for participants, each program $p_{i,j}$ is accompanied by the error message $e_{i,j}$ and two feedback strings $f_{i,j,1},f_{i,j,2}$ sampled from GPT-4. We obtain these feedback strings by randomly sampling from the feedback-repair pairs used in the previous experiments and removing the code block. Note that each of the 40 programs will be shown to two different participants, to reduce variance caused by participants’ skill levels and writing style. Participants were told to spend approximately one hour on the study overall, and were compensated with a $15 gift card. This human data collection was approved by our Institutional Review Board (IRB) and carried out exclusively through an online survey. See Appendix B for a complete, concrete copy of the instructions which we provide to our participants. Quantitative Analysis. Having obtained two human-written pieces of feedback $h_{i,j,1},h_{i,j,2}$ for each program $p_{i,j}$ , we sample 25 repaired programs $$ \{r_{l}\}_{l=1}^{25}\stackrel{{\scriptstyle i.i.d.}}{{\sim}}\text{GPT-4}(\psi_% {i};p_{i,j};e_{i,j};f) $$ for $f∈\{h_{i,j,1},h_{i,j,2},f_{i,j,1},f_{i,j,2}\}$ . That is: we ask GPT-4 to generate 25 candidate repairs for each program, conditioned on the specification, the initial program, and a feedback string which is either set to one of GPT-4’s own feedback strings or to one provided by a participant. Finally, we execute all of these candidate repairs against the test bed, and take note of how often they pass. The results are summarized in Table 6, with a complete task-by-task breakdown in Appendix C. We note first of all that the overall success rate is increased by over $1.57×$ when we replace GPT-4’s own debugging with that of our human participants. Perhaps unsurprisingly, the relative difference increases as the problems get harder, indicating that GPT-4’s ability to produce accurate and useful feedback trails further behind our human participants’ when the task (and code) becomes more complex. Qualitative Analysis. In this section, we qualitatively analyze the difference between the feedback provided by the human participants and the feedback provided by GPT-4. We manually go through all of GPT-4’s and the participants’ feedback and note down whether the feedback: (a) seems, at a cursory glance, to be correct, or if it is obviously inaccurate; (b) explicitly suggests a small change to the code (e.g. "change the condition on line X"); (c) explicitly suggests a large change to the code (e.g. "frame the problem as min-cut instead of shortest-path"); (d) contains blocks of pseudocode or Python (which GPT-4’s feedback never does, per our experiment design); or (e) expresses uncertainty (using phrases such as "unsure", "it appears", etc.). We do not count individual single-line statements/expressions such as “ $x=5$ ” as pseudocode or Python. Examples of each category are shown in Appendix D. We find that - Only 2/80 human-contributed feedback strings include pseudocode or explicit Python; that is, almost all human feedback we obtain is natural language interleaved with occasional single-statement math/code expressions. - GPT-4’s feedback is much more likely to be obviously inaccurate (32/80 vs. 7/80 for human feedback). - GPT-4 is more likely to explicitly suggest small changes (54/80 vs 42/80; 28/48 vs. 38/73 when seemingly correct), while our human participants show a slightly greater tendency to suggest high-level changes (23/80 vs. 18/80 for GPT-4; 21/73 vs. 13/48 when seemingly correct). - Our human participants sometimes express uncertainty (7/80); GPT-4 never does (0/80). This further analysis suggests that the results in Table 6 are not due to artefacts such as our participants providing explicit code blocks which the model simply copies. Instead, the difference in performance appears to be caused by a combination of more accurate feedback, a greater ability to suggest high-level, large-scale changes to the code when needed, and our participants’ ability to express their uncertainty (instead of confidently giving potentially inaccurate feedback). 5 Limitations Firstly, to reduce computational cost, we pre-populate and then sub-sample from large repair trees, which introduces statistical bias. We mitigate this by being generous in our uncertainty of the pass@t, using the maximum standard deviation across all points. We also note that this standard deviation, which is obtained at values of $(n_{p},n_{f},n_{r})$ that are small enough that we have very many samples thereof in our pre-populated repair trees, is very low ( $<2\%$ pass rate for all models). While these measures do not completely eliminate the risk of bias in our results, not performing this amortization would have required significantly larger amounts of compute. Secondly, we assume access to an executable suite of unit tests for each task. We do not, for example, require the model to extract tests from textual specifications. While this assumption may seem out of place in the era of chat-style assistants like ChatGPT [OpenAI, 2022], it does align well with established software engineering practices like Test-Driven Development [Astels, 2003]. Furthermore, techniques which automatically synthesize test cases given a specification [Li et al., 2022, Chen et al., 2023a] may relieve some of the user burden. Finally, our study on human data did not track how much time the participants took to debug the programs. As a result, we can only evaluate the quality of the feedback (and the impact this has on repair). Further research at the intersection of HCI, AI, and program synthesis is needed to explore when and how human intervention should be leveraged, as well as how programming assistants should be designed to facilitate this style of interaction. 6 Broader Impact Any tool that improves the productivity of people writing software will necessarily also increase the productivity of people writing software with malicious intent. It is also important to remember that research on LLMs comes at a very high environmental cost. Although we exclusively use publicly available pre-trained models in this work, and so do not train any models of our own, even inference comes with a significant carbon footprint at scale. At the same time, this work—in which we weigh model performance against the computational cost of obtaining it, and through which we learn more about when and how these models do and do not work—is a step towards more sample-efficient usage paradigms. 7 Conclusion In this paper, we investigated the role of textual feedback in self-repair. We presented pass@t, a new evaluation strategy which takes the cost of carrying out repair into account, and then used this metric to show that (1) GPT-3.5 is not capable of carrying out self-repair on challenging coding tasks, and (2) while performance gains are seen in GPT-4, they are modest and rely on achieving sufficient diversity in the initial programs. Furthermore, by ablating the feedback stage we found that (3) substituting GPT-3.5’s feedback with GPT-4’s improved performance, even surpassing GPT-3.5’s baseline. Finally, we carried out an experiment with human participants, in which we found that (4) replacing GPT-4’s self-generated feedback with feedback provided by an experienced programmer increased the number of repaired programs which pass all unit tests by 57%. Acknowledgments and Disclosure of Funding T.X. Olausson is supported by the Defense Advanced Research Projects Agency (DARPA) under the ASKEM program, award HR00112220042. T.X. Olausson was also supported through a position at Microsoft Research for part of the time period during which this work was carried out. A. Solar-Lezama is supported by the National Science Foundation (NSF) and Intel Corporation through NSF Grant CCF:2217064. This work benefited greatly from discussion with several colleagues at Microsoft Research. 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The chart shows how the mean pass rate changes as the number of tokens generated increases, for different values of `np` and `nfr`. ### Components/Axes * **X-axis:** Mean number of tokens generated, ranging from 0 to 10000. * **Y-axis:** Mean pass rate, ranging from 0.0 to 1.0. * **Legend (Left):** Located on the left side of the chart, it identifies the lines corresponding to different values of `np`: * Brown line: `np = 1` * Yellow line: `np = 2` * Light Blue line: `np = 5` * Blue line: `np = 10` * Dark Blue line: `np = 25` * **Legend (Right):** Located on the right side of the chart, it identifies the markers corresponding to different values of `nfr`: * Dark Gray circle: `nfr = 1` * Dark Gray downward-pointing triangle: `nfr = 3` * Dark Gray square: `nfr = 5` * Dark Gray upward-pointing triangle: `nfr = 10` * A gray shaded region represents a confidence interval or standard deviation around the mean pass rate. ### Detailed Analysis * **Data Series Trends:** * The lines for `np = 1`, `np = 2`, `np = 5`, `np = 10`, and `np = 25` all show an upward trend initially, indicating that the mean pass rate increases as the number of tokens generated increases. The rate of increase slows down as the number of tokens generated gets larger, and the lines appear to plateau. * **Data Points:** * For `np = 1` (brown line): * At approximately 2000 tokens, the mean pass rate is around 0.65. * For `np = 2` (yellow line): * At approximately 2000 tokens, the mean pass rate is around 0.75. * For `np = 5` (light blue line): * At approximately 2000 tokens, the mean pass rate is around 0.82. * For `np = 10` (blue line): * At approximately 2000 tokens, the mean pass rate is around 0.82. * For `np = 25` (dark blue line): * At approximately 2000 tokens, the mean pass rate is around 0.82. * For `nfr = 1` (dark gray circle): * At approximately 200 tokens, the mean pass rate is around 0.6. * At approximately 5500 tokens, the mean pass rate is around 0.85. * For `nfr = 3` (dark gray downward-pointing triangle): * At approximately 1500 tokens, the mean pass rate is around 0.7. * At approximately 4000 tokens, the mean pass rate is around 0.83. * At approximately 8000 tokens, the mean pass rate is around 0.87. * For `nfr = 5` (dark gray square): * At approximately 1500 tokens, the mean pass rate is around 0.7. * At approximately 5500 tokens, the mean pass rate is around 0.85. * At approximately 9000 tokens, the mean pass rate is around 0.86. * For `nfr = 10` (dark gray upward-pointing triangle): * At approximately 1500 tokens, the mean pass rate is around 0.7. * At approximately 5500 tokens, the mean pass rate is around 0.85. * At approximately 9000 tokens, the mean pass rate is around 0.86. ### Key Observations * The mean pass rate generally increases with the mean number of tokens generated, but the rate of increase diminishes as the number of tokens increases. * The lines for different values of `np` converge as the number of tokens generated increases, suggesting that the impact of `np` on the mean pass rate becomes less significant at higher token counts. * The markers for different values of `nfr` are scattered, but generally show a similar trend of increasing mean pass rate with the number of tokens generated. * The gray shaded region indicates the variability or uncertainty in the mean pass rate. ### Interpretation The chart suggests that increasing the number of tokens generated generally improves the mean pass rate, but there is a point of diminishing returns. The values of `np` and `nfr` also influence the mean pass rate, but their impact may be less significant at higher token counts. The gray shaded region provides information about the reliability of the observed trends. The data could represent the performance of a language model or some other system that generates tokens, where the pass rate indicates the proportion of successful generations. </details> <details> <summary>x9.png Details</summary>  ### Visual Description ## Heatmap: Performance vs. Number of Feedback Repairs and Initial Programs ### Overview The image is a heatmap displaying performance values for different combinations of "Number of feedback-repairs" (nfr) and "Number of initial programs" (np). The heatmap uses a color gradient, with darker shades of orange representing lower values and lighter shades of yellow representing higher values. Some cells are marked "O.O.B." in dark grey, indicating "Out of Bounds". ### Components/Axes * **X-axis (Horizontal):** "Number of initial programs (np)" with values 1, 2, 5, 10, and 25. * **Y-axis (Vertical):** "Number of feedback-repairs (nfr)" with values 1, 3, 5, and 10. * **Data:** The cells within the heatmap contain numerical values or the label "O.O.B.". The color of each cell corresponds to the value it represents. ### Detailed Analysis The heatmap presents a matrix of performance values. Here's a breakdown of the data: | nfr | np = 1 | np = 2 | np = 5 | np = 10 | np = 25 | |---|---|---|---|---|---| | 10 | 0.87 | 0.93 | 0.97 | O.O.B. | O.O.B. | | 5 | 0.87 | 0.94 | 0.98 | 1.00 | O.O.B. | | 3 | 0.88 | 0.94 | 0.99 | 1.00 | O.O.B. | | 1 | 0.92 | 0.97 | 1.00 | 1.01 | 1.01 | * **nfr = 10:** The performance values are 0.87, 0.93, and 0.97 for np = 1, 2, and 5, respectively. The values for np = 10 and np = 25 are "O.O.B.". * **nfr = 5:** The performance values are 0.87, 0.94, 0.98, and 1.00 for np = 1, 2, 5, and 10, respectively. The value for np = 25 is "O.O.B.". * **nfr = 3:** The performance values are 0.88, 0.94, 0.99, and 1.00 for np = 1, 2, 5, and 10, respectively. The value for np = 25 is "O.O.B.". * **nfr = 1:** The performance values are 0.92, 0.97, 1.00, 1.01, and 1.01 for np = 1, 2, 5, 10, and 25, respectively. ### Key Observations * The performance generally increases as the number of initial programs (np) increases, up to a certain point. * For lower values of nfr (1, 3, 5), the performance tends to increase as np increases. * For higher values of nfr (10), the performance values are "O.O.B." for higher values of np (10 and 25). * The highest performance values (1.00 and 1.01) are observed when nfr = 1. * The lowest performance values (0.87 and 0.88) are observed when np = 1. ### Interpretation The heatmap suggests that increasing the number of initial programs (np) generally improves performance, but this effect is limited by the number of feedback repairs (nfr). When the number of feedback repairs is high (nfr = 10), the system may become unstable or encounter issues, resulting in "O.O.B." values for higher numbers of initial programs. The best performance is achieved with a low number of feedback repairs (nfr = 1) and a moderate to high number of initial programs (np = 5, 10, or 25). This indicates that a balance between exploration (initial programs) and refinement (feedback repairs) is crucial for optimal performance. The "O.O.B." values suggest that there are limits to how much the system can benefit from increasing both parameters simultaneously. </details> <details> <summary>x10.png Details</summary>  ### Visual Description ## Scatter Plot: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a scatter plot showing the relationship between the mean pass rate and the mean number of tokens generated. The plot includes data points for different values of `np` (represented by lines) and `nfr` (represented by markers). A gray line with a shaded area represents a general trend. ### Components/Axes * **X-axis:** Mean number of tokens generated, with ticks at 0, 2000, 4000, 6000, 8000, and 10000. * **Y-axis:** Mean pass rate, with ticks at 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. * **Legend (Top-Left):** * Brown line: `np = 1` * Yellow line: `np = 2` * Teal line: `np = 5` * Blue line: `np = 10` * Dark Blue line: `np = 25` * **Legend (Top-Right):** * Gray circle: `nfr = 1` * Gray downward-pointing triangle: `nfr = 3` * Gray square: `nfr = 5` * Gray upward-pointing triangle: `nfr = 10` ### Detailed Analysis **Data Series:** * **`np = 1` (Brown):** The data points are circles. The trend is generally increasing, starting around 0.25 at 0 tokens and reaching approximately 0.32 at 4000 tokens. * (0, ~0.23) * (2000, ~0.30) * (4000, ~0.32) * (6000, ~0.40) * **`np = 2` (Yellow):** The data points are circles. The trend is generally increasing, starting around 0.25 at 0 tokens and reaching approximately 0.40 at 6000 tokens. * (0, ~0.25) * (2000, ~0.35) * (4000, ~0.37) * (6000, ~0.40) * **`np = 5` (Teal):** The data points are circles. The trend is generally increasing, starting around 0.25 at 0 tokens and reaching approximately 0.47 at 8000 tokens. * (0, ~0.22) * (2000, ~0.40) * (4000, ~0.47) * (8000, ~0.47) * **`np = 10` (Blue):** The data points are circles. The trend is generally increasing, starting around 0.25 at 0 tokens and reaching approximately 0.52 at 10000 tokens. * (0, ~0.22) * (4000, ~0.47) * (8000, ~0.50) * (10000, ~0.52) * **`np = 25` (Dark Blue):** The data points are circles. The trend is generally increasing, starting around 0.25 at 0 tokens and reaching approximately 0.52 at 10000 tokens. * (0, ~0.22) * (10000, ~0.52) * **`nfr = 1` (Gray Circle):** * (0, ~0.22) * (10000, ~0.52) * **`nfr = 3` (Gray Downward-Pointing Triangle):** * (2000, ~0.30) * (4000, ~0.44) * (8000, ~0.50) * **`nfr = 5` (Gray Square):** * (2000, ~0.32) * (4000, ~0.32) * **`nfr = 10` (Gray Upward-Pointing Triangle):** * (2000, ~0.28) * (6000, ~0.32) **General Trend (Gray Line with Shaded Area):** The gray line represents a general trend, starting around 0.2 at 0 tokens and increasing to approximately 0.5 at 10000 tokens. The shaded area around the line indicates a confidence interval or variability. ### Key Observations * The mean pass rate generally increases with the mean number of tokens generated. * The rate of increase appears to diminish as the number of tokens generated increases, suggesting a saturation effect. * The data points for different values of `np` and `nfr` are scattered around the general trend line. ### Interpretation The plot suggests that increasing the number of tokens generated generally improves the mean pass rate, but there are diminishing returns. The different values of `np` and `nfr` introduce variability in the relationship, indicating that these parameters also influence the pass rate. The gray line and shaded area provide a general expectation for the pass rate given the number of tokens generated, while the individual data points show the specific outcomes for different parameter settings. The saturation effect implies that there is a limit to how much the pass rate can be improved by simply increasing the number of tokens generated. </details> <details> <summary>x11.png Details</summary>  ### Visual Description ## Heatmap: Performance vs. Number of Feedback Repairs and Initial Programs ### Overview The image is a heatmap visualizing performance (represented by color intensity) as a function of two parameters: the number of feedback repairs (nfr) and the number of initial programs (np). The heatmap displays numerical values within each cell, with some cells marked as "O.O.B." (likely indicating "Out Of Bounds" or a similar constraint). ### Components/Axes * **X-axis (Horizontal):** Number of initial programs (np). Values: 1, 2, 5, 10, 25. * **Y-axis (Vertical):** Number of feedback-repairs (nfr). Values: 1, 3, 5, 10. * **Color Gradient:** The color of each cell represents the performance value, with darker shades indicating lower values and lighter shades indicating higher values. * **Cell Values:** Each cell contains a numerical value (e.g., 0.73, 0.82) or the label "O.O.B.". ### Detailed Analysis The heatmap presents performance values for different combinations of 'Number of feedback-repairs' and 'Number of initial programs'. Here's a breakdown of the values: | nfr | np = 1 | np = 2 | np = 5 | np = 10 | np = 25 | |---|---|---|---|---|---| | 10 | 0.73 | 0.82 | O.O.B. | O.O.B. | O.O.B. | | 5 | 0.75 | 0.82 | 0.91 | O.O.B. | O.O.B. | | 3 | 0.77 | 0.84 | 0.91 | 0.98 | O.O.B. | | 1 | 0.84 | 0.89 | 0.93 | 0.97 | O.O.B. | * **Trend along X-axis (increasing np):** For a fixed number of feedback-repairs (nfr), the performance generally increases as the number of initial programs (np) increases, until it reaches "O.O.B.". * **Trend along Y-axis (increasing nfr):** For a fixed number of initial programs (np), the performance generally decreases as the number of feedback-repairs (nfr) increases. * **"O.O.B." Values:** All cells where np = 25 are marked as "O.O.B.". Also, cells with higher nfr and np = 5 or 10 are marked as "O.O.B.". ### Key Observations * The highest performance values (0.97 and 0.98) are achieved with a lower number of feedback-repairs (nfr = 1 or 3) and a moderate number of initial programs (np = 10). * Increasing the number of initial programs (np) generally improves performance, but only up to a certain point, after which the system becomes "Out Of Bounds". * Increasing the number of feedback-repairs (nfr) generally reduces performance for a given number of initial programs. ### Interpretation The heatmap suggests that there is an optimal balance between the number of feedback repairs and the number of initial programs. Too many feedback repairs can degrade performance, while a sufficient number of initial programs is needed to achieve good performance. The "O.O.B." values indicate that there are constraints or limitations on the system, possibly related to resource limitations or algorithmic constraints. The data suggests that the system performs best with a lower number of feedback repairs and a moderate number of initial programs, before hitting the "Out Of Bounds" condition. </details> <details> <summary>x12.png Details</summary>  ### Visual Description ## Line Chart: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a line chart showing the relationship between the mean pass rate and the mean number of tokens generated. The chart includes data series for different values of 'np' (represented by lines) and 'nfr' (represented by markers). Error bars are present on the data points. A shaded region indicates uncertainty. ### Components/Axes * **X-axis:** "Mean number of tokens generated". The scale ranges from 0 to 10000, with tick marks at intervals of 2000. * **Y-axis:** "Mean pass rate". The scale ranges from 0.0 to 1.0, with tick marks at intervals of 0.2. * **Legend (Top-Left):** * Brown line: `np = 1` * Yellow line: `np = 2` * Teal line: `np = 5` * Cyan line: `np = 10` * Dark Blue line: `np = 25` * **Legend (Top-Right):** * Gray circle: `nfr = 1` * Gray inverted triangle: `nfr = 3` * Gray square: `nfr = 5` * Gray triangle: `nfr = 10` ### Detailed Analysis * **General Trend:** The mean pass rate generally increases as the mean number of tokens generated increases. The rate of increase appears to diminish as the number of tokens generated gets larger. * **Data Series Analysis:** * **nfr = 1 (Gray Circle):** Starts at approximately (0, 0.04), increases to approximately (6000, 0.15), and ends around (8000, 0.14). * **nfr = 3 (Gray Inverted Triangle):** Starts at approximately (1500, 0.07), increases to approximately (6000, 0.15), and ends around (8000, 0.15). * **nfr = 5 (Gray Square):** Starts at approximately (2500, 0.08), increases to approximately (6000, 0.14), and ends around (7000, 0.15). * **nfr = 10 (Gray Triangle):** Starts at approximately (3500, 0.10), increases to approximately (6000, 0.14), and ends around (8000, 0.14). * **Error Bars:** Error bars are present on each data point, indicating the uncertainty in the mean pass rate. The error bars appear to be relatively consistent in size across the different data series. * **Shaded Region:** A gray shaded region surrounds the data points, likely representing a confidence interval or standard deviation. ### Key Observations * The mean pass rate increases with the mean number of tokens generated, but the rate of increase slows down as the number of tokens increases. * The different values of 'nfr' do not appear to have a significant impact on the mean pass rate. The data points for different 'nfr' values are clustered closely together. * The error bars and shaded region indicate a degree of uncertainty in the mean pass rate. ### Interpretation The chart suggests that increasing the number of tokens generated generally leads to a higher pass rate. However, there appears to be a point of diminishing returns, where generating more tokens does not significantly improve the pass rate. The values of 'nfr' do not seem to have a strong influence on the pass rate, suggesting that other factors may be more important in determining the outcome. The uncertainty in the data, as indicated by the error bars and shaded region, should be considered when interpreting the results. </details> <details> <summary>x13.png Details</summary>  ### Visual Description ## Heatmap: Performance vs. Number of Feedback Repairs and Initial Programs ### Overview The image is a heatmap visualizing performance based on the number of feedback repairs (nfr) and the number of initial programs (np). The heatmap uses color to represent performance values, with specific numerical values displayed within each cell. "O.O.B." is also used as a value. ### Components/Axes * **X-axis (Horizontal):** Number of initial programs (np) with values 1, 2, 5, 10, and 25. * **Y-axis (Vertical):** Number of feedback-repairs (nfr) with values 1, 3, 5, and 10. * **Cells:** Each cell represents a combination of nfr and np, with a color and a numerical value (or "O.O.B.") indicating performance. ### Detailed Analysis The heatmap displays performance values for different combinations of the number of feedback repairs (nfr) and the number of initial programs (np). The values are as follows: * **nfr = 10:** * np = 1: 0.78 (brown) * np = 2: 0.93 (orange) * np = 5: O.O.B. (dark gray) * np = 10: O.O.B. (dark gray) * np = 25: O.O.B. (dark gray) * **nfr = 5:** * np = 1: 0.79 (brown) * np = 2: 0.91 (orange) * np = 5: 1.09 (light green) * np = 10: O.O.B. (dark gray) * np = 25: O.O.B. (dark gray) * **nfr = 3:** * np = 1: 0.81 (brown) * np = 2: 0.91 (orange) * np = 5: 1.08 (light green) * np = 10: O.O.B. (dark gray) * np = 25: O.O.B. (dark gray) * **nfr = 1:** * np = 1: 0.87 (brown) * np = 2: 0.93 (orange) * np = 5: 1.05 (yellow-green) * np = 10: 1.13 (light blue-green) * np = 25: O.O.B. (dark gray) ### Key Observations * Performance generally increases as the number of initial programs (np) increases from 1 to 5, for a given number of feedback repairs (nfr). * For np values of 10 and 25, the performance is consistently "O.O.B." (Out of Bounds), except for nfr=1 and np=10, which has a value of 1.13. * The highest performance value (1.13) is observed when nfr = 1 and np = 10. * The lowest performance values (0.78, 0.79, 0.81, 0.87) are observed when np = 1. ### Interpretation The heatmap suggests that increasing the number of initial programs (np) initially improves performance, but beyond a certain point (np = 5 or 10), the system may become "Out of Bounds" (O.O.B.) or performance may plateau. The number of feedback repairs (nfr) also plays a role, with lower nfr values sometimes leading to better performance when combined with a moderate number of initial programs. The "O.O.B." values indicate that the system may not be stable or may not produce meaningful results under those conditions. Further investigation is needed to understand the meaning of "O.O.B." and the factors that cause it. </details> Figure 7: GPT-3.5 results from Figure 3 (Section 4.1) per difficulty (row), from top to bottom: introductory, interview, and competition. <details> <summary>x14.png Details</summary>  ### Visual Description ## Line Chart: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a line chart that plots the mean pass rate against the mean number of tokens generated. There are multiple data series, each representing a different configuration of parameters denoted as 'np' and 'nfr'. The chart shows how the pass rate changes as the number of tokens increases for various parameter settings. ### Components/Axes * **X-axis:** Mean number of tokens generated. The scale ranges from 0 to 10000, with tick marks at intervals of 2000. * **Y-axis:** Mean pass rate. The scale ranges from 0.0 to 1.0, with tick marks at intervals of 0.2. * **Legend (Left):** Located on the left side of the chart. It identifies the lines corresponding to different values of 'np': * Brown line: np = 1 * Yellow line: np = 2 * Teal line: np = 5 * Light Blue line: np = 10 * Dark Blue line: np = 25 * **Legend (Right):** Located on the right side of the chart. It identifies the markers corresponding to different values of 'nfr': * Dark Gray circle: nfr = 1 * Dark Gray downward-pointing triangle: nfr = 3 * Dark Gray square: nfr = 5 * Dark Gray upward-pointing triangle: nfr = 10 * A gray shaded region exists, which likely represents a confidence interval or standard deviation around an underlying trend line. ### Detailed Analysis * **np = 1 (Brown Line):** Starts at approximately 0.7, rises sharply, and plateaus around 0.85 after 2000 tokens. * Data point at approximately (100, 0.78) * Data point at approximately (1000, 0.84) * **np = 2 (Yellow Line):** Starts at approximately 0.75, rises sharply, and plateaus around 0.87 after 2000 tokens. * Data point at approximately (100, 0.75) * Data point at approximately (1000, 0.86) * **np = 5 (Teal Line):** Starts at approximately 0.8, rises sharply, and plateaus around 0.9 after 2000 tokens. * Data point at approximately (100, 0.80) * Data point at approximately (1000, 0.88) * **np = 10 (Light Blue Line):** Starts at approximately 0.8, rises sharply, and plateaus around 0.92 after 2000 tokens. * Data point at approximately (100, 0.80) * Data point at approximately (1000, 0.90) * **np = 25 (Dark Blue Line):** Starts at approximately 0.8, rises sharply, and plateaus around 0.95 after 2000 tokens. * Data point at approximately (100, 0.80) * Data point at approximately (1000, 0.92) * **nfr = 1 (Dark Gray Circle):** Data points are scattered, generally increasing with the number of tokens. * Data point at approximately (100, 0.78) * Data point at approximately (1000, 0.84) * Data point at approximately (4000, 0.94) * **nfr = 3 (Dark Gray Downward-Pointing Triangle):** Data points are scattered, generally increasing with the number of tokens. * Data point at approximately (1000, 0.92) * Data point at approximately (2000, 0.92) * Data point at approximately (4000, 0.94) * **nfr = 5 (Dark Gray Square):** Data points are scattered, generally increasing with the number of tokens. * Data point at approximately (2000, 0.92) * Data point at approximately (6000, 0.96) * **nfr = 10 (Dark Gray Upward-Pointing Triangle):** Data points are scattered, generally increasing with the number of tokens. * Data point at approximately (2000, 0.90) * Data point at approximately (8000, 0.97) * The gray shaded region appears to represent the confidence interval for the mean pass rate. It is wider at the beginning of the curve and narrows as the number of tokens increases. ### Key Observations * The mean pass rate generally increases with the mean number of tokens generated. * The rate of increase diminishes as the number of tokens increases, suggesting a saturation effect. * Higher values of 'np' generally lead to higher mean pass rates. * The 'nfr' values are scattered and do not show a clear trend. * The confidence interval narrows as the number of tokens increases, indicating more consistent results with a larger number of tokens. ### Interpretation The chart suggests that increasing the number of tokens generated generally improves the mean pass rate, but the improvement diminishes as the number of tokens gets larger. The parameter 'np' seems to have a positive correlation with the mean pass rate, meaning that higher values of 'np' lead to better performance. The parameter 'nfr' does not show a clear trend, suggesting that it may not have a significant impact on the mean pass rate or that its effect is more complex and requires further investigation. The narrowing confidence interval indicates that the results become more consistent with a larger number of tokens, which is expected. </details> <details> <summary>x15.png Details</summary>  ### Visual Description ## Heatmap: Performance Metric vs. Number of Feedback Repairs and Initial Programs ### Overview The image is a heatmap visualizing a performance metric as a function of two parameters: the number of feedback repairs (nfr) and the number of initial programs (np). The color intensity represents the value of the performance metric, with darker shades generally indicating higher values. The heatmap also indicates when the process goes "Out of Bounds" (O.O.B.). ### Components/Axes * **X-axis:** Number of initial programs (np), with values 1, 2, 5, 10, and 25. * **Y-axis:** Number of feedback-repairs (nfr), with values 1, 3, 5, and 10. * **Color Scale:** The color scale is not explicitly shown, but the color intensity varies from light yellow to dark orange, with darker colors representing higher values. A dark gray color indicates "O.O.B." (Out of Bounds). * **Labels:** The cells of the heatmap contain numerical values representing the performance metric. ### Detailed Analysis The heatmap displays the performance metric for different combinations of the number of feedback repairs (nfr) and the number of initial programs (np). Here's a breakdown of the values: | nfr \ np | 1 | 2 | 5 | 10 | 25 | | :------- | :---- | :---- | :---- | :---- | :----- | | 10 | 0.98 | 1.01 | 1.02 | 1.03 | O.O.B. | | 5 | 1.00 | 1.02 | 1.03 | 1.03 | O.O.B. | | 3 | 1.02 | 1.03 | 1.04 | 1.04 | 1.04 | | 1 | 1.05 | 1.04 | 1.04 | 1.04 | 1.04 | * **nfr = 10:** * np = 1: 0.98 * np = 2: 1.01 * np = 5: 1.02 * np = 10: 1.03 * np = 25: O.O.B. (Out of Bounds) * **nfr = 5:** * np = 1: 1.00 * np = 2: 1.02 * np = 5: 1.03 * np = 10: 1.03 * np = 25: O.O.B. (Out of Bounds) * **nfr = 3:** * np = 1: 1.02 * np = 2: 1.03 * np = 5: 1.04 * np = 10: 1.04 * np = 25: 1.04 * **nfr = 1:** * np = 1: 1.05 * np = 2: 1.04 * np = 5: 1.04 * np = 10: 1.04 * np = 25: 1.04 ### Key Observations * The performance metric generally increases as the number of initial programs (np) increases, up to a point. * For nfr = 3 and nfr = 1, the performance metric plateaus at np = 5. * For nfr = 5 and nfr = 10, the process goes "Out of Bounds" (O.O.B.) when np = 25. * The highest performance metric value is 1.05, achieved when nfr = 1 and np = 1. * The lowest performance metric value is 0.98, achieved when nfr = 10 and np = 1. ### Interpretation The heatmap suggests that increasing the number of initial programs (np) generally improves the performance metric, but only up to a certain point. Beyond that point, the performance either plateaus or the process becomes unstable and goes "Out of Bounds." The optimal combination of nfr and np depends on the specific application, but the heatmap provides a visual representation of the trade-offs involved. The "Out of Bounds" condition for higher nfr values (5 and 10) when np is 25 indicates a potential instability or resource limitation in the system being modeled. The data suggests that a lower number of feedback repairs (nfr = 1 or 3) is more stable across a wider range of initial programs (np). </details> <details> <summary>x16.png Details</summary>  ### Visual Description ## Line Chart: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a line chart that plots the mean pass rate against the mean number of tokens generated. The chart displays multiple data series, each representing a different configuration of parameters denoted as *n_p* and *n_fr*. The chart aims to show how the mean pass rate changes as the number of tokens generated increases, under different parameter settings. ### Components/Axes * **X-axis:** Mean number of tokens generated, ranging from 0 to 10000, with tick marks at intervals of 2000. * **Y-axis:** Mean pass rate, ranging from 0.0 to 1.0, with tick marks at intervals of 0.2. * **Legend:** Located in the center-right of the chart, it identifies the different data series based on the parameters *n_p* and *n_fr*. * *n_p* = 1 (brown line) * *n_p* = 2 (yellow line) * *n_p* = 5 (light blue line) * *n_p* = 10 (darker blue line) * *n_p* = 25 (darkest blue line) * *n_fr* = 1 (dark gray circles) * *n_fr* = 3 (dark gray downward triangles) * *n_fr* = 5 (dark gray squares) * *n_fr* = 10 (dark gray upward triangles) ### Detailed Analysis **Data Series Trends and Values:** * **n_p = 1 (Brown Line):** The line starts at approximately 0.45 at 0 tokens and increases to approximately 0.52 at 1000 tokens, 0.55 at 2000 tokens, 0.59 at 4000 tokens, and plateaus around 0.65 at 8000 tokens. * **n_p = 2 (Yellow Line):** The line starts at approximately 0.40 at 0 tokens and increases to approximately 0.58 at 1000 tokens, 0.60 at 2000 tokens, 0.62 at 4000 tokens, and plateaus around 0.65 at 8000 tokens. * **n_p = 5 (Light Blue Line):** The line starts at approximately 0.40 at 0 tokens and increases to approximately 0.60 at 1000 tokens, 0.62 at 2000 tokens, 0.67 at 4000 tokens, and plateaus around 0.70 at 8000 tokens. * **n_p = 10 (Darker Blue Line):** The line starts at approximately 0.40 at 0 tokens and increases to approximately 0.60 at 1000 tokens, 0.63 at 2000 tokens, 0.68 at 4000 tokens, and plateaus around 0.71 at 8000 tokens. * **n_p = 25 (Darkest Blue Line):** The line starts at approximately 0.40 at 0 tokens and increases to approximately 0.62 at 1000 tokens, 0.64 at 2000 tokens, 0.70 at 4000 tokens, and plateaus around 0.72 at 8000 tokens. * **n_fr = 1 (Dark Gray Circles):** The data points are scattered. At 0 tokens, the mean pass rate is approximately 0.45. At 6000 tokens, the mean pass rate is approximately 0.72. At 8000 tokens, the mean pass rate is approximately 0.70. * **n_fr = 3 (Dark Gray Downward Triangles):** The data points are scattered. At 1000 tokens, the mean pass rate is approximately 0.50. At 4000 tokens, the mean pass rate is approximately 0.60. At 6000 tokens, the mean pass rate is approximately 0.70. * **n_fr = 5 (Dark Gray Squares):** The data points are scattered. At 1000 tokens, the mean pass rate is approximately 0.52. At 2000 tokens, the mean pass rate is approximately 0.55. At 7000 tokens, the mean pass rate is approximately 0.72. * **n_fr = 10 (Dark Gray Upward Triangles):** The data points are scattered. At 1000 tokens, the mean pass rate is approximately 0.48. At 4000 tokens, the mean pass rate is approximately 0.61. At 7000 tokens, the mean pass rate is approximately 0.71. ### Key Observations * The mean pass rate generally increases with the mean number of tokens generated for all values of *n_p*. * The rate of increase diminishes as the number of tokens generated increases, suggesting a saturation effect. * Higher values of *n_p* generally result in higher mean pass rates. * The data points for *n_fr* are scattered, making it difficult to discern a clear trend. ### Interpretation The chart suggests that increasing the number of tokens generated initially improves the mean pass rate, but this improvement plateaus as the number of tokens continues to increase. The parameter *n_p* appears to have a positive correlation with the mean pass rate, indicating that higher values of *n_p* lead to better performance. The scattered data points for *n_fr* suggest that this parameter may have a less predictable or consistent impact on the mean pass rate compared to *n_p*. The gray shaded region around each line indicates the uncertainty or variability in the data. </details> <details> <summary>x17.png Details</summary>  ### Visual Description ## Heatmap: Performance vs. Number of Feedback Repairs and Initial Programs ### Overview The image is a heatmap visualizing performance (represented by color intensity) as a function of two variables: the number of feedback repairs (nfr) and the number of initial programs (np). The heatmap displays numerical values within each cell, and some cells are marked "O.O.B." (likely indicating "Out Of Bounds"). ### Components/Axes * **X-axis (Horizontal):** Number of initial programs (np). Values: 1, 2, 5, 10, 25. * **Y-axis (Vertical):** Number of feedback-repairs (nfr). Values: 1, 3, 5, 10. * **Color Gradient:** The color gradient represents performance, with darker orange indicating lower values, transitioning to yellow, then green for higher values, and finally black for "O.O.B.". * **Cells:** Each cell contains a numerical value or the label "O.O.B.". ### Detailed Analysis or Content Details The heatmap contains the following data points: * **nfr = 10:** * np = 1: 0.88 (dark orange) * np = 2: 0.97 (orange) * np = 5: 1.06 (yellow-green) * np = 10: O.O.B. (black) * np = 25: O.O.B. (black) * **nfr = 5:** * np = 1: 0.89 (dark orange) * np = 2: 0.96 (orange) * np = 5: 1.04 (yellow-green) * np = 10: 1.09 (green) * np = 25: O.O.B. (black) * **nfr = 3:** * np = 1: 0.91 (orange) * np = 2: 0.97 (orange) * np = 5: 1.04 (yellow-green) * np = 10: 1.08 (green) * np = 25: O.O.B. (black) * **nfr = 1:** * np = 1: 0.96 (orange) * np = 2: 0.99 (yellow) * np = 5: 1.03 (yellow) * np = 10: 1.05 (yellow-green) * np = 25: 1.09 (green) ### Key Observations * **Trend:** Generally, performance increases as the number of initial programs (np) increases, up to a point. * **O.O.B.:** For higher numbers of feedback repairs (nfr = 5 and 10), the system goes "Out Of Bounds" (O.O.B.) when the number of initial programs (np) is high (10 and 25). * **Optimal Region:** The best performance (highest values) seems to be achieved with a moderate number of feedback repairs (nfr = 1, 3, 5) and a moderate number of initial programs (np = 5, 10, 25). * **Lower Performance:** Lower performance (lower values) is observed with a low number of initial programs (np = 1, 2) regardless of the number of feedback repairs. ### Interpretation The heatmap suggests that there is an optimal combination of feedback repairs and initial programs for achieving the best performance. Increasing the number of initial programs generally improves performance, but only up to a certain point. Beyond that point, especially with a high number of feedback repairs, the system may become unstable or "Out Of Bounds." The data indicates that a balance between exploration (initial programs) and refinement (feedback repairs) is crucial. The "O.O.B." values suggest a limitation or constraint in the system being analyzed, where certain combinations of parameters lead to failure or undefined behavior. </details> <details> <summary>x18.png Details</summary>  ### Visual Description ## Scatter Plot: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a scatter plot showing the relationship between the mean pass rate and the mean number of tokens generated. The plot includes data for different values of `np` (represented by lines) and `nfr` (represented by markers). A gray shaded region indicates a confidence interval or standard deviation around a central trend line. ### Components/Axes * **X-axis:** Mean number of tokens generated, with ticks at 0, 2000, 4000, 6000, 8000, and 10000. * **Y-axis:** Mean pass rate, with ticks at 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. * **Legend (Top-Left):** * Brown line: `np = 1` * Yellow line: `np = 2` * Teal line: `np = 5` * Light Blue line: `np = 10` * Dark Blue line: `np = 25` * **Legend (Top-Right):** * Gray circle: `nfr = 1` * Gray inverted triangle: `nfr = 3` * Gray square: `nfr = 5` * Gray triangle: `nfr = 10` ### Detailed Analysis **Data Series Trends and Values:** * **General Trend:** The mean pass rate generally increases as the mean number of tokens generated increases, approaching a plateau. A dark gray line with a light gray confidence interval represents this overall trend. * **`np` Series (Lines):** * **`np = 1` (Brown):** Starts at approximately (0, 0.12) and increases to approximately (2000, 0.25). * **`np = 2` (Yellow):** Starts at approximately (0, 0.10) and increases to approximately (2000, 0.30). * **`np = 5` (Teal):** Starts at approximately (0, 0.11) and increases to approximately (2000, 0.35). * **`np = 10` (Light Blue):** Starts at approximately (0, 0.13) and increases to approximately (4000, 0.42). * **`np = 25` (Dark Blue):** Not clearly distinguishable from the trend line. Appears to reach approximately 0.5 at 10000. * **`nfr` Series (Markers):** * **`nfr = 1` (Gray Circle):** Data point at approximately (10000, 0.50). * **`nfr = 3` (Gray Inverted Triangle):** Data points at approximately (2000, 0.25) and (8000, 0.47). * **`nfr = 5` (Gray Square):** Data points at approximately (2000, 0.28) and (6000, 0.35). * **`nfr = 10` (Gray Triangle):** Data points at approximately (2000, 0.24) and (6000, 0.30). ### Key Observations * The mean pass rate increases rapidly initially and then plateaus as the mean number of tokens generated increases. * The `np` values seem to influence the initial rate of increase, with higher `np` values showing a slightly faster increase in the mean pass rate. * The `nfr` values are scattered and do not show a clear trend. * Error bars are present on the data points, indicating the uncertainty in the measurements. ### Interpretation The data suggests that increasing the mean number of tokens generated improves the mean pass rate, but only up to a certain point. The parameter `np` may influence the initial rate of improvement. The parameter `nfr` does not appear to have a strong or consistent effect on the mean pass rate. The gray shaded region around the trend line indicates the variability or uncertainty in the data. The plot demonstrates diminishing returns, where increasing the number of tokens generated beyond a certain point yields little improvement in the pass rate. </details> <details> <summary>x19.png Details</summary>  ### Visual Description ## Heatmap: Performance vs. Number of Feedback Repairs and Initial Programs ### Overview The image is a heatmap visualizing the performance of a system based on two parameters: the number of feedback repairs (nfr) and the number of initial programs (np). The heatmap displays performance values for different combinations of these parameters, with darker colors generally indicating lower performance and lighter colors indicating higher performance. The label "O.O.B." appears to indicate an out-of-bounds condition or a failure state. ### Components/Axes * **X-axis (Horizontal):** Number of initial programs (np). Values: 1, 2, 5, 10, 25. * **Y-axis (Vertical):** Number of feedback-repairs (nfr). Values: 1, 3, 5, 10. * **Color Gradient:** Represents performance values. Darker colors (brown/black) indicate lower values, while lighter colors (yellow/green/cyan) indicate higher values. * **Data Values:** Numerical values are displayed within each cell of the heatmap, representing the performance for the corresponding combination of nfr and np. The value "O.O.B." is also present. ### Detailed Analysis The heatmap presents performance values for different combinations of the number of feedback repairs (nfr) and the number of initial programs (np). The values are as follows: | nfr | np = 1 | np = 2 | np = 5 | np = 10 | np = 25 | |---|---|---|---|---|---| | 10 | 0.81 | 0.97 | O.O.B. | O.O.B. | O.O.B. | | 5 | 0.83 | 0.97 | 1.10 | O.O.B. | O.O.B. | | 3 | 0.85 | 0.97 | 1.10 | 1.16 | O.O.B. | | 1 | 1.01 | 1.05 | 1.10 | 1.13 | 1.19 | * **nfr = 10:** * np = 1: 0.81 (dark brown) * np = 2: 0.97 (dark yellow) * np = 5: O.O.B. (black) * np = 10: O.O.B. (black) * np = 25: O.O.B. (black) * **nfr = 5:** * np = 1: 0.83 (brown) * np = 2: 0.97 (dark yellow) * np = 5: 1.10 (light green) * np = 10: O.O.B. (black) * np = 25: O.O.B. (black) * **nfr = 3:** * np = 1: 0.85 (brown) * np = 2: 0.97 (dark yellow) * np = 5: 1.10 (light green) * np = 10: 1.16 (cyan) * np = 25: O.O.B. (black) * **nfr = 1:** * np = 1: 1.01 (yellow) * np = 2: 1.05 (light yellow) * np = 5: 1.10 (light green) * np = 10: 1.13 (cyan) * np = 25: 1.19 (light cyan) ### Key Observations * Performance generally improves (higher values) as the number of initial programs (np) increases, up to a point. * For higher numbers of feedback repairs (nfr = 5 and 10), the system results in "O.O.B." for larger numbers of initial programs (np = 5, 10, and 25). * The best performance (highest values) is observed when the number of feedback repairs is low (nfr = 1) and the number of initial programs is relatively high (np = 25). * The worst performance (lowest values) is observed when the number of feedback repairs is high (nfr = 10) and the number of initial programs is low (np = 1). ### Interpretation The heatmap suggests that there is an optimal balance between the number of feedback repairs and the number of initial programs for maximizing system performance. Increasing the number of initial programs generally improves performance, but only up to a certain point. When the number of feedback repairs is too high, the system becomes unstable or encounters an out-of-bounds condition ("O.O.B.") for larger numbers of initial programs. This could indicate that excessive feedback repairs can lead to overfitting or instability, especially when combined with a large number of initial programs. The best performance is achieved with a low number of feedback repairs and a relatively high number of initial programs, suggesting that a more diverse initial population combined with limited feedback is more effective. The "O.O.B." values indicate a failure state, which needs to be investigated to understand the conditions under which the system becomes unstable. </details> Figure 8: GPT-4 results from Figure 4 (Section 4.1) per difficulty (row), from top to bottom: introductory, interview, and competition. <details> <summary>x20.png Details</summary>  ### Visual Description ## Line Chart: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a line chart comparing the mean pass rate of different GPT models against the mean number of tokens generated. The chart displays five different configurations of GPT models, with shaded regions around each line indicating variability. The x-axis represents the mean number of tokens generated, ranging from 0 to 10,000. The y-axis represents the mean pass rate, ranging from 0.0 to 1.0. ### Components/Axes * **X-axis:** Mean number of tokens generated, ranging from 0 to 10000, with tick marks at 0, 2000, 4000, 6000, 8000, and 10000. * **Y-axis:** Mean pass rate, ranging from 0.0 to 1.0, with tick marks at 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. * **Legend:** Located in the center-left of the chart, it identifies the five different GPT model configurations: * Dark Blue: *M_P* = GPT-4 (no repair) * Teal: *M_P* = GPT-4; *M_F* = GPT-4 * Gray: *M_P* = GPT-3.5 (no repair) * Brown: *M_P* = GPT-3.5; *M_F* = GPT-3.5 * Light Blue: *M_P* = GPT-3.5; *M_F* = GPT-4 ### Detailed Analysis * **Dark Blue Line:** *M_P* = GPT-4 (no repair). This line starts at approximately 0.52 pass rate at 0 tokens and quickly rises to approximately 0.85 by 1000 tokens. It continues to increase, reaching approximately 0.92 around 6000 tokens, where it plateaus. * **Teal Line:** *M_P* = GPT-4; *M_F* = GPT-4. This line starts at approximately 0.60 pass rate at 0 tokens and rises to approximately 0.88 by 1000 tokens. It plateaus around 0.94 after 4000 tokens. * **Gray Line:** *M_P* = GPT-3.5 (no repair). This line starts at approximately 0.50 pass rate at 0 tokens and rises to approximately 0.80 by 2000 tokens. It plateaus around 0.85 after 6000 tokens. * **Brown Line:** *M_P* = GPT-3.5; *M_F* = GPT-3.5. This line starts at approximately 0.58 pass rate at 0 tokens and rises to approximately 0.78 by 1000 tokens. It plateaus around 0.84 after 4000 tokens. * **Light Blue Line:** *M_P* = GPT-3.5; *M_F* = GPT-4. This line starts at approximately 0.58 pass rate at 0 tokens and rises to approximately 0.82 by 1000 tokens. It plateaus around 0.86 after 4000 tokens. ### Key Observations * All lines show a rapid increase in the mean pass rate with an increasing number of tokens generated, especially in the initial 2000 tokens. * The GPT-4 models (dark blue and teal lines) generally outperform the GPT-3.5 models (gray, brown, and light blue lines). * The "no repair" GPT-4 model (dark blue line) performs slightly worse than the GPT-4 model with repair (teal line). * Among the GPT-3.5 models, using GPT-4 for repair (*M_F* = GPT-4, light blue line) results in a higher pass rate than using GPT-3.5 for repair (*M_F* = GPT-3.5, brown line). * The "no repair" GPT-3.5 model (gray line) performs slightly worse than the GPT-3.5 model with GPT-4 repair (light blue line). ### Interpretation The chart demonstrates the relationship between the number of tokens generated and the mean pass rate for different GPT model configurations. The data suggests that: 1. **Model Version Matters:** GPT-4 models generally achieve higher pass rates than GPT-3.5 models, indicating a performance improvement in the newer model. 2. **Repair Mechanisms Improve Performance:** Using a repair mechanism (indicated by *M_F*) improves the pass rate compared to using no repair. 3. **Using a Stronger Model for Repair is Beneficial:** When using GPT-3.5, employing GPT-4 for the repair mechanism leads to a higher pass rate than using GPT-3.5 for repair. 4. **Diminishing Returns:** The rapid increase in pass rate slows down as the number of tokens generated increases, suggesting diminishing returns in performance beyond a certain number of tokens. The shaded regions around each line likely represent the standard deviation or confidence interval, indicating the variability in the pass rate for each model configuration. The consistent trends across all configurations suggest that the observed differences are statistically significant. </details> <details> <summary>x21.png Details</summary>  ### Visual Description ## Line Chart: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a line chart comparing the mean pass rate against the mean number of tokens generated for different GPT models and repair configurations. The chart displays five data series, each representing a different model configuration, with shaded regions indicating uncertainty. ### Components/Axes * **X-axis:** Mean number of tokens generated, ranging from 0 to 10000, with tick marks at intervals of 2000. * **Y-axis:** Mean pass rate, ranging from 0.0 to 1.0, with tick marks at intervals of 0.2. * **Legend (located in the center-right of the chart):** * Dark Blue: *M_P* = GPT-4 (no repair) * Light Green: *M_P* = GPT-4; *M_F* = GPT-4 * Gray: *M_P* = GPT-3.5 (no repair) * Brown: *M_P* = GPT-3.5; *M_F* = GPT-3.5 * Teal: *M_P* = GPT-3.5; *M_F* = GPT-4 ### Detailed Analysis * **Dark Blue Line: *M_P* = GPT-4 (no repair)** * Trend: The line slopes upward, starting at approximately 0.4 and reaching approximately 0.65, then plateaus. * Data Points: * At 0 tokens, the mean pass rate is approximately 0.4. * At 2000 tokens, the mean pass rate is approximately 0.6. * At 6000 tokens, the mean pass rate is approximately 0.65. * At 10000 tokens, the mean pass rate is approximately 0.65. * **Light Green Line: *M_P* = GPT-4; *M_F* = GPT-4** * Trend: The line slopes upward, starting at approximately 0.25 and reaching approximately 0.7, then plateaus. * Data Points: * At 0 tokens, the mean pass rate is approximately 0.25. * At 2000 tokens, the mean pass rate is approximately 0.62. * At 6000 tokens, the mean pass rate is approximately 0.7. * **Gray Line: *M_P* = GPT-3.5 (no repair)** * Trend: The line slopes upward, starting at approximately 0.2 and reaching approximately 0.52, then plateaus. * Data Points: * At 0 tokens, the mean pass rate is approximately 0.2. * At 2000 tokens, the mean pass rate is approximately 0.4. * At 6000 tokens, the mean pass rate is approximately 0.5. * At 10000 tokens, the mean pass rate is approximately 0.52. * **Brown Line: *M_P* = GPT-3.5; *M_F* = GPT-3.5** * Trend: The line slopes upward, starting at approximately 0.25 and reaching approximately 0.5, then plateaus. * Data Points: * At 0 tokens, the mean pass rate is approximately 0.25. * At 2000 tokens, the mean pass rate is approximately 0.38. * At 6000 tokens, the mean pass rate is approximately 0.48. * At 10000 tokens, the mean pass rate is approximately 0.5. * **Teal Line: *M_P* = GPT-3.5; *M_F* = GPT-4** * Trend: The line slopes upward, starting at approximately 0.28 and reaching approximately 0.57, then plateaus. * Data Points: * At 0 tokens, the mean pass rate is approximately 0.28. * At 2000 tokens, the mean pass rate is approximately 0.45. * At 6000 tokens, the mean pass rate is approximately 0.55. * At 10000 tokens, the mean pass rate is approximately 0.57. ### Key Observations * GPT-4 models generally outperform GPT-3.5 models. * The "no repair" GPT-4 model has a higher initial pass rate but plateaus earlier than the GPT-4 model with repair. * Using GPT-4 for repair (*M_F*) on GPT-3.5 (*M_P*) improves the pass rate compared to using GPT-3.5 for both. * All models show diminishing returns in pass rate as the number of tokens generated increases. ### Interpretation The chart illustrates the relationship between the number of tokens generated and the mean pass rate for different GPT models and repair configurations. The data suggests that using a more advanced model (GPT-4) generally leads to a higher pass rate. Furthermore, the use of a repair mechanism (indicated by *M_F*) can improve the performance of the models, especially in the initial stages of token generation. The plateauing of the pass rates indicates that there is a limit to the improvement that can be achieved by simply generating more tokens. The shaded regions around the lines represent the uncertainty in the measurements, which should be considered when interpreting the results. </details> <details> <summary>x22.png Details</summary>  ### Visual Description ## Line Chart: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a line chart comparing the mean pass rate against the mean number of tokens generated for different GPT models. The chart displays five different configurations of GPT models, each represented by a distinct colored line with a shaded area indicating uncertainty. The x-axis represents the mean number of tokens generated, ranging from 0 to 10000. The y-axis represents the mean pass rate, ranging from 0.0 to 1.0. ### Components/Axes * **X-axis:** Mean number of tokens generated, with tick marks at 0, 2000, 4000, 6000, 8000, and 10000. * **Y-axis:** Mean pass rate, with tick marks at 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. * **Legend:** Located in the top-right corner, the legend identifies each line by the GPT model configuration. * Dark Blue: *M_P* = GPT-4 (no repair) * Light Green: *M_P* = GPT-4; *M_F* = GPT-4 * Gray: *M_P* = GPT-3.5 (no repair) * Brown: *M_P* = GPT-3.5; *M_F* = GPT-3.5 * Teal: *M_P* = GPT-3.5; *M_F* = GPT-4 ### Detailed Analysis * **Dark Blue Line: *M_P* = GPT-4 (no repair)** * Trend: The line starts at approximately 0.1 at 0 tokens and increases rapidly, then plateaus around 0.38 at approximately 4000 tokens, remaining relatively flat until 10000 tokens. * Data Points: (0, 0.1), (2000, 0.3), (4000, 0.38), (10000, 0.4) * **Light Green Line: *M_P* = GPT-4; *M_F* = GPT-4** * Trend: The line starts at approximately 0.15 at 0 tokens and increases rapidly, then plateaus around 0.45 at approximately 6000 tokens, remaining relatively flat until 10000 tokens. * Data Points: (0, 0.15), (2000, 0.35), (6000, 0.45), (10000, 0.5) * **Gray Line: *M_P* = GPT-3.5 (no repair)** * Trend: The line starts at approximately 0.04 at 0 tokens and increases gradually, reaching approximately 0.15 at 10000 tokens. * Data Points: (0, 0.04), (2000, 0.08), (6000, 0.12), (10000, 0.15) * **Brown Line: *M_P* = GPT-3.5; *M_F* = GPT-3.5** * Trend: The line starts at approximately 0.05 at 0 tokens and increases gradually, reaching approximately 0.18 at 10000 tokens. * Data Points: (0, 0.05), (2000, 0.1), (6000, 0.15), (10000, 0.18) * **Teal Line: *M_P* = GPT-3.5; *M_F* = GPT-4** * Trend: The line starts at approximately 0.08 at 0 tokens and increases gradually, reaching approximately 0.2 at 10000 tokens. * Data Points: (0, 0.08), (2000, 0.12), (6000, 0.17), (10000, 0.2) ### Key Observations * The GPT-4 models (*M_P* = GPT-4) consistently outperform the GPT-3.5 models in terms of mean pass rate. * Using GPT-4 for both *M_P* and *M_F* yields the highest mean pass rate. * The mean pass rate increases rapidly for all models initially, then plateaus as the number of tokens generated increases. * The shaded areas around each line indicate the uncertainty or variability in the mean pass rate. ### Interpretation The data suggests that GPT-4 models are more effective at generating passing outputs compared to GPT-3.5 models. Furthermore, using GPT-4 for both the primary model (*M_P*) and the repair model (*M_F*) results in the highest pass rate, indicating that the combination of a strong primary model and a strong repair model is beneficial. The initial rapid increase in pass rate followed by a plateau suggests that the models quickly learn to generate passing outputs, but there is a limit to how much the pass rate can be improved with additional tokens. The uncertainty, represented by the shaded areas, highlights the variability in the model's performance. </details> Figure 9: Results from Figure 6 (Section 4.2) per difficulty (row), from top to bottom: introductory, interview, and competition. Appendix B Human Experiment: Study Instructions For our study on human data, participants were given a slide deck with instructions. The following ten images show the instructions, which include an example of a task shown to a participant: <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/1.jpg Details</summary>  ### Visual Description ## Task List: Debugging Python Programs ### Overview The image presents a task list outlining the steps and requirements for debugging Python programs. It specifies the setup, the debugging task itself, and the format for submitting the answers. ### Components/Axes * **Title:** Tasks * **Task 1:** Setup * Use a laptop or desktop computer, not a phone * **Task 2:** Debug five incorrect Python programs * Each program is an incorrect attempt to solve a coding challenge * Your answer should explain what the program is doing wrong * Expect ~10 minutes per task * **Task 3:** Task format * Each task is in a separate website * Submit your answer using the Google form embedded in each page * No other data is being collected ### Detailed Analysis or ### Content Details The task list is structured as a bulleted list with sub-bullets providing further details for each task. * **Setup:** The first task emphasizes using a laptop or desktop computer instead of a phone. * **Debugging Task:** The second task involves debugging five incorrect Python programs. Each program is designed as an incorrect attempt to solve a coding challenge. The instructions highlight the importance of explaining what the program is doing wrong in the answer. The estimated time per task is approximately 10 minutes. * **Task Format:** The third task specifies that each task is located on a separate website. Answers should be submitted using the Google form embedded in each page. It is explicitly stated that no other data is being collected. ### Key Observations * The instructions are clear and concise, providing specific guidance for each task. * The emphasis on explaining the errors in the Python programs suggests a focus on understanding the underlying logic and debugging process. * The estimated time per task provides a guideline for time management. * The statement about no other data being collected may be intended to reassure participants about privacy. ### Interpretation The task list outlines a debugging exercise involving Python programs. The instructions emphasize the importance of understanding the errors and providing clear explanations. The use of separate websites and Google forms for each task suggests a structured and organized approach to the exercise. The statement about data collection indicates a concern for user privacy. The overall goal appears to be to enhance debugging skills and problem-solving abilities in Python programming. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/2.jpg Details</summary>  ### Visual Description ## Text Document: Instructions for Answering a Question ### Overview The image presents instructions and guidelines for answering a question, likely related to a programming problem. It provides guidance on the level of detail expected in the answer, offers example answers, and includes information about data collection and available tools. ### Components/Axes The document is structured as follows: * **Title:** "Your Answer" * **Instructions:** A paragraph explaining the desired content of the answer. * **Examples:** Two bullet points providing different levels of detail for the answer. * **Example Answers:** Two bullet points providing specific examples of answers. * **Data Collection Notice:** A statement about data collection practices. * **Tool Suggestion:** A suggestion of tools that can be used. ### Detailed Analysis or ### Content Details * **Title:** "Your Answer" * **Instructions:** "Your answer should briefly explain what the program is doing wrong. If it helps you explain your thoughts, you can also say what you would do differently." * **Examples:** * "Can be precise: "the formula used to calculate X on line 5 is wrong, it should be..."" * "Or high-level: "the program is treating the task as a min-cut graph problem, but it is actually shortest-path... it could be rewritten using Dijkstra's algorithm..."" * **Example Answers:** * "The problem description states that numbers which start or end with zeros (such as `010` and `00`) are NOT considered valid numerical palindromes. However, the code above does not take this into account and therefore returns `00` as a valid palindrome." * "The main issue with the provided code is that it only considers direct subordinates when trying to find the k-th officer in the command spreading sequence. However, the problem asks for the order in which officers receive the command, including indirect subordinates. To fix this, we need to traverse the tree of officers and construct the command spreading sequence before finding the k-th element." * **Data Collection Notice:** "We are not collecting any data about how you use the website. Only your submitted answer is recorded." * **Tool Suggestion:** "Feel free to use external tools: pen and paper, a Python IDE, etc!" ### Key Observations * The instructions emphasize explaining the program's errors and suggesting alternative approaches. * The examples illustrate different levels of detail acceptable in the answer. * The example answers provide concrete scenarios and solutions. * The data collection notice assures users that only their submitted answers are recorded. * The tool suggestion encourages the use of external resources. ### Interpretation The document provides clear and concise instructions for answering a programming-related question. It aims to guide users in identifying and explaining errors in a program, while also encouraging them to think critically and propose alternative solutions. The inclusion of example answers and a data collection notice further enhances the user experience by providing clarity and reassurance. The suggestion of external tools promotes a flexible and resourceful approach to problem-solving. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/3.jpg Details</summary>  ### Visual Description ## Image: Text on White Background ### Overview The image contains the word "Example" in a blue font, centered on a white background. ### Components/Axes * **Text:** "Example" * **Color:** Blue * **Background:** White * **Position:** Centered ### Detailed Analysis or ### Content Details The word "Example" is written in a simple, sans-serif font. The blue color is a medium shade. The background is a uniform white. ### Key Observations The image is very simple, containing only a single word. ### Interpretation The image serves as a placeholder or a label, indicating that the content is an example. The simplicity suggests it's meant to be easily replaceable or illustrative. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/4.jpg Details</summary>  ### Visual Description ## Problem Specification: Counting Votes ### Overview The image presents a problem specification for a program designed to count votes from a school board election. It includes a description of the election context, input format, output requirements, and example input/output. ### Components/Axes * **Title:** "1. Problem Specification" * **Section:** "Specification" * Describes the context of the school board election and the task of writing a program to count the votes. * **Section:** "-----Input-----" * Specifies the input format: a list of votes, one candidate name per line, ending with "***". * Constraints: At least 2 votes, up to 100,000 valid votes. * **Section:** "----Output----" * Specifies the output format: the name of the candidate with a simple majority, or "Runoff!" if no candidate has a majority. * **Section:** "-----Examples-----" * Provides a "Sample Input" and "Sample Output" to illustrate the expected program behavior. * **Note:** "Remember: all input/output of the program should be handled through stdin and stdout." * **Right-Side Text:** * "Each page starts with a specification of what the program should do." * "Begin by carefully reading the problem specification." ### Detailed Analysis or ### Content Details * **Election Context:** The school board elections involved contentious issues such as school start times, dress codes, and taxes for a football facility. * **Input Format:** * Each line contains the name of a candidate. * Names can consist of multiple words separated by spaces. * Words contain letters or hyphens. * The input ends with a line containing "***". * **Output Requirements:** * If a candidate has a simple majority, output their name. * If no candidate has a simple majority, output "Runoff!". * **Sample Input:** * Penny Franklin * Marti Graham * Connie Froggatt * Joseph Ivers * Connie Froggatt * Penny Franklin * Connie Froggatt * Bruce Stanger * Connie Froggatt * Barbara Skinner * Barbara Skinner * *** * **Sample Output:** * Connie Froggatt ### Key Observations * The problem specification is clearly defined with input and output requirements. * The example input and output provide a concrete understanding of the expected program behavior. * The note about stdin and stdout emphasizes the standard input/output handling. ### Interpretation The problem specification outlines the task of creating a program to count votes and determine the winner of a school board election. The program must handle a list of votes, identify the candidate with a simple majority, and output either the winner's name or "Runoff!" if no candidate has a majority. The specification is designed to guide programmers in developing a solution that accurately counts votes and determines the election outcome. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/5.jpg Details</summary>  ### Visual Description ## Code Snippet: Incorrect Program ### Overview The image presents an incorrect Python program designed to determine the winner of a vote. The code snippet includes errors in logic that could lead to incorrect results. Alongside the program is a text block explaining that the user will be shown the incorrect program, encouraging the user to debug the program on their machine, and clarifying how input and output are handled. ### Components/Axes * **Title:** "2. Incorrect Program" * **Code Block Title:** "Incorrect Program" * **Code:** Python code snippet (described below) * **Description Block**: Description of the code presented ### Detailed Analysis or ### Content Details The code consists of the following elements: * **Imports:** * `from collections import defaultdict` * **Variables:** * `votes = defaultdict(int)`: Initializes a dictionary `votes` with integer default values. * `candidate = input()`: Takes an input for the candidate. * `total_votes = sum(votes.values())`: Calculates the total number of votes. * `max_votes = max(votes.values())`: Determines the maximum number of votes. * `winner = [name for name, count in votes.items() if count == max_votes]`: Creates a list of winners with the maximum number of votes. * **Loop:** * `while candidate != "*****":`: Loops until the candidate is "*****". * `votes[candidate] -= 1`: Decrements the votes count for the candidate. * `candidate = input()`: Takes the next candidate input. * **Conditional Statement:** * `if len(winner) == 1 and max_votes > total_votes // 2:`: Checks if there is one winner and the maximum votes are greater than half of the total votes. * `print(winner[0])`: Prints the winner. * `else:`: If the condition is not met. * `print("Runoff!")`: Prints "Runoff!". * **Accompanying Text**: * "Next, you will be shown the incorrect program." * "Tip: If you are struggling with debugging the program, try running it on your machine!" * "Note: the programs handle inputs through 'input()', and outputs through 'print()'." ### Key Observations * The condition within the `while` loop, `candidate != "*****"`, dictates that the loop continues as long as the input candidate is not equal to five asterisks, implying that the asterisk sequence is used to signal the end of the voting inputs. * The line `votes[candidate] -= 1` decrements the count which is incorrect, it should add to the vote. * The final conditional statement checks if `max_votes` is greater than `total_votes // 2`, suggesting the program is intended to determine a winner requiring more than half the total votes. ### Interpretation The program aims to determine the winner of a vote based on user inputs. The use of a `defaultdict` allows the program to automatically handle new candidate entries without requiring explicit initialization. The program attempts to find a winner with more than half of the total votes, but the logic contains errors, particularly `votes[candidate] -= 1`, that will likely produce incorrect results. The suggestion to run the code on a local machine hints that debugging is a key learning aspect intended. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/6.jpg Details</summary>  ### Visual Description ## Error Message: Example Error ### Overview The image shows an example error message that occurs when a program fails a test. It includes the input, the program's incorrect output, and the expected output. ### Components/Axes The image is divided into three main sections: 1. **Error Box (Top-Left):** Contains the error message and a tip. 2. **Description (Right):** Explains what the error message contains and provides a tip. 3. **Input/Output Example (Bottom-Left):** Shows the input, program output, and expected output. ### Detailed Analysis or ### Content Details **Error Box (Top-Left):** * **Title:** Error * **Tip:** "If you're executing the code on your machine, copy-paste the input into a file and pipe it to the program with 'python3 program.py < input.txt'!" * **Input:** * Penny Franklin * Marti Graham * Connie Froggatt * Joseph Ivers * Connie Froggatt * Penny Franklin * Connie Froggatt * Bruce Stanger * Connie Froggatt * Barbara Skinner * Barbara Skinner * \*\*\* * **Program Output:** Runoff! * **Expected Output:** Connie Froggatt **Description (Right):** * "The error message shows you the test that the program failed on." * "It contains:" * "An example input" * "The program's incorrect output" * "The expected output" * "Tip: try copy-pasting the input to a file and piping it to the program." ### Key Observations * The error message provides a clear example of the input, the program's output, and the expected output. * The tip suggests a way to resolve the error by copying the input into a file and piping it to the program. * The input section contains a list of names, some of which are repeated. * The program output is "Runoff!", while the expected output is "Connie Froggatt". ### Interpretation The error message demonstrates a scenario where the program's output does not match the expected output. This could be due to a bug in the program's logic or an incorrect input. The provided tip suggests a method for debugging the program by isolating the input and piping it to the program. The example input, program output, and expected output provide valuable information for identifying the root cause of the error. The repetition of names in the input might be relevant to the program's functionality and the error itself. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/7.jpg Details</summary>  ### Visual Description ## Text Block: Model Explanations and Debugging Tips ### Overview The image presents model explanations and debugging tips. It includes two example explanations generated by the model and suggests considering them as CoPilot suggestions. ### Components/Axes * **Title:** "4. Model Explanations" * **Section:** "Model Explanations" * **Explanation 1:** A concise explanation of an issue related to code checking maximum votes for a majority. * **Explanation 2:** A concise explanation of an issue related to code checking for a simple majority by comparing 'max_votes' to 'total_votes // 2'. * **Debugging Tips:** A section providing guidance on using the model-generated explanations for debugging. ### Detailed Analysis or ### Content Details * **Explanation 1:** * "The concise explanation of the issue is: The code checks if the maximum votes are strictly greater than half of the total votes to determine if there's a majority. However, it should check if the maximum votes are greater than or equal to half of the total votes." * **Explanation 2:** * "The following is a concise explanation of the issue: The code checks for a simple majority by comparing 'max_votes' to 'total_votes // 2', which will return the floor division result. This means that if 'max_votes' is equal to half of the 'total_votes', it will not be considered a simple majority. Instead, the condition should check if 'max_votes' is strictly greater than half of the 'total_votes'." * **Debugging Tips:** * "To help you get started with the debugging, each page lists two example explanations." * "These explanations are generated by the model itself. They might be completely wrong. You don't have to use them." * "Think of these like CoPilot suggestions." ### Key Observations * The model-generated explanations are presented as suggestions and might not be accurate. * The explanations focus on potential issues in code related to determining majority based on vote counts. ### Interpretation The image provides model-generated explanations to aid in debugging. However, it explicitly states that these explanations might be incorrect and should be treated as suggestions rather than definitive solutions. The explanations highlight potential flaws in the logic used to determine majority based on vote counts, specifically focusing on the comparison between 'max_votes' and 'total_votes'. The image encourages users to critically evaluate these explanations and use them as a starting point for further investigation. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/8.jpg Details</summary>  ### Visual Description ## Form: Answer Form ### Overview The image shows a digital form titled "Answer Form," likely part of a larger online survey or assignment. The form includes a section for "Your Explanation," with a text input field for the answer. The form is designed to be anonymous, and it is embedded within a Google Form. Instructions are provided, indicating that the answer should be self-contained and explain what the program is doing wrong. ### Components/Axes * **Title:** "5. Answer Form" * **Section Title:** "Your Explanation" * **Anonymity Notice:** "REDACTED FOR ANONYMITY" (displayed in a black box) * **Google Sign-in Prompt:** "Sign in to Google to save your progress. Learn more" * **Required Question Indicator:** "* Indicates required question" * **Question Label:** "Your Explanation *" * **Input Field:** "Your answer" (placeholder text) * **Submit Button:** "Submit" (purple button) * **Clear Form Button:** "Clear form" * **Instructions (Right Side):** * "Finally, each page contains an embedded Google Form. No login is required." * "Submit your explanation of what the program is doing wrong." * "Your answer must be self-contained; it should *not* be of the form 'Just like the first model explanation describes, the issue with the code is that ...'" ### Detailed Analysis or Content Details The form is structured to collect a textual explanation. The "REDACTED FOR ANONYMITY" notice suggests that user identities are being protected. The instructions emphasize the need for a clear and self-contained explanation of the program's issue, discouraging vague or derivative answers. The form is embedded within Google Forms, but no login is required. ### Key Observations * The form prioritizes anonymity. * The instructions are specific about the type of answer expected. * The form is designed for ease of use, with clear labels and buttons. ### Interpretation The form is designed to gather specific, self-contained explanations while ensuring user anonymity. The instructions aim to elicit thoughtful and original responses, rather than generic or copied answers. The use of Google Forms provides a convenient platform for data collection, and the lack of login requirement further enhances accessibility and anonymity. The form is likely part of a larger assessment or feedback process where detailed explanations are valued. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/9.jpg Details</summary>  ### Visual Description ## Document: Study Tips ### Overview The image presents a list of study tips, formatted as bullet points, with an introductory statement expressing gratitude for the user's help. The tips cover understanding the task, writing clear explanations, using model explanations, time allocation, using external tools, and asking questions. ### Components/Axes * **Title:** Study Tips * **Introductory Statement:** "We are very grateful for your help! 😊" * **Bullet Points:** * "Make sure you understand the task first! The programs have subtle logic errors, not just simple compiler errors." * "Try to write clear and concise explanations, with proper grammar and punctuation." * "Feel free to use (or not use) the model explanations when writing your answers; but make sure your answer is self-contained!" * "The tasks vary in difficulty. Feel free to allocate your time as you see fit; we are not measuring how quickly you complete the tasks or anything like that!" * "Feel free to use external tools:" * "Use pen and paper or a whiteboard to help you reason about the task at hand." * "Use a Python IDE to execute and debug the code." * "Search online for help." * "Have a question? Ask [redacted] before moving on with the study! 😊" ### Detailed Analysis or ### Content Details The document provides a series of recommendations for approaching a study task. It emphasizes understanding the task thoroughly, writing clear and concise explanations, and using available resources effectively. It also encourages users to manage their time and seek help when needed. The use of a smiley face emoji adds a friendly tone. ### Key Observations * The tips are practical and actionable. * The document encourages a flexible approach to studying, allowing users to choose whether or not to use model explanations. * The document acknowledges the varying difficulty of tasks and encourages users to allocate their time accordingly. * The document suggests specific external tools, including pen and paper, a Python IDE, and online search. * The document encourages users to ask questions before proceeding. ### Interpretation The document aims to provide helpful guidance for users undertaking a study task. The tips are designed to promote effective learning and problem-solving. The emphasis on understanding the task, writing clear explanations, and using available resources suggests a focus on deep learning and critical thinking. The encouragement to manage time and seek help indicates an awareness of the challenges that learners may face. The overall tone is supportive and encouraging. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/10.jpg Details</summary>  ### Visual Description ## FAQ: Study Information ### Overview The image presents a Frequently Asked Questions (FAQ) section, likely from a website or document related to a research study. It addresses questions about data collection, the study's purpose, and the usefulness of model explanations. ### Components/Axes The FAQ section consists of three questions, each followed by an answer. The questions are: 1. Are you collecting data as I visit the website? 2. What is the point of the study? 3. Are you evaluating how useful the model explanations were to me? ### Detailed Analysis or ### Content Details * **Question 1:** "Are you collecting data as I visit the website?" * **Answer:** "No - none at all. Only your final answers are recorded." * **Question 2:** "What is the point of the study?" * **Answer:** "To investigate how much better the models are at fixing code when given human feedback, instead of having to debug the code themselves." * **Question 3:** "Are you evaluating how useful the model explanations were to me?" * **Answer:** "No - they are just there to help you get started with the debugging. We only care about your final answer." ### Key Observations * The study does not collect data passively as users browse the website. * The study aims to assess the impact of human feedback on the performance of models in fixing code. * The model explanations are intended to assist users in debugging, but their usefulness is not a primary focus of evaluation. ### Interpretation The FAQ section provides transparency about the study's data collection practices and objectives. It clarifies that user privacy is respected by only recording final answers, and that the study's primary goal is to understand how human feedback can improve code-fixing models. The explanation regarding model explanations suggests that the study is more interested in the final outcome (fixed code) than the process of how users utilize the explanations. </details> Figure 10: Appendix C Human Experiment (Quantitative Analysis): Results Per Task In the table below, we give a complete breakdown of the quantitative results presented in Section 4.3. Note that each program is associated with four different pieces of feedback: two sampled from GPT-4, and two given by our human participants. Each cell is the number of repair candidates (out of 25) that passed all the unit tests. See Section 4.3 for details, as well as Appendix B for the instructions given to participants. | 2106 | interview | A | 7 | 10 | 10 | 0 | | --- | --- | --- | --- | --- | --- | --- | | B | 0 | 2 | 20 | 16 | | | | 2673 | interview | A | 4 | 7 | 17 | 24 | | B | 3 | 25 | 25 | 25 | | | | 2923 | interview | A | 0 | 0 | 0 | 0 | | B | 0 | 0 | 0 | 0 | | | | 3070 | competition | A | 0 | 0 | 0 | 0 | | B | 3 | 0 | 5 | 0 | | | | 3286 | competition | A | 2 | 6 | 10 | 25 | | B | 0 | 0 | 0 | 4 | | | | 3754 | competition | A | 0 | 0 | 0 | 0 | | B | 0 | 0 | 0 | 0 | | | | 4182 | introductory | A | 25 | 25 | 25 | 24 | | B | 25 | 0 | 25 | 25 | | | | 4195 | introductory | A | 25 | 3 | 24 | 23 | | B | 23 | 25 | 25 | 25 | | | | 4281 | introductory | A | 0 | 4 | 0 | 0 | | B | 0 | 0 | 0 | 0 | | | | 4333 | introductory | A | 25 | 0 | 25 | 0 | | B | 23 | 24 | 24 | 25 | | | | 4347 | introductory | A | 0 | 0 | 7 | 25 | | B | 0 | 0 | 25 | 25 | | | | 4426 | introductory | A | 25 | 25 | 25 | 25 | | B | 25 | 25 | 25 | 25 | | | | 4450 | introductory | A | 0 | 0 | 0 | 0 | | B | 24 | 0 | 22 | 24 | | | | 4507 | introductory | A | 0 | 0 | 0 | 0 | | B | 0 | 0 | 1 | 0 | | | | 4514 | introductory | A | 15 | 21 | 1 | 16 | | B | 0 | 0 | 25 | 0 | | | | 4704 | introductory | A | 0 | 25 | 0 | 25 | | B | 25 | 25 | 24 | 23 | | | | 4741 | introductory | A | 25 | 25 | 25 | 25 | | B | 25 | 25 | 25 | 25 | | | | 4855 | introductory | A | 0 | 1 | 17 | 25 | | B | 0 | 2 | 3 | 23 | | | | 4873 | introductory | A | 0 | 0 | 0 | 0 | | B | 0 | 0 | 0 | 18 | | | | 4952 | introductory | A | 0 | 0 | 2 | 25 | | B | 24 | 8 | 24 | 21 | | | Appendix D Human Experiment (Qualitative Analysis): Examples In this appendix, we give examples of each category used to classify the responses in the qualitative analysis of Section 4.3. For each category, we give one example from the human participants and one from GPT-4 (when possible). Each example contains: the textual specification of the task; the incorrect program; the error message (in the format it was shown to participants); the feedback in question; and a short comment motivating its classification. D.1 Category (a): obviously incorrect feedback D.1.1 GPT-4: Example ⬇ ### SPECIFICATION The recent schoolboard elections were hotly contested: a proposal to swap school start times for elementary and high school students, a controversial new dress code proposal that bans athletic clothes in school, and a proposal to raise real - estate taxes to pay for a new football practice facility, and the list goes on and on. It is now hours after the polls have closed and a winner has yet to emerge! In their desperation, the election officials turn to you and ask you to write a program to count the vote! ----- Input ----- The input consists of a single test case, which is a list of votes cast. Each line in the input contains the name of a candidate for whom a vote was cast. A name may consist of multiple words, separated by spaces. Words contain letters or hyphens, but no other punctuation characters. There will be at least votes on the list. The list of votes ends with a single line containing the characters ***. This line should not be counted. There can be up to valid votes. ----- Output ----- If a candidate obtained a simple or absolute majority of all votes cast (that is, more than any other candidate), output the name of this candidate! If no candidate obtained a simple majority, output: " Runoff!" (don ’ t forget to include the exclamation mark!) ----- Examples ----- Sample Input: Penny Franklin Marti Graham Connie Froggatt Joseph Ivers Connie Froggatt Penny Franklin Connie Froggatt Bruce Stanger Connie Froggatt Barbara Skinner Barbara Skinner *** Sample Output: Connie Froggatt ### INCORRECT PROGRAM from collections import defaultdict votes = defaultdict (int) candidate = input () while candidate != "***": votes [candidate] += 1 candidate = input () total_votes = sum (votes. values ()) max_votes = max (votes. values ()) winner = [name for name, count in votes. items () if count == max_votes] if len (winner) == 1 and max_votes > total_votes // 2: print (winner [0]) else: print (" Runoff!") ### ERROR MESSAGE === Input === Penny Franklin Marti Graham Connie Froggatt Joseph Ivers Connie Froggatt Penny Franklin Connie Froggatt Bruce Stanger Connie Froggatt Barbara Skinner Barbara Skinner *** === Program Output === Runoff! === Expected Output === Connie Froggatt ### FEEDBACK The concise explanation of the issue is: The code checks if the maximum votes are strictly greater than half of the total votes to determine if there ’ s a majority. However, it should check if the maximum votes are greater than or equal to half of the total votes. ### COMMENT The issue with the code is not that the ">" should have been a ">=", but rather that it is not allowing for a simple majority. D.1.2 Human: Example ⬇ ### SPECIFICATION Snuke and Raccoon have a heap of N cards. The i - th card from the top has the integer a_i written on it. They will share these cards. First, Snuke will take some number of cards from the top of the heap, then Raccoon will take all the remaining cards. Here, both Snuke and Raccoon have to take at least one card. Let the sum of the integers on Snuke ’ s cards and Raccoon ’ s cards be x and y, respectively. They would like to minimize | x - y |. Find the minimum possible value of | x - y |. ----- Constraints ----- - 2 \ leq N \ leq 2 \ times 10^5 - -10^{9} \ leq a_i \ leq 10^{9} - a_i is an integer. ----- Input ----- Input is given from Standard Input in the following format: N a_1 a_2 ... a_ {N} ----- Output ----- Print the answer. ----- Sample Input ----- 6 1 2 3 4 5 6 ----- Sample Output ----- 1 If Snuke takes four cards from the top, and Raccoon takes the remaining two cards, x =10, y =11, and thus | x - y |=1. This is the minimum possible value. ### INCORRECT PROGRAM def main (): n = int (input ()) a = list (map (int, input (). split ())) Snuke_sum = 0 Raccoon_sum = sum (a) min_diff = abs (Raccoon_sum) for i in range (n -1): Snuke_sum += a [i] Raccoon_sum -= a [i] diff = abs (Snuke_sum - Raccoon_sum) min_diff = min (min_diff, diff) print (min_diff) main () ### ERROR MESSAGE === Input === 2 10 -10 === Program Output === 0 === Expected Output === 20 ### FEEDBACK The code initializes the result ‘ min_diff ‘ to ‘ abs (Raccoon_sum)‘ corresponding to the case where Raccoon takes all the cards, however this is incorrect because of the constraint " Snuke and Raccoon have to take at least one card ". Instead just setting ‘ min_diff ‘ to negative infinity initially would fix it. ### COMMENT This human participant was on the right track, but note that setting ‘ min_diff ‘ to * negative * infinity would cause it to never be updated inside of the for loop, and so the program would in fact always return negative infinity. D.2 Category (b): feedback explicitly suggests a minor change to the code D.2.1 GPT-4: Example ⬇ ### SPECIFICATION There is a square in the xy - plane. The coordinates of its four vertices are (x_1, y_1),(x_2, y_2),(x_3, y_3) and (x_4, y_4) in counter - clockwise order. (Assume that the positive x - axis points right, and the positive y - axis points up.) Takahashi remembers (x_1, y_1) and (x_2, y_2), but he has forgot (x_3, y_3) and (x_4, y_4). Given x_1, x_2, y_1, y_2, restore x_3, y_3, x_4, y_4. It can be shown that x_3, y_3, x_4 and y_4 uniquely exist and have integer values. ----- Constraints ----- - | x_1 |,| y_1 |,| x_2 |,| y_2 | \ leq 100 - (x_1, y_1) != (x_2, y_2) - All values in input are integers. ----- Input ----- Input is given from Standard Input in the following format: x_1 y_1 x_2 y_2 ----- Output ----- Print x_3, y_3, x_4 and y_4 as integers, in this order. ----- Sample Input ----- 0 0 0 1 ----- Sample Output ----- -1 1 -1 0 (0,0),(0,1),(-1,1),(-1,0) is the four vertices of a square in counter - clockwise order. Note that (x_3, y_3)=(1,1),(x_4, y_4)=(1,0) is not accepted, as the vertices are in clockwise order. ### INCORRECT PROGRAM x1, y1, x2, y2 = map (int, input (). split ()) x3 = x2 + (y2 - y1) y3 = y2 - (x2 - x1) x4 = x1 + (y2 - y1) y4 = y1 - (x2 - x1) print (x3, y3, x4, y4) ### ERROR MESSAGE === Input === 0 0 0 1 === Program Output === 1 1 1 0 === Expected Output === -1 1 -1 0 ### FEEDBACK The issue with the code is that it doesn ’ t consider the counter - clockwise order of the vertices. To fix this, we need to swap the signs of (y2 - y1) and (x2 - x1) in the calculations. ### COMMENT Swapping the listed signs is a concrete suggestion of a way to fix the code. Since the overall structure of the code would remain the same, we count this as a minor change. D.2.2 Human: Example ⬇ ### SPECIFICATION Given is a string S representing the day of the week today. S is SUN, MON, TUE, WED, THU, FRI, or SAT, for Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday, respectively. After how many days is the next Sunday (tomorrow or later)? ----- Constraints ----- - S is SUN, MON, TUE, WED, THU, FRI, or SAT. ----- Input ----- Input is given from Standard Input in the following format: S ----- Output ----- Print the number of days before the next Sunday. ----- Sample Input ----- SAT ----- Sample Output ----- 1 It is Saturday today, and tomorrow will be Sunday. ### INCORRECT PROGRAM S = input () days = [’ SUN ’, ’ MON ’, ’ TUE ’, ’ WED ’, ’ THU ’, ’ FRI ’, ’ SAT ’] print ((7 - days. index (S)) % 7) ### ERROR MESSAGE === Input === SUN === Program Output === 0 === Expected Output === 7 ### FEEDBACK The logic is incorrect. There should be no modulo operator. ### COMMENT Suggesting that the modulo operator should be removed is a relatively small, but explicit, change. D.3 Category (c): feedback explicitly suggests a large change to the code D.3.1 GPT-4: Example ⬇ ### SPECIFICATION Takahashi is about to assemble a character figure, consisting of N parts called Part 1, Part 2, ..., Part N and N -1 connecting components. Parts are distinguishable, but connecting components are not. Part i has d_i holes, called Hole 1, Hole 2, ..., Hole d_i, into which a connecting component can be inserted. These holes in the parts are distinguishable. Each connecting component will be inserted into two holes in different parts, connecting these two parts. It is impossible to insert multiple connecting components into a hole. The character figure is said to be complete when it has the following properties: - All of the N -1 components are used to connect parts. - Consider a graph with N vertices corresponding to the parts and N -1 undirected edges corresponding to the pairs of vertices connected by a connecting component. Then, this graph is connected. Two ways A and B to make the figure complete are considered the same when the following is satisfied: for every pair of holes, A uses a connecting component to connect these holes if and only if B uses one to connect them. Find the number of ways to make the figure complete. Since the answer can be enormous, find the count modulo 998244353. ----- Constraints ----- - All values in input are integers. - 2 \ leq N \ leq 2 \ times 10^5 - 1 \ leq d_i < 998244353 ----- Input ----- Input is given from Standard Input in the following format: N d_1 d_2 \ cdots d_N ----- Output ----- Print the answer. ----- Sample Input ----- 3 1 1 3 ----- Sample Output ----- 6 One way to make the figure complete is to connect Hole 1 in Part 1 and Hole 3 in Part 3 and then connect Hole 1 in Part 2 and Hole 1 in Part 3. ### INCORRECT PROGRAM def main (): N = int (input ()) d = list (map (int, input (). split ())) MOD = 998244353 fact = [1] * (N +1) for i in range (1, N +1): fact [i] = fact [i -1] * i % MOD ans = 0 for ki in range (N): ans += d [ki] * fact [ki] % MOD * fact [N - ki -1] % MOD ans %= MOD ans = ans * fact [N -1] % MOD print (ans) main () ### ERROR MESSAGE === Input === 3 1 1 3 === Program Output === 18 === Expected Output === 6 ### FEEDBACK The following is a concise explanation of the issue: The code above calculates the total number of ways to connect the parts, but it does not ensure that each connecting component is used only once. This results in overcounting the number of ways to make the figure complete. To fix the issue, we need to ensure that each connecting component is used exactly once. ### COMMENT The feedback suggests changing the code so that each connecting component is used exactly once, which does not seem to be taken into account in the current approach. Changing the code to satisfy this part of the specification seems to require a major rewrite. D.3.2 Human: Example ⬇ ### SPECIFICATION Oh, New Year. The time to gather all your friends and reflect on the heartwarming events of the past year... $n$ friends live in a city which can be represented as a number line. The $i$ - th friend lives in a house with an integer coordinate $x_i$. The $i$ - th friend can come celebrate the New Year to the house with coordinate $x_i -1 $, $x_i +1 $ or stay at $x_i$. Each friend is allowed to move no more than once. For all friends $1 \ le x_i \ le n$ holds, however, they can come to houses with coordinates $0$ and $n +1 $ (if their houses are at $1$ or $n$, respectively). For example, let the initial positions be $x = [1, 2, 4, 4] $. The final ones then can be $ [1, 3, 3, 4] $, $ [0, 2, 3, 3] $, $ [2, 2, 5, 5] $, $ [2, 1, 3, 5] $ and so on. The number of occupied houses is the number of distinct positions among the final ones. So all friends choose the moves they want to perform. After that the number of occupied houses is calculated. What is the minimum and the maximum number of occupied houses can there be? ----- Input ----- The first line contains a single integer $n$ ($1 \ le n \ le 2 \ cdot 10^5 $) - the number of friends. The second line contains $n$ integers $x_1, x_2, \ dots, x_n$ ($1 \ le x_i \ le n$) - the coordinates of the houses of the friends. ----- Output ----- Print two integers - the minimum and the maximum possible number of occupied houses after all moves are performed. ----- Examples ----- Input 4 1 2 4 4 Output 2 4 Input 9 1 1 8 8 8 4 4 4 4 Output 3 8 Input 7 4 3 7 1 4 3 3 Output 3 6 ----- Note ----- In the first example friends can go to $ [2, 2, 3, 3] $. So friend $1$ goes to $x_1 +1 $, friend $2$ stays at his house $x_2$, friend $3$ goes to $x_3 -1 $ and friend $4$ goes to $x_4 -1 $. $ [1, 1, 3, 3] $, $ [2, 2, 3, 3] $ or $ [2, 2, 4, 4] $ are also all valid options to obtain $2$ occupied houses. For the maximum number of occupied houses friends can go to $ [1, 2, 3, 4] $ or to $ [0, 2, 4, 5] $, for example. ### INCORRECT PROGRAM from collections import Counter def main (): n = int (input ()) x = list (map (int, input (). split ())) cnt = Counter (x) max_houses = 0 for pos in range (1, n + 1): if cnt [pos]: max_houses += 1 occupied = [0] * (n + 2) for pos in x: if not occupied [pos - 1]: occupied [pos - 1] = 1 elif not occupied [pos]: occupied [pos] = 1 elif not occupied [pos + 1]: occupied [pos + 1] = 1 min_houses = sum (occupied) print (min_houses, max_houses) main () ### ERROR MESSAGE === Input === 4 1 2 4 4 === Program Output === 4 3 === Expected Output === 2 4 ### FEEDBACK The code calculates both the minimum and maximum count of houses incorrectly. The correct solution requires conducting a tree search to determine the true maximum and minimum. This can be further optimized by first sorting the list of occupied houses and using a sliding window to process independent segments of the number line. ### COMMENT The feedback suggests conducting a tree search to determine the max and min, as well as a way to optimize this search. These constitute major changes to the program as it is currently written. D.4 Category (d): Feedback contains blocks of pseudocode or Python code D.4.1 GPT-4: Example GPT-4’s feedback never contains blocks of Python per our experiment design, in which the code block is stripped (Section 4.3). We find that GPT-4 never utilizes blocks of pseudocode, either. D.4.2 Human: Example ⬇ ### SPECIFICATION Given is a string S representing the day of the week today. S is SUN, MON, TUE, WED, THU, FRI, or SAT, for Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday, respectively. After how many days is the next Sunday (tomorrow or later)? ----- Constraints ----- - S is SUN, MON, TUE, WED, THU, FRI, or SAT. ----- Input ----- Input is given from Standard Input in the following format: S ----- Output ----- Print the number of days before the next Sunday. ----- Sample Input ----- SAT ----- Sample Output ----- 1 It is Saturday today, and tomorrow will be Sunday. ### INCORRECT PROGRAM day = input () days = [’ SUN ’, ’ MON ’, ’ TUE ’, ’ WED ’, ’ THU ’, ’ FRI ’, ’ SAT ’] index = days. index (day) result = (7 - index) % 7 print (result) ### ERROR MESSAGE === Input === SUN === Program Output === 0 === Expected Output === 7 ### FEEDBACK before returning the result, we should just check to see if result ==0. so we just need to add: if result == 0: result = 7 ### COMMENT The feedback contains a block of Python code that the model can simply copy in order to fix the program. D.5 Category (e): feedback which expresses uncertainty D.5.1 GPT-4: Example In the $20· 2· 2=80$ examples we study, we do not find that GPT-4 ever expresses uncertainty. D.5.2 Human: Example ⬇ ### SPECIFICATION Two kingdoms had been at war for a long time, until the emperor intervened to bring an end to the conflict. The territory in question comprises an $M$ by $N$ rectangular grid. At the emperor ’ s insistence, the two kings have withdrawn their troops until no two opposing troops are in adjacent squares of the map (adjacent being horizontal or vertical - diagonal is not considered). The emperor proposes to designate certain squares of the map as neutral territory. Neither king will be allowed to move troops into those squares, and the emperor ’ s own forces will patrol them to be sure that both kings observe these rules. The emperor is frugal and does not want to commit more soldiers to this effort than absolutely necessary. His generals have marked each square of the map with the number of soldiers required to secure that square. What remains is to choose which of those squares should be patrolled. Write a program to determine the minimum number of soldiers that the emperor will need to be deploy to guarantee that the troops of one kingdom cannot move, in one or more steps, into squares occupied by the troops of the second kingdom (moving horizontally or vertically) without encountering the emperor ’ s own soldiers. ----- Input ----- Input begins with a line containing $2$ integers, $w$ and $h$, denoting the width and height of the map, where $1 \ leq w, h \ leq 40 $. This is followed by $h$ lines. Each line contains $w$ characters, left justified. These characters will be ’ A ’ or ’ B ’, designating a position held by king A or king B, or a single numeric digit, designating a currently unoccupied position that can be secured by the use of that number of soldiers. For example, a ’2’ would indicate that two soldiers must be deployed to that square to secure it against passage of other troops. A ’0’ indicates terrain that is impassible - the emperor need not commit soldiers there because the kingdom troops cannot pass through that square. No ’ A ’ will be adjacent, horizontally or vertically, to any ’ B ’. There will be at least one ’ A ’ and one ’ B ’ in the input. ----- Output ----- Print a single line containing an integer denoting the minimum number of soldiers that the emperor must deploy to guarantee that there is no open path between any ’ A ’ position and any ’ B ’ position, using any combination of horizontal or vertical moves. ----- Examples ----- Sample Input: 8 5 A11111AA AA7B111A 111 BB111 11 BBB111 11 BBB11B Sample Output: 13 ### INCORRECT PROGRAM def main (): w, h = map (int, input (). split ()) grid = [input () for _ in range (h)] def bfs (x, y, z): dist = [[float (" inf ")] * w for _ in range (h)] dist [x][y] = 0 q = [(x, y)] for x, y in q: for dx, dy in [(-1, 0), (1, 0), (0, -1), (0, 1)]: nx, ny = x + dx, y + dy if 0 <= nx < h and 0 <= ny < w and dist [nx][ny] == float (" inf "): if grid [nx][ny] == z: dist [nx][ny] = dist [x][y] q. append ((nx, ny)) if "0" <= grid [nx][ny] <= "9": dist [nx][ny] = dist [x][y] + int (grid [nx][ny]) q. append ((nx, ny)) return dist ans = float (" inf ") for i in range (h): for j in range (w): if grid [i][j] == " A ": ans = min (ans, min (x for row in bfs (i, j, " B ") for x in row)) print (ans) main () ### ERROR MESSAGE === Input === 8 5 A11111AA AA7B111A 111 BB111 11 BBB111 11 BBB11B === Program Output === 0 === Expected Output === 13 ### FEEDBACK This code appears to be finding the minimum " distance " between an A position and a B position, where distance is measured in the number of soldiers required to secure the intermediate positions. This isn ’ t really addressing the question at all, because even occupying the positions along some path from a particular A -> B won ’ t necessarily block the kings from reaching each other from those positions through a different, longer path. You probably need some sort of min - cut algorithm to divide the graph into two connected components, one each for A and B nodes. ### COMMENT The feedback expresses mild uncertainty in two aspects. First, the user indicates that they are not completely certain in their understanding of the code ’ s current behaviour by using the phrase " appears to be ". Then, they express uncertainty in their suggestion for what to do instead, saying that one * probably * needs some sort of min - cut algorithm. Appendix E Prompts In this appendix, we describe the prompting structure used for our experiments. All of our experiments use one-shot prompting, in which a single example is given in the prompt before the desired task. For initial code generation (the first sample from $M_{P}$ ), we use different prompts for the two types of tasks in APPS: call-based tasks, in which the desired program should take the input as a parameter to a function and return the output in the function’s return statement; and stdio-based tasks, in which inputs should be read from stdin and outputs should be written to stdout. These prompts are shown in Listing 1 and 2, respectively. The example tasks and programs were taken from APPS’ training set. For feedback samples (i.e., samples from $M_{F}$ ), we use the prompt in Listing 3. This prompt contains an example in which the user provides the textual specification, the incorrect program and the error message, and the assistant generates feedback. Similarly, for repair samples (i.e., samples from $M_{P}$ which follow $M_{F}$ ) we use the prompt in Listing 4, in which the user also supplies the feedback, and the assistant returns only the fixed version of the program. Finally, for joint feedback-repair samples (i.e., when sampling $(f,r)\sim M_{P}$ ), we use the prompt in Listing 6. This prompt combines the prompts from Listing 4 and 5 into one prompt, in which the assistant returns both the feedback and the fixed program. In all of these prompts, the specification used was taken from APPS’ training set, while the programs and the feedback were constructed manually. Listing 1: Code generation prompt for call-based tasks. ⬇ ===== system ===== You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. You will NOT return anything except for the program. Put your fixed program within code delimiters, for example: ‘‘‘ python # YOUR CODE HERE ‘‘‘. ===== user ===== ### QUESTION A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward as forward. Examples of numerical palindromes are: ‘2332, 110011, 54322345‘ For a given number ‘‘‘ num ‘‘‘, write a function which returns an array of all the numerical palindromes contained within each number. The array should be sorted in ascending order and any duplicates should be removed. In this kata, single digit numbers and numbers which start or end with zeros (such as ‘010‘ and ‘00‘) are ** NOT ** considered valid numerical palindromes. If ‘ num ‘ contains no valid palindromes, return ‘" No palindromes found "‘. Otherwise, return ‘" Not valid "‘ if the input is not an integer or is less than ‘0‘. ## Examples ‘‘‘ palindrome (1221) => [22, 1221] palindrome (34322122) => [22, 212, 343, 22122] palindrome (1001331) => [33, 1001, 1331] palindrome (1294) => " No palindromes found " palindrome ("1221") => " Not valid " ‘‘‘ --- ### Other Kata in this Series: Numerical Palindrome #1 Numerical Palindrome #1.5 Numerical Palindrome #2 Numerical Palindrome #3 Numerical Palindrome #3.5 Numerical Palindrome #4 Numerical Palindrome #5 ### Use Call - Based Format ===== assistant ===== ‘‘‘ python def is_pal (s): return s == s [::-1] def palindrome (num): if not isinstance (num, int) or num < 0: return ’ Not valid ’ s = str (num) pals = set () for i, ch in enumerate (s): if ch == ’0’: continue for j in range (i + 2, len (s) + 1): test = s [i: j] if is_pal (test): pals. add (test) return sorted (int (x) for x in pals) or ’ No palindromes found ’ ‘‘‘ Listing 2: Code generation prompt for stdio-based tasks. ⬇ ===== system ===== You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. You will NOT return anything except for the program. Put your fixed program within code delimiters, for example: ‘‘‘ python # YOUR CODE HERE ‘‘‘. ===== user ===== ### QUESTION Polycarp has $n$ different binary words. A word called binary if it contains only characters ’0’ and ’1’. For example, these words are binary: "0001", "11", "0" and "0011100". Polycarp wants to offer his set of $n$ binary words to play a game " words ". In this game, players name words and each next word (starting from the second) must start with the last character of the previous word. The first word can be any. For example, these sequence of words can be named during the game: "0101", "1", "10", "00", "00001". Word reversal is the operation of reversing the order of the characters. For example, the word "0111" after the reversal becomes "1110", the word "11010" after the reversal becomes "01011". Probably, Polycarp has such a set of words that there is no way to put them in the order correspondent to the game rules. In this situation, he wants to reverse some words from his set so that: the final set of $n$ words still contains different words (i. e. all words are unique); there is a way to put all words of the final set of words in the order so that the final sequence of $n$ words is consistent with the game rules. Polycarp wants to reverse minimal number of words. Please, help him. ----- Input ----- The first line of the input contains one integer $t$ ($1 \ le t \ le 10\^4 $) - the number of test cases in the input. Then $t$ test cases follow. The first line of a test case contains one integer $n$ ($1 \ le n \ le 2\ cdot10 ^5 $) - the number of words in the Polycarp ’ s set. Next $n$ lines contain these words. All of $n$ words aren ’ t empty and contains only characters ’0’ and ’1’. The sum of word lengths doesn ’ t exceed $4 \ cdot10 ^6 $. All words are different. Guaranteed, that the sum of $n$ for all test cases in the input doesn ’ t exceed $2 \ cdot10 ^5 $. Also, guaranteed that the sum of word lengths for all test cases in the input doesn ’ t exceed $4 \ cdot10 ^6 $. ----- Output ----- Print answer for all of $t$ test cases in the order they appear. If there is no answer for the test case, print -1. Otherwise, the first line of the output should contain $k$ ($0 \ le k \ le n$) - the minimal number of words in the set which should be reversed. The second line of the output should contain $k$ distinct integers - the indexes of the words in the set which should be reversed. Words are numerated from $1$ to $n$ in the order they appear. If $k =0 $ you can skip this line (or you can print an empty line). If there are many answers you can print any of them. ----- Example ----- Input 4 4 0001 1000 0011 0111 3 010 101 0 2 00000 00001 4 01 001 0001 00001 Output 1 3 -1 0 2 1 2 ### Use Standard Input Format (read inputs with ‘ input ()‘, write results with ‘ print ()‘) ===== assistant ===== ‘‘‘ python for _ in range (int (input ())): n = int (input ()) mass = [] zo = 0 oz = 0 zz = 0 oo = 0 ozs = [] zos = [] ozss = set () zoss = set () for j in range (n): k = input () mass. append (k) if k [0] == ’0’ and k [-1] == ’1’: zoss. add (k) zos. append (j + 1) zo += 1 elif k [0] == ’1’ and k [-1] == ’0’: ozss. add (k) ozs. append (j + 1) oz += 1 elif k [0] == ’0’ and k [-1] == ’0’: zz += 1 else: oo += 1 if zz and oo and not oz and not zo: print (-1) continue else: if zo > oz: print ((zo - oz) // 2) ans = [] need = (zo - oz) // 2 i = 0 while need: zzz = mass [zos [i] - 1][len (mass [zos [i] - 1]) - 1:: -1] if zzz not in ozss: ans. append (zos [i]) need -= 1 i += 1 print (* ans) else: print ((oz - zo) // 2) ans = [] need = (oz - zo) // 2 i = 0 while need: zzz = mass [ozs [i] - 1][len (mass [ozs [i] - 1]) - 1:: -1] if zzz not in zoss: ans. append (ozs [i]) need -= 1 i += 1 print (* ans) ‘‘‘ Listing 3: Feedback-only prompt. ⬇ ===== system ===== You are a helpful programming assistant and an expert Python programmer. You are helping a user debug a program. The user has written some code, but it has some errors and is not passing the tests. You will help the user by giving a concise (at most 2-3 sentences) textual explanation of what is wrong with the code. You will * not * generate any code, because the user wants to fix the code themselves. ===== user ===== ### QUESTION A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward as forward. Examples of numerical palindromes are: ‘2332, 110011, 54322345‘ For a given number ‘‘‘ num ‘‘‘, write a function which returns an array of all the numerical palindromes contained within each number. The array should be sorted in ascending order and any duplicates should be removed. In this kata, single digit numbers and numbers which start or end with zeros (such as ‘010‘ and ‘00‘) are ** NOT ** considered valid numerical palindromes. If ‘ num ‘ contains no valid palindromes, return ‘" No palindromes found "‘. Otherwise, return ‘" Not valid "‘ if the input is not an integer or is less than ‘0‘. ## Examples ‘‘‘ palindrome (1221) => [22, 1221] palindrome (34322122) => [22, 212, 343, 22122] palindrome (1001331) => [33, 1001, 1331] palindrome (1294) => " No palindromes found " palindrome ("1221") => " Not valid " ‘‘‘ --- ### Other Kata in this Series: Numerical Palindrome #1 Numerical Palindrome #1.5 Numerical Palindrome #2 Numerical Palindrome #3 Numerical Palindrome #3.5 Numerical Palindrome #4 Numerical Palindrome #5 ### Use Call - Based Format ### INCORRECT PYTHON CODE ‘‘‘ python def is_pal (s): return s == s [::-1] def palindrome (num): if not isinstance (num, int) or num < 0: return ’ Not valid ’ s = str (num) pals = set () for i, ch in enumerate (s): for j in range (i + 2, len (s) + 1): test = s [i: j] if is_pal (test): pals. add (test) return sorted (int (x) for x in pals) or ’ No palindromes found ’ ‘‘‘ The code above is wrong and contains a bug. Given input "1001331" the output was "[’0’, ’33’, ’1001’, ’1331’]" but the expected output was "[’33’, ’1001’, ’1331’]". ===== assistant ===== The following is a concise explanation of the issue: The problem description states that numbers which start or end with zeros (such as ‘010‘ and ‘00‘) are NOT considered valid numerical palindromes. However, the code above does not take this into account and therefore returns ‘00‘ as a valid palindrome. This can be fixed by checking if the first or last character is ‘0‘ before adding the string to the set of palindromes. Listing 4: Repair-only prompt. ⬇ ===== system ===== You are a helpful programming assistant and an expert Python programmer. You are helping a user write a program to solve a problem. The user has written some code, but it has some errors and is not passing the tests. The user has spent some time debugging the program and will provide you with a concise textual explanation of what is wrong with the code. You will use this explanation to generate a fixed version of the program. Put your fixed program within code delimiters, for example: ‘‘‘ python # YOUR CODE HERE ‘‘‘. ===== user ===== ### QUESTION A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward as forward. Examples of numerical palindromes are: ‘2332, 110011, 54322345‘ For a given number ‘‘‘ num ‘‘‘, write a function which returns an array of all the numerical palindromes contained within each number. The array should be sorted in ascending order and any duplicates should be removed. In this kata, single digit numbers and numbers which start or end with zeros (such as ‘010‘ and ‘00‘) are ** NOT ** considered valid numerical palindromes. If ‘ num ‘ contains no valid palindromes, return ‘" No palindromes found "‘. Otherwise, return ‘" Not valid "‘ if the input is not an integer or is less than ‘0‘. ## Examples ‘‘‘ palindrome (1221) => [22, 1221] palindrome (34322122) => [22, 212, 343, 22122] palindrome (1001331) => [33, 1001, 1331] palindrome (1294) => " No palindromes found " palindrome ("1221") => " Not valid " ‘‘‘ --- ### Other Kata in this Series: Numerical Palindrome #1 Numerical Palindrome #1.5 Numerical Palindrome #2 Numerical Palindrome #3 Numerical Palindrome #3.5 Numerical Palindrome #4 Numerical Palindrome #5 ### Use Call - Based Format ### INCORRECT PYTHON CODE ‘‘‘ python def is_pal (s): return s == s [::-1] def palindrome (num): if not isinstance (num, int) or num < 0: return ’ Not valid ’ s = str (num) pals = set () for i, ch in enumerate (s): for j in range (i + 2, len (s) + 1): test = s [i: j] if is_pal (test): pals. add (test) return sorted (int (x) for x in pals) or ’ No palindromes found ’ ‘‘‘ The code above is wrong and contains a bug. Given input "1001331" the output was "[’0’, ’33’, ’1001’, ’1331’]" but the expected output was "[’33’, ’1001’, ’1331’]". The following is a concise explanation of the issue: The problem description states that numbers which start or end with zeros (such as ‘010‘ and ‘00‘) are NOT considered valid numerical palindromes. However, the code above does not take this into account and therefore returns ‘00‘ as a valid palindrome. This can be fixed by checking if the first or last character is ‘0‘ before adding the string to the set of palindromes. ===== assistant ===== ### FIXED PYTHON CODE ‘‘‘ python def is_pal (s): return s == s [::-1] def palindrome (num): if not isinstance (num, int) or num < 0: return ’ Not valid ’ s = str (num) pals = set () for i, ch in enumerate (s): if ch == ’0’: continue for j in range (i + 2, len (s) + 1): test = s [i: j] if is_pal (test): pals. add (test) return sorted (int (x) for x in pals) or ’ No palindromes found ’ ‘‘‘ Listing 5: Joint feedback-repair prompt. ⬇ ===== system ===== You are a helpful programming assistant and an expert Python programmer. You are helping a user write a program to solve a problem. The user has written some code, but it has some errors and is not passing the tests. You will help the user by first giving a concise (at most 2-3 sentences) textual explanation of what is wrong with the code. After you have pointed out what is wrong with the code, you will then generate a fixed version of the program. Put your fixed program within code delimiters, for example: ‘‘‘ python # YOUR CODE HERE ‘‘‘. ===== user ===== ### QUESTION A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward as forward. Examples of numerical palindromes are: ‘2332, 110011, 54322345‘ For a given number ‘‘‘ num ‘‘‘, write a function which returns an array of all the numerical palindromes contained within each number. The array should be sorted in ascending order and any duplicates should be removed. In this kata, single digit numbers and numbers which start or end with zeros (such as ‘010‘ and ‘00‘) are ** NOT ** considered valid numerical palindromes. If ‘ num ‘ contains no valid palindromes, return ‘" No palindromes found "‘. Otherwise, return ‘" Not valid "‘ if the input is not an integer or is less than ‘0‘. ## Examples ‘‘‘ palindrome (1221) => [22, 1221] palindrome (34322122) => [22, 212, 343, 22122] palindrome (1001331) => [33, 1001, 1331] palindrome (1294) => " No palindromes found " palindrome ("1221") => " Not valid " ‘‘‘ --- ### Other Kata in this Series: Numerical Palindrome #1 Numerical Palindrome #1.5 Numerical Palindrome #2 Numerical Palindrome #3 Numerical Palindrome #3.5 Numerical Palindrome #4 Numerical Palindrome #5 ### Use Call - Based Format ### INCORRECT PYTHON CODE ‘‘‘ python def is_pal (s): return s == s [::-1] def palindrome (num): if not isinstance (num, int) or num < 0: return ’ Not valid ’ s = str (num) pals = set () for i, ch in enumerate (s): for j in range (i + 2, len (s) + 1): test = s [i: j] if is_pal (test): pals. add (test) return sorted (int (x) for x in pals) or ’ No palindromes found ’ ‘‘‘ The code above is wrong and contains a bug. Given input "1001331" the output was "[’0’, ’33’, ’1001’, ’1331’]" but the expected output was "[’33’, ’1001’, ’1331’]". ===== assistant ===== The following is a concise explanation of the issue: The problem description states that numbers which start or end with zeros (such as ‘010‘ and ‘00‘) are NOT considered valid numerical palindromes. However, the code above does not take this into account and therefore returns ‘00‘ as a valid palindrome. This can be fixed by checking if the first or last character is ‘0‘ before adding the string to the set of palindromes. # The code below is the correct version of the code above, where the issue has been fixed: ### FIXED PYTHON CODE ‘‘‘ python def is_pal (s): return s == s [::-1] def palindrome (num): if not isinstance (num, int) or num < 0: return ’ Not valid ’ s = str (num) pals = set () for i, ch in enumerate (s): if ch == ’0’: continue for j in range (i + 2, len (s) + 1): test = s [i: j] if is_pal (test): pals. add (test) return sorted (int (x) for x in pals) or ’ No palindromes found ’ ‘‘‘ Appendix F Dataset: APPS Tasks Used For Our Evaluations These tasks were randomly sampled from APPS’ test set. To avoid distribution shift, we sampled according to the relative frequency of difficulties in the full dataset. We report the resulting list of tasks to aid reproducibility. | introductory | ’4004’, ’4058’, ’4063’, ’4065’, ’4100’, ’4108’, ’4117’, ’4155’, ’4164’, ’4182’, ’4193’, ’4195’, ’4211’, ’4217’, ’4241’, ’4249’, ’4270’, ’4275’, ’4281’, ’4293’, ’4333’, ’4347’, ’4350’, ’4356’, ’4409’, ’4426’, ’4431’, ’4450’, ’4465’, ’4484’, ’4498’, ’4505’, ’4507’, ’4514’, ’4544’, ’4553’, ’4586’, ’4610’, ’4662’, ’4663’, ’4667’, ’4677’, ’4681’, ’4704’, ’4716’, ’4741’, ’4750’, ’4786’, ’4787’, ’4801’, ’4855’, ’4862’, ’4864’, ’4870’, ’4873’, ’4890’, ’4897’, ’4952’, ’4966’, ’4984’ | | --- | --- | | interview | ’0004’, ’0013’, ’0033’, ’0056’, ’0073’, ’0074’, ’0089’, ’0091’, ’0124’, ’0131’, ’0139’, ’0162’, ’0166’, ’0183’, ’0186’, ’0191’, ’0199’, ’0205’, ’0249’, ’0253’, ’0268’, ’0274’, ’0300’, ’0304’, ’0341’, ’0342’, ’0413’, ’0427’, ’0434’, ’0466’, ’0467’, ’0496’, ’0501’, ’0511’, ’0537’, ’0564’, ’0571’, ’0575’, ’0579’, ’0592’, ’0597’, ’0626’, ’0637’, ’0676’, ’0704’, ’0728’, ’0757’, ’0765’, ’0788’, ’0794’, ’0804’, ’0805’, ’0811’, ’0829’, ’0879’, ’0904’, ’0915’, ’0925’, ’0937’, ’0948’, ’0954’, ’0955’, ’0972’, ’0985’, ’0989’, ’1018’, ’1019’, ’1033’, ’1046’, ’1076’, ’1133’, ’1140’, ’1141’, ’1145’, ’1146’, ’1149’, ’1168’, ’1185’, ’1221’, ’1232’, ’1256’, ’1257’, ’1280’, ’1285’, ’1299’, ’1317’, ’1347’, ’1380’, ’1392’, ’1393’, ’1418’, ’1444’, ’1448’, ’1458’, ’1489’, ’1517’, ’1533’, ’1573’, ’1635’, ’1653’, ’1668’, ’1672’, ’1721’, ’1736’, ’1748’, ’1756’, ’1759’, ’1775’, ’1777’, ’1825’, ’1850’, ’1863’, ’1865’, ’1870’, ’1875’, ’1906’, ’1917’, ’1956’, ’1962’, ’1967’, ’1976’, ’2024’, ’2049’, ’2062’, ’2092’, ’2093’, ’2097’, ’2106’, ’2172’, ’2176’, ’2203’, ’2231’, ’2246’, ’2264’, ’2266’, ’2295’, ’2326’, ’2328’, ’2332’, ’2342’, ’2361’, ’2369’, ’2407’, ’2408’, ’2418’, ’2455’, ’2463’, ’2511’, ’2515’, ’2516’, ’2535’, ’2585’, ’2623’, ’2629’, ’2642’, ’2651’, ’2662’, ’2668’, ’2673’, ’2698’, ’2701’, ’2709’, ’2735’, ’2742’, ’2752’, ’2759’, ’2765’, ’2787’, ’2802’, ’2832’, ’2835’, ’2844’, ’2858’, ’2885’, ’2897’, ’2923’, ’2932’, ’2945’, ’2973’, ’2980’ | | competition | ’3017’, ’3019’, ’3054’, ’3062’, ’3063’, ’3066’, ’3070’, ’3077’, ’3083’, ’3097’, ’3117’, ’3135’, ’3161’, ’3186’, ’3209’, ’3220’, ’3286’, ’3287’, ’3323’, ’3335’, ’3353’, ’3355’, ’3371’, ’3375’, ’3376’, ’3388’, ’3404’, ’3411’, ’3433’, ’3441’, ’3445’, ’3470’, ’3481’, ’3484’, ’3548’, ’3557’, ’3605’, ’3609’, ’3634’, ’3635’, ’3671’, ’3679’, ’3709’, ’3754’, ’3769’, ’3792’, ’3798’, ’3799’, ’3804’, ’3810’, ’3819’, ’3823’, ’3836’, ’3843’, ’3849’, ’3876’, ’3913’, ’3934’, ’3972’, ’3974’ | Appendix G More Examples of Feedback from GPT-4 and our Human Participants In this appendix, we give five more examples from the study in Section 4.3, so that the keen reader may themself compare and contrast the feedback generated by GPT-4 and by our human participants. Each listing (6-10) contains a textual specification, an incorrect program, an error message, both examples of GPT-4 feedback which were shown to the participants assigned to this task, and the responses from the participants. For each piece of feedback, we also list the number of resulting repaired programs which passed all the tests (c.f. the full results table in Appendix C). Listing 6: Task 2106, Program A. ⬇ ### SPECIFICATION There are n cities in the country where the Old Peykan lives. These cities are located on a straight line, we ’ ll denote them from left to right as c_1, c_2, ..., c_ {n}. The Old Peykan wants to travel from city c_1 to c_ {n} using roads. There are (n - 1) one way roads, the i - th road goes from city c_ {i} to city c_ {i} + 1 and is d_ {i} kilometers long. The Old Peykan travels 1 kilometer in 1 hour and consumes 1 liter of fuel during this time. Each city c_ {i} (except for the last city c_ {n}) has a supply of s_ {i} liters of fuel which immediately transfers to the Old Peykan if it passes the city or stays in it. This supply refreshes instantly k hours after it transfers. The Old Peykan can stay in a city for a while and fill its fuel tank many times. Initially (at time zero) the Old Peykan is at city c_1 and s_1 liters of fuel is transferred to it ’ s empty tank from c_1 ’ s supply. The Old Peykan ’ s fuel tank capacity is unlimited. Old Peykan can not continue its travel if its tank is emptied strictly between two cities. Find the minimum time the Old Peykan needs to reach city c_ {n}. ----- Input ----- The first line of the input contains two space - separated integers m and k (1 <= m, k <= 1000). The value m specifies the number of roads between cities which is equal to n - 1. The next line contains m space - separated integers d_1, d_2, ..., d_ {m} (1 <= d_ {i} <= 1000) and the following line contains m space - separated integers s_1, s_2, ..., s_ {m} (1 <= s_ {i} <= 1000). ----- Output ----- In the only line of the output print a single integer - the minimum time required for The Old Peykan to reach city c_ {n} from city c_1. ----- Examples ----- Input 4 6 1 2 5 2 2 3 3 4 Output 10 Input 2 3 5 6 5 5 Output 14 ### INCORRECT PROGRAM def main (): m, k = map (int, input (). split ()) ds = list (map (int, input (). split ())) ss = list (map (int, input (). split ())) time = 0 fuel = ss [0] min_time = 0 max_s = ss [0] for i in range (m): fuel -= ds [i] max_s = max (max_s, ss [i]) while fuel < 0: time += k fuel += max_s time += ds [i] print (time) main () ### ERROR MESSAGE === Input === 4 6 1 2 5 2 2 3 3 4 === Program Output === 28 === Expected Output === 10 ### GPT -4 FEEDBACK #1 The issue with the code is that it does not consider the time spent in the current city before moving to the next city, resulting in an overestimation of the minimum time required. This can be fixed by updating the time spent in the current city before calculating the fuel used and accounting for the time it takes to travel to the next city. # Number of passing repairs: 7/25 ### GPT -4 FEEDBACK #2 The following is a concise explanation of the issue: The code incorrectly calculates the waiting time at each city. It should minimize the waiting time by considering the maximum fuel supply that can be collected during the waiting time. The code needs to be updated to account for this. # Number of passing repairs: 10/25 ### PARTICIPANT FEEDBACK #1 The program doesn ’ t add the fuel for passing through cities, only if it needs to actually stay in the city to refuel. Whenever it passes through a city, it should add ss [i] to the fuel. # Number of passing repairs: 10/25 ### PARTICIPANT FEEDBACK #2 The code is incorrect because it doesn ’ t take into account the fuel at each city that is immediately transferred after entering the city (aside for the fuel received at the first city). As a result, this program overestimates the time needed, because it assumes that the Old Peykan always has to wait for a refill (besides the fuel they are given in the first city). # Number of passing repairs: 0/25 Listing 7: Task 3070, Program B. ⬇ ### SPECIFICATION In the free - market, ruthlessly capitalist world of train fares, only one thing matters: incentives. Train companies are incentivised with bonuses for high throughput, successful journeys, and customer satisfaction. Conversely, the companies are disincentivised from failure via mandatory refunds for customers delayed by $30$ minutes or more. Being a ruthless capitalist yourself, you have decided to take advantage of this generous delay compensation provision. The refund is awarded provided that no matter the combination of trains you had taken (provided they followed the same route of stations as planned), you would still be unable to reach your destination in strictly less time than $30$ minutes (or $1800$ seconds), of the time you would have arrived assuming your booked journey was exactly on time. Armed with your printout of the day ’ s delays, and the original timetable, you must ask yourself only one question: what is the earliest time you can book a train for from station $1$, in order to earn this restitutive reward? ----- Input ----- - One line containing two integers: $N$ ($1 \ le N \ le 100 $), the number of stations, and $M$ ($1 \ le M \ le 10^5 $), the number of scheduled trains. - The next $M$ lines each contain 4 integers: - $X$, the starting station ($1 \ le X \ le N -1 $), - $S$ and $T$ ($0 \ le S \ le T < 86400 $), the planned departure and arrival times in seconds, - and $L$ ($0 \ le L < 86400 $), the duration by which the train ’ s departure and arrival times are delayed. Stations are numbered from $1$ to $N$ in the order you will visit them. Each train goes between stations $X$ and $X +1 $. It is possible to change between trains instantanesouly. ----- Output ----- - One line containing one integer: the start time of the earliest train journey you could book in order to earn your compensation, or impossible if no such journey is possible. ----- Examples ----- Sample Input 1: 2 3 1 1800 9000 1800 1 2000 9200 1600 1 2200 9400 1400 Sample Output 1: 1800 Sample Input 2: 2 2 1 1800 3600 1800 1 1900 3600 1600 Sample Output 2: impossible ### INCORRECT PROGRAM def main (): N, M = map (int, input (). split ()) train_data = [tuple (map (int, input (). split ())) for _ in range (M)] train_data. sort (key = lambda x: (x [0], x [1])) times = [1 e9] * (N + 1) times [1] = 0 for X, S, T, L in train_data: if times [X] <= S: times [X + 1] = min (times [X + 1], T + L) if times [N] >= 1800: print (int (times [1])) else: print (" impossible ") main () ### ERROR MESSAGE === Input === 2 3 1 1800 9000 1800 1 2000 9200 1600 1 2200 9400 1400 === Program Output === 0 === Expected Output === 1800 ### GPT -4 FEEDBACK #1 The issue with the code is that it prints ‘ times [1]‘ instead of the earliest possible train start time. The code needs to get the minimum start time from the train_data list that has a valid delay for compensation. # Number of passing repairs: 3/25 ### GPT -4 FEEDBACK #2 The issue with the code is that it directly prints the value of ‘ times [1]‘, which is initialized to ‘0‘ and never updated. The correct output should be the starting time of the earliest train journey that satisfies the condition. To fix this, we need to track the earliest possible start time and update it if a valid train journey is found. # Number of passing repairs: 0/25 ### PARTICIPANT FEEDBACK #1 This code is clearly wrong as times [1] is initialized to 0 then never updated and it is returned as the answer. Also, in the sorting line ‘ int (x [0])‘ should be used in place of ‘ x [0]‘ and likewise for ‘ int (x [1])‘ in place of ‘ x1 ‘ because we want numerical order sorting not string order sorting. The goal in this problem is calculate for each station what the earliest - arriving undelayed path to the station is and what the earliest - arriving delayed path to the station is, take the difference between the two, and see if it results in a total delay of >= 30 minutes (then to return the earliest departure from station 1 for this path. Given this, first the current code based around ‘ times ‘ can remain - this is the delayed time. However, the if - statement within the for - loop should be ‘<= S + L ‘ since the departure time is also delayed. Then ‘ undelayed_times ‘ should be tracked as well, updated in the foor loop when ‘ undelayed_times [X] <= S ‘ and set to a min () between the current undelayed time an ‘ T ‘ (not T + L). Finally the if - statement for time printing can use the difference between the delayed and undelayed times and see if any () are >= 1800. Finally we need to print the earliest arriving train for that path # Number of passing repairs: 5/25 ### PARTICIPANT FEEDBACK #2 One of the main issues is that the code prints ’ times [1]’, which is set to 0 and never updated. However, there are also some larger issues with the code. First, instead of checking if you reach your destination within 30 minutes of the expected time, it checks if you reach your destination in 30 minutes. To fix this, the program would need to keep track of the time you ’ d reach your destination if there were not delays, which it currently doesn ’ t. Second, instead of printing times [1], it should be keeping track of the start time of the train that leads to a delay and printing this. # Number of passing repairs: 0/25 Listing 8: Task 4333, Program A. ⬇ ### SPECIFICATION There is a square in the xy - plane. The coordinates of its four vertices are (x_1, y_1),(x_2, y_2),(x_3, y_3) and (x_4, y_4) in counter - clockwise order. (Assume that the positive x - axis points right, and the positive y - axis points up.) Takahashi remembers (x_1, y_1) and (x_2, y_2), but he has forgot (x_3, y_3) and (x_4, y_4). Given x_1, x_2, y_1, y_2, restore x_3, y_3, x_4, y_4. It can be shown that x_3, y_3, x_4 and y_4 uniquely exist and have integer values. ----- Constraints ----- - | x_1 |,| y_1 |,| x_2 |,| y_2 | \ leq 100 - (x_1, y_1) != (x_2, y_2) - All values in input are integers. ----- Input ----- Input is given from Standard Input in the following format: x_1 y_1 x_2 y_2 ----- Output ----- Print x_3, y_3, x_4 and y_4 as integers, in this order. ----- Sample Input ----- 0 0 0 1 ----- Sample Output ----- -1 1 -1 0 (0,0),(0,1),(-1,1),(-1,0) is the four vertices of a square in counter - clockwise order. Note that (x_3, y_3)=(1,1),(x_4, y_4)=(1,0) is not accepted, as the vertices are in clockwise order. ### INCORRECT PROGRAM x1, y1, x2, y2 = map (int, input (). split ()) x3 = x2 + (y2 - y1) y3 = y2 - (x2 - x1) x4 = x1 + (y2 - y1) y4 = y1 - (x2 - x1) print (x3, y3, x4, y4) ### ERROR MESSAGE === Input === 0 0 0 1 === Program Output === 1 1 1 0 === Expected Output === -1 1 -1 0 ### GPT -4 FEEDBACK #1 The issue with the code is that it doesn ’ t consider the counter - clockwise order of the vertices. To fix this, we need to swap the signs of (y2 - y1) and (x2 - x1) in the calculations. # Number of passing repairs: 25/25 ### GPT -4 FEEDBACK #2 The following is a concise explanation of the issue: The code above does not ensure that the vertices are in counter - clockwise order. It calculates x3, y3, x4, and y4 in the wrong order, which results in the coordinates being in clockwise order instead. To fix this, we need to swap the calculations for x3 and x4, and y3 and y4. # Number of passing repairs: 0/25 ### PARTICIPANT FEEDBACK #1 The program calculates vertices for a clockwise - oriented square, not counter - clockwise. To fix this, (y2 - y1) and (x2 - x1) should be negated in the equations. # Number of passing repairs: 25/25 ### PARTICIPANT FEEDBACK #2 The calculation for y3 and y4 incorrectly subtract the x direction vector to y0 and y1 respectively. In each of these cases, the calculation can be fixed by changing the first subtraction to addition. # Number of passing repairs: 0/25 Listing 9: Task 4347, Program B. ⬇ ### SPECIFICATION One day, $n$ people ($n$ is an even number) met on a plaza and made two round dances, each round dance consists of exactly $ \ frac {n}{2} $ people. Your task is to find the number of ways $n$ people can make two round dances if each round dance consists of exactly $ \ frac {n}{2} $ people. Each person should belong to exactly one of these two round dances. Round dance is a dance circle consisting of $1$ or more people. Two round dances are indistinguishable (equal) if one can be transformed to another by choosing the first participant. For example, round dances $ [1, 3, 4, 2] $, $ [4, 2, 1, 3] $ and $ [2, 1, 3, 4] $ are indistinguishable. For example, if $n =2 $ then the number of ways is $1$: one round dance consists of the first person and the second one of the second person. For example, if $n =4 $ then the number of ways is $3$. Possible options: one round dance - $ [1,2] $, another - $ [3,4] $; one round dance - $ [2,4] $, another - $ [3,1] $; one round dance - $ [4,1] $, another - $ [3,2] $. Your task is to find the number of ways $n$ people can make two round dances if each round dance consists of exactly $ \ frac {n}{2} $ people. ----- Input ----- The input contains one integer $n$ ($2 \ le n \ le 20 $), $n$ is an even number. ----- Output ----- Print one integer - the number of ways to make two round dances. It is guaranteed that the answer fits in the $64$ - bit integer data type. ----- Examples ----- Input 2 Output 1 Input 4 Output 3 Input 8 Output 1260 Input 20 Output 12164510040883200 ### INCORRECT PROGRAM def factorial (n): if n == 0: return 1 else: return n * factorial (n -1) n = int (input ()) ans = (factorial (n) // (n // 2)**2) // (2 * n) print (ans) ### ERROR MESSAGE === Input === 2 === Program Output === 0 === Expected Output === 1 ### GPT -4 FEEDBACK #1 The issue with the code is that it uses integer division when calculating the final answer, which may cause the result to be rounded down incorrectly. To fix this, we can use float division and then convert the result to an integer. # Number of passing repairs: 0/25 ### GPT -4 FEEDBACK #2 The following is a concise explanation of the issue: The code attempts to calculate the number of ways using integer division, which may result in a loss of precision and incorrect results. To fix the issue, change integer division to regular division, then round the result to the nearest integer using ‘ round ()‘. # Number of passing repairs: 0/25 ### PARTICIPANT FEEDBACK #1 The problem is that the formula used is incorrect. For n <= 4, n! is less than n ^3 / 2 and so this is why we see a 0. There is an erroneous additional division by n which is the true reason for the wrong answer. # Number of passing repairs: 25/25 ### PARTICIPANT FEEDBACK #2 On line 11, the program calculates a term with a correct numerator, but an incorrect denominator. It divides by (2* n), when it should just divide by 2. # Number of passing repairs: 25/25 Listing 10: Task 4855, Program A. ⬇ ### SPECIFICATION The impact factor of a scientific journal is a measure reflecting the average number of citations to articles published in science journals. For this task we are using a simplified formula for calculating the impact factor:\[ \ frac {\ text {Total count of citations received by articles published in the journal}}{\ text {Total number of articles published}} \] Rounding is always performed upwards. For example the impact factor of the " Journal for ore research and time wasting " that published $38$ articles cited $894$ times is $894 / 38 = 23.53 $ rounding up to $24$. You are the editor of one scientific journal. You know how many articles you are going to publish and the owners are pushing you to reach a specific impact factor. You are wondering how many scientists you will have to bribe to cite your articles to meet the owners demands. Since money is tight you want to bribe the minimal amount of scientists. Each bribed scientist buys you a single citation. ----- Input ----- First and only line of input will contain $2$ integers, $A$ ($1 \ leq A \ leq 100 $), the number of articles you plan to publish and $I$ ($1 \ leq I \ leq 100 $), the impact factor the owners require. ----- Output ----- The first and only line of output should contain one integer, the minimal number of scientists you need to bribe. ----- Examples ----- Sample Input 1: 38 24 Sample Output 1: 875 Sample Input 2: 1 100 Sample Output 2: 100 ### INCORRECT PROGRAM import math A, I = map (int, input (). split ()) needed_citations = math. ceil (A * (I - 0.5)) scientists_to_bribe = needed_citations - A * (I - 1) print (scientists_to_bribe) ### ERROR MESSAGE === Input === 38 24 === Program Output === 19 === Expected Output === 875 ### GPT -4 FEEDBACK #1 The following is a concise explanation of the issue: The calculation for the number of scientists to bribe is incorrect. It should be calculated by first finding the minimum number of citations needed: ‘ A * I ‘, and then subtracting the current number of citations: ‘ A * (I - 1)‘. # Number of passing repairs: 0/25 ### GPT -4 FEEDBACK #2 The following is a concise explanation of the issue: The code calculates the required number of scientists to bribe by subtracting the current number of citations from the number of needed citations. However, it incorrectly calculates the current number of citations. # Number of passing repairs: 1/25 ### PARTICIPANT FEEDBACK #1 The scientists_to_bribe variable on line 3 is unnecessary., It ’ s sufficient to just do A * (I - 1) + 1. # Number of passing repairs: 17/25 ### PARTICIPANT FEEDBACK #2 The program seems to have a conceptual misunderstanding. Specifically, the number of scientists needed to bribe is equal to the number of required citations (‘ citations_needed ‘). However, the calculation of ‘ citation_needed ‘ is also incorrect -- it implies rounding impact factor conventionally (e. g. 3.49 goes to 3, 3.51 goes to 4), whereas rounding here is a ceiling function on the impact factor. As such, the actual formula for ‘ citation_needed ‘ should be ‘ A *(I -1) + 1‘ # Number of passing repairs: 25/25