## Scatter Plot: Response Time vs. Problem Size ### Overview The image is a scatter plot comparing the response time (in seconds) against the problem size for the 'gemini-2.0-flash-thinking-exp-01-21' experiment. The plot distinguishes between successful and failed attempts, with successful attempts marked in blue and failed attempts in orange. ### Components/Axes * **X-axis:** Problem Size, ranging from 0 to 400. Axis markers are present at 0, 100, 200, 300, and 400. * **Y-axis:** Response Time (s), ranging from 0 to 150. Axis markers are present at 0, 25, 50, 75, 100, 125, and 150. * **Legend:** Located in the bottom-right corner. * Blue circles: 'gemini-2.0-flash-thinking-exp-01-21 (Successful)' * Orange squares: 'gemini-2.0-flash-thinking-exp-01-21 (Failed)' ### Detailed Analysis * **Successful Attempts (Blue):** * All successful attempts are clustered at the lower left of the graph, with problem sizes between 0 and approximately 50. * Response times for successful attempts range from approximately 5 seconds to 40 seconds. * Trend: Successful attempts are concentrated at smaller problem sizes and lower response times. * Specific Data Points: * (Problem Size ~10, Response Time ~10) * (Problem Size ~10, Response Time ~15) * (Problem Size ~10, Response Time ~20) * (Problem Size ~20, Response Time ~10) * (Problem Size ~20, Response Time ~25) * (Problem Size ~30, Response Time ~35) * (Problem Size ~50, Response Time ~40) * **Failed Attempts (Orange):** * Failed attempts are scattered across the plot, with problem sizes ranging from approximately 10 to 400. * Response times for failed attempts range from approximately 10 seconds to 155 seconds. * Trend: Failed attempts are more prevalent at larger problem sizes and higher response times, but are present across the entire problem size range. * Specific Data Points: * (Problem Size ~10, Response Time ~10) * (Problem Size ~20, Response Time ~10) * (Problem Size ~20, Response Time ~15) * (Problem Size ~20, Response Time ~20) * (Problem Size ~30, Response Time ~60) * (Problem Size ~40, Response Time ~80) * (Problem Size ~50, Response Time ~90) * (Problem Size ~60, Response Time ~60) * (Problem Size ~70, Response Time ~90) * (Problem Size ~80, Response Time ~75) * (Problem Size ~90, Response Time ~90) * (Problem Size ~100, Response Time ~75) * (Problem Size ~110, Response Time ~45) * (Problem Size ~120, Response Time ~75) * (Problem Size ~130, Response Time ~75) * (Problem Size ~140, Response Time ~155) * (Problem Size ~150, Response Time ~75) * (Problem Size ~160, Response Time ~75) * (Problem Size ~170, Response Time ~75) * (Problem Size ~180, Response Time ~75) * (Problem Size ~190, Response Time ~75) * (Problem Size ~200, Response Time ~100) * (Problem Size ~210, Response Time ~110) * (Problem Size ~220, Response Time ~75) * (Problem Size ~230, Response Time ~130) * (Problem Size ~240, Response Time ~75) * (Problem Size ~250, Response Time ~75) * (Problem Size ~260, Response Time ~75) * (Problem Size ~270, Response Time ~75) * (Problem Size ~280, Response Time ~75) * (Problem Size ~290, Response Time ~75) * (Problem Size ~300, Response Time ~75) * (Problem Size ~310, Response Time ~75) * (Problem Size ~320, Response Time ~75) * (Problem Size ~330, Response Time ~75) * (Problem Size ~340, Response Time ~75) * (Problem Size ~350, Response Time ~75) * (Problem Size ~360, Response Time ~75) * (Problem Size ~370, Response Time ~75) * (Problem Size ~380, Response Time ~75) * (Problem Size ~390, Response Time ~100) * (Problem Size ~400, Response Time ~30) ### Key Observations * Successful attempts are limited to smaller problem sizes. * Failed attempts occur across a wide range of problem sizes and response times. * There is a clear separation between successful and failed attempts based on problem size. ### Interpretation The data suggests that the 'gemini-2.0-flash-thinking-exp-01-21' experiment is only successful for smaller problem sizes. As the problem size increases, the experiment is more likely to fail, and the response time tends to be higher. This could indicate a limitation in the algorithm's ability to handle larger, more complex problems within a reasonable time frame. The clustering of successful attempts at low problem sizes and response times indicates a region of efficiency for the algorithm. The scattering of failed attempts suggests that factors beyond just problem size may contribute to failures, as some failures occur even at smaller problem sizes, albeit with longer response times.

\n ## Scatter Plot: Response Time vs. Problem Size for Gemini 2.0 Flash Thinking Experiments ### Overview This scatter plot visualizes the relationship between Problem Size and Response Time for two sets of experiments: successful and failed runs of "gemini-2.0-flash-thinking-exp-01-21". The plot displays individual data points representing each experiment's outcome, with color-coding used to distinguish between successful and failed attempts. ### Components/Axes * **X-axis:** Problem Size (ranging from approximately 0 to 400). * **Y-axis:** Response Time (s) (ranging from approximately 0 to 160 seconds). * **Legend:** Located in the bottom-left corner. * Blue circles: "gemini-2.0-flash-thinking-exp-01-21 (Successful)" * Orange squares: "gemini-2.0-flash-thinking-exp-01-21 (Failed)" * **Gridlines:** Light gray horizontal and vertical lines provide a visual reference for data point positioning. ### Detailed Analysis The plot shows a distribution of data points for both successful and failed experiments. **Successful Runs (Blue Circles):** The successful runs exhibit a clear trend: as Problem Size increases, Response Time generally increases, but with significant variability. * At Problem Size ≈ 0, Response Time ranges from approximately 10s to 30s. * At Problem Size ≈ 50, Response Time ranges from approximately 20s to 60s. * At Problem Size ≈ 100, Response Time ranges from approximately 30s to 50s. * At Problem Size ≈ 200, Response Time ranges from approximately 30s to 60s. * At Problem Size ≈ 300, Response Time ranges from approximately 30s to 50s. * At Problem Size ≈ 400, Response Time ranges from approximately 20s to 40s. **Failed Runs (Orange Squares):** The failed runs also show a general trend of increasing Response Time with increasing Problem Size, but with a wider range of values and a tendency towards longer response times compared to successful runs. * At Problem Size ≈ 0, Response Time ranges from approximately 10s to 30s. * At Problem Size ≈ 50, Response Time ranges from approximately 40s to 120s. * At Problem Size ≈ 100, Response Time ranges from approximately 50s to 150s. * At Problem Size ≈ 200, Response Time ranges from approximately 60s to 120s. * At Problem Size ≈ 300, Response Time ranges from approximately 50s to 130s. * At Problem Size ≈ 400, Response Time ranges from approximately 80s to 120s. ### Key Observations * **Response Time Distribution:** Failed runs generally have higher response times than successful runs for the same problem size. * **Variability:** There is significant variability in response times for both successful and failed runs, suggesting other factors influence performance. * **Outliers:** Several failed runs exhibit exceptionally long response times (e.g., around Problem Size 100, Response Time ≈ 150s). * **Overlap:** There is overlap in response times between successful and failed runs, particularly at smaller problem sizes. ### Interpretation The data suggests that as the problem size increases, the response time for the Gemini 2.0 flash thinking experiments also tends to increase. However, the success or failure of the experiment is strongly correlated with the response time; failed runs consistently exhibit longer response times. This could indicate that exceeding a certain response time threshold leads to experiment failure. The variability in response times suggests that factors beyond problem size influence performance, such as the specific characteristics of the problem instance or the system's current load. The outliers in the failed run data may represent particularly challenging problem instances or instances where the system encountered unexpected issues. The overlap in response times between successful and failed runs at smaller problem sizes suggests that the system can handle smaller problems relatively efficiently, but its performance degrades as the problem size increases. Further investigation is needed to understand the underlying causes of the variability and the factors that contribute to experiment failure.

\n ## Scatter Plot: Response Time vs. Problem Size for gemini-2.0-flash-thinking-exp-01-21 ### Overview This is a scatter plot comparing the response time (in seconds) against problem size for two outcome categories of a model named "gemini-2.0-flash-thinking-exp-01-21". The plot visualizes the performance distribution for successful versus failed attempts. ### Components/Axes * **Chart Type:** Scatter Plot. * **X-Axis:** Labeled "Problem Size". The scale runs from 0 to 400, with major tick marks at 0, 100, 200, 300, and 400. * **Y-Axis:** Labeled "Response Time (s)". The scale runs from 0 to 150, with major tick marks at 0, 25, 50, 75, 100, 125, and 150. * **Legend:** Located in the bottom-left quadrant of the plot area. It contains two entries: 1. A blue circle symbol labeled `gemini-2.0-flash-thinking-exp-01-21 (Successful)`. 2. An orange square symbol labeled `gemini-2.0-flash-thinking-exp-01-21 (Failed)`. ### Detailed Analysis **Data Series 1: Successful Attempts (Blue Circles)** * **Trend Verification:** The data points form a tight cluster with a slight upward trend, confined to the lower-left corner of the plot. * **Spatial Grounding & Data Points:** All blue circle points are located at very low problem sizes and low response times. * **Problem Size Range:** Approximately 10 to 40. * **Response Time Range:** Approximately 10 to 40 seconds. * **Cluster Density:** The points are densely packed, with many overlapping, indicating consistent performance within this narrow band. The highest response time for a successful attempt appears to be just below 40 seconds. **Data Series 2: Failed Attempts (Orange Squares)** * **Trend Verification:** The data points are widely scattered across the entire plot area with no single, clear linear trend. There is a broad distribution. * **Spatial Grounding & Data Points:** Orange square points are found across the full range of problem sizes and a wide range of response times. * **Problem Size Range:** Spans from approximately 10 to 400. * **Response Time Range:** Spans from approximately 10 to just over 150 seconds. * **Distribution:** There is a high density of points between problem sizes 20-150 and response times 50-110s. Points become more sparse but remain present at higher problem sizes (200-400). Several outliers exist with very high response times (e.g., ~150s at problem size ~80 and ~120). ### Key Observations 1. **Clear Separation:** There is a stark visual separation between the two outcome clusters. Successful attempts are exclusively confined to a small region of low problem size and low response time. 2. **Performance Threshold:** No successful attempts are visible for problem sizes greater than approximately 40. This suggests a potential performance or capability threshold for the model in this test. 3. **High Variability in Failures:** Failed attempts show enormous variability in both problem size and response time. A failure can occur quickly on a small problem or take a very long time on a large problem. 4. **Overlap at Low End:** At the very lowest problem sizes (~10-20) and response times (~10-20s), there is some overlap between the blue and orange markers, indicating that both successes and failures can occur under similar, minimal conditions. ### Interpretation The data suggests a strong correlation between problem complexity (size) and the model's ability to succeed. The model "gemini-2.0-flash-thinking-exp-01-21" appears to reliably succeed only on a narrow band of small, simple problems, completing them quickly (under 40 seconds). Once the problem size exceeds a certain threshold (around 40), the model consistently fails, regardless of the time taken. The wide scatter of failed attempts indicates that failure mode is not predictable by problem size alone; some large problems fail quickly, while others take the maximum observed time. This pattern could indicate a fundamental limitation in the model's reasoning capacity or resource allocation for complex tasks, where it either solves the problem efficiently or enters a prolonged, unsuccessful processing state. The lack of any successful attempts in the mid-to-high problem size range is the most critical finding, pointing to a clear boundary in the model's effective operational domain for this specific task.

## Scatter Plot: Response Time vs Problem Size for Gemini-2.0-Flash-Thinking Experiments ### Overview The image is a scatter plot comparing response times (in seconds) to problem sizes for two experimental conditions: "Successful" and "Failed" outcomes from the Gemini-2.0-flash-thinking-exp-01-21 experiment. The plot uses distinct markers (blue circles for successful, orange squares for failed) to differentiate outcomes. ### Components/Axes - **X-axis (Problem Size)**: Ranges from 0 to 400 in increments of 100. - **Y-axis (Response Time (s))**: Ranges from 0 to 150 in increments of 25. - **Legend**: Located in the bottom-left corner, with: - **Blue circles**: "gemini-2.0-flash-thinking-exp-01-21 (Successful)" - **Orange squares**: "gemini-2.0-flash-thinking-exp-01-21 (Failed)" - **Gridlines**: Light gray horizontal and vertical lines for reference. ### Detailed Analysis 1. **Successful Cases (Blue Circles)**: - **Distribution**: Clustered tightly in the lower-left quadrant. - **Response Time**: Approximately 10–30 seconds. - **Problem Size**: Mostly ≤50, with a few outliers up to ~75. - **Trend**: Response time increases slightly with problem size but remains low overall. 2. **Failed Cases (Orange Squares)**: - **Distribution**: Spread across the entire plot, with higher density in the upper-right quadrant. - **Response Time**: Ranges from ~50 to 150 seconds. - **Problem Size**: Extends up to 400, with a notable concentration between 200–400. - **Trend**: Response time increases significantly with problem size, especially beyond 200. 3. **Outliers**: - A single successful case (blue circle) at problem size ~100 and response time ~25 seconds. - A failed case (orange square) at problem size ~350 and response time ~150 seconds (highest observed). ### Key Observations - **Problem Size vs. Response Time**: Both successful and failed cases show a positive correlation between problem size and response time, but the relationship is much stronger for failed cases. - **Success Threshold**: Successful outcomes are predominantly associated with problem sizes ≤75, while failures dominate at larger sizes. - **Response Time Variability**: Failed cases exhibit greater variability in response times, with some instances exceeding 125 seconds. ### Interpretation The data suggests that problem size is a critical factor in determining the success of the Gemini-2.0-flash-thinking-exp-01-21 experiment. Successful outcomes are consistently achieved for smaller problem sizes (≤75), with response times remaining efficient (10–30 seconds). As problem size increases beyond 75, the likelihood of failure rises sharply, accompanied by a proportional increase in response time. This implies potential limitations in the model's ability to handle larger inputs efficiently, possibly due to computational constraints or algorithmic complexity. The failed cases at the highest problem sizes (300–400) with response times near 150 seconds may indicate timeouts or resource exhaustion, highlighting a need for optimization or scaling strategies for larger-scale applications.