## 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.

## Chart Type: Scatter Plot with Fitted Curve: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview This image displays a scatter plot illustrating the relationship between the "Mean number of tokens generated" on the x-axis and the "Mean pass rate" on the y-axis. The plot includes a fitted curve with a confidence interval, representing the overall trend. Individual data points are categorized by two parameters, `n_p` (represented by color) and `n_fr` (represented by marker shape), as detailed in the legend. The chart primarily shows how different configurations of these parameters affect the pass rate and the computational cost in terms of tokens generated. ### Components/Axes The chart is structured with a main plotting area, an x-axis at the bottom, a y-axis on the left, and a legend positioned in the bottom-center-right of the plotting area. * **X-axis Label**: "Mean number of tokens generated" * **X-axis Range**: From 0 to 10000. * **X-axis Major Ticks**: 0, 2000, 4000, 6000, 8000, 10000. The tick labels are rotated approximately 45 degrees counter-clockwise. * **Y-axis Label**: "Mean pass rate" * **Y-axis Range**: From 0.0 to 1.0. * **Y-axis Major Ticks**: 0.0, 0.2, 0.4, 0.6, 0.8, 1.0. * **Legend**: Located within the plot area, spanning from approximately X=3000 to X=8000 and Y=0.05 to Y=0.35. It is divided into two columns: * **Left Column (Line styles, representing `n_p` values):** * Brown line: `n_p = 1` * Orange/Gold line: `n_p = 2` * Teal/Light Green line: `n_p = 5` * Light Blue line: `n_p = 10` * Dark Blue/Indigo line: `n_p = 25` * **Right Column (Marker shapes, representing `n_fr` values):** * Gray circle: `n_fr = 1` * Gray downward triangle: `n_fr = 3` * Gray square: `n_fr = 5` * Gray upward triangle: `n_fr = 10` ### Detailed Analysis The chart displays a dark gray fitted curve with a lighter gray shaded confidence interval, representing the overall trend. Superimposed on this curve are 20 individual data points, each colored according to its `n_p` value and shaped according to its `n_fr` value. **Fitted Curve Trend and Approximate Values:** The dark gray fitted curve shows a clear positive correlation: as the "Mean number of tokens generated" increases, the "Mean pass rate" also increases. The rate of increase is steep initially and then gradually flattens out, suggesting diminishing returns. The light gray band around the curve indicates a confidence interval. * At X ≈ 0, Y ≈ 0.40 * At X ≈ 1000, Y ≈ 0.55 * At X ≈ 2000, Y ≈ 0.60 * At X ≈ 4000, Y ≈ 0.63 * At X ≈ 6000, Y ≈ 0.65 * At X ≈ 8000, Y ≈ 0.66 **Individual Data Points (Scatter Plot):** The data points generally follow the trend of the fitted curve. Each point represents a unique combination of `n_p` and `n_fr`. * **`n_p = 1` (Brown points):** * Circle (`n_fr = 1`): (X ≈ 450, Y ≈ 0.45) * Downward Triangle (`n_fr = 3`): (X ≈ 700, Y ≈ 0.48) * Square (`n_fr = 5`): (X ≈ 1000, Y ≈ 0.51) * Upward Triangle (`n_fr = 10`): (X ≈ 1500, Y ≈ 0.53) * **`n_p = 2` (Orange/Gold points):** * Circle (`n_fr = 1`): (X ≈ 600, Y ≈ 0.50) * Downward Triangle (`n_fr = 3`): (X ≈ 1000, Y ≈ 0.53) * Square (`n_fr = 5`): (X ≈ 1500, Y ≈ 0.58) * Upward Triangle (`n_fr = 10`): (X ≈ 2000, Y ≈ 0.60) * **`n_p = 5` (Teal/Light Green points):** * Circle (`n_fr = 1`): (X ≈ 1000, Y ≈ 0.58) * Downward Triangle (`n_fr = 3`): (X ≈ 1500, Y ≈ 0.61) * Square (`n_fr = 5`): (X ≈ 2500, Y ≈ 0.65) * Upward Triangle (`n_fr = 10`): (X ≈ 3500, Y ≈ 0.62) * **`n_p = 10` (Light Blue points):** * Circle (`n_fr = 1`): (X ≈ 1500, Y ≈ 0.60) * Downward Triangle (`n_fr = 3`): (X ≈ 2500, Y ≈ 0.68) * Square (`n_fr = 5`): (X ≈ 4500, Y ≈ 0.69) * Upward Triangle (`n_fr = 10`): (X ≈ 7500, Y ≈ 0.69) * **`n_p = 25` (Dark Blue/Indigo points):** * Circle (`n_fr = 1`): (X ≈ 2000, Y ≈ 0.62) * Downward Triangle (`n_fr = 3`): (X ≈ 3000, Y ≈ 0.67) * Square (`n_fr = 5`): (X ≈ 5500, Y ≈ 0.70) * Upward Triangle (`n_fr = 10`): (X ≈ 7000, Y ≈ 0.71) ### Key Observations 1. **General Trend**: There is a clear positive correlation between the mean number of tokens generated and the mean pass rate. The pass rate increases rapidly at lower token counts and then plateaus, indicating diminishing returns for generating more tokens beyond a certain point. 2. **Effect of `n_p`**: Higher values of `n_p` (represented by colors shifting from brown to dark blue) generally correspond to higher mean pass rates for a given range of tokens generated. For instance, `n_p=25` points achieve pass rates around 0.70-0.71, while `n_p=1` points peak around 0.53. 3. **Effect of `n_fr`**: Within each `n_p` group (i.e., for points of the same color), increasing `n_fr` (represented by marker shapes from circle to upward triangle) generally leads to a higher "Mean number of tokens generated." This suggests `n_fr` directly influences the output length or computational effort. 4. **Interaction of `n_p` and `n_fr`**: For a fixed `n_p`, increasing `n_fr` tends to move the data point to the right (more tokens generated) and generally upwards (higher pass rate), following the overall curve. 5. **Outlier/Anomaly**: The teal upward triangle point (`n_p = 5`, `n_fr = 10`) is located at approximately (X ≈ 3500, Y ≈ 0.62). This point appears to have a slightly lower pass rate compared to the general trend of increasing pass rate with increasing `n_fr` for `n_p=5` (where `n_fr=5` is at Y ≈ 0.65). It also falls slightly below the fitted curve, suggesting a potential deviation from the expected performance for this specific configuration. ### Interpretation The data presented in this chart likely illustrates the performance characteristics of a system (e.g., a language model or code generation system) where `n_p` and `n_fr` are configurable parameters. * **Performance vs. Cost Trade-off**: The chart fundamentally demonstrates a trade-off. To achieve a higher "Mean pass rate" (better performance), one generally needs to increase the "Mean number of tokens generated" (higher computational cost or longer output). * **Role of `n_p`**: The parameter `n_p` appears to be a critical factor in determining the *potential maximum pass rate*. Higher `n_p` values enable the system to achieve significantly better performance, suggesting it might relate to the number of parallel attempts, diverse candidates, or overall model capacity. Increasing `n_p` shifts the performance curve upwards. * **Role of `n_fr`**: The parameter `n_fr` seems to control the *granularity or extent of generation* for each `n_p` setting. Higher `n_fr` values lead to more tokens being generated, which in turn generally contributes to a higher pass rate, but also increases the computational burden. It scales the x-axis for a given `n_p`. * **Diminishing Returns**: The flattening of the curve indicates that there's a point where further increasing the number of tokens generated yields only marginal improvements in the pass rate. This is crucial for optimizing resource allocation. * **Potential for Optimization**: The observed outlier (`n_p=5, n_fr=10`) suggests that simply increasing `n_fr` might not always lead to monotonic improvements, especially for intermediate `n_p` values. There might be an optimal `n_fr` for each `n_p` beyond which performance either plateaus or even slightly degrades due to factors like increased noise, irrelevant output, or computational overhead without corresponding quality gains. This highlights the need for careful tuning of both parameters. * **Practical Implications**: For practical deployment, one would need to balance the desired pass rate with the acceptable computational cost (tokens generated). If high pass rates are critical, higher `n_p` values are necessary. If computational efficiency is paramount, lower `n_p` and `n_fr` values might be chosen, accepting a lower pass rate.

\n ## Line Chart: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview This chart displays the relationship between the mean pass rate and the mean number of tokens generated, with different lines representing different values of *n_p* (presumably a parameter related to prompt engineering or model configuration). Data points are overlaid on the lines, differentiated by *n_fr* values. The chart aims to show how the pass rate changes as the number of tokens generated increases, for various parameter settings. ### Components/Axes * **X-axis:** Mean number of tokens generated (Scale: 0 to 10000, approximately). * **Y-axis:** Mean pass rate (Scale: 0.0 to 1.0, approximately). * **Lines:** Represent different values of *n_p*: 1, 2, 5, 10, and 25. * **Markers:** Represent different values of *n_fr*: 1, 3, 5, and 10. * **Legend (bottom-right):** Clearly identifies the color and corresponding *n_p* and *n_fr* values. ### Detailed Analysis The chart shows five lines, each representing a different *n_p* value. The data points are overlaid on these lines, each representing a different *n_fr* value. * **n_p = 1 (Brown Line):** The line starts at approximately 0.45 at 0 tokens, rises sharply to around 0.62 at 1000 tokens, and then plateaus around 0.65-0.70 for higher token counts. Data points for *n_fr* = 1 are overlaid on this line. * (0, 0.45) - *n_fr* = 1 * (1000, 0.62) - *n_fr* = 1 * (4000, 0.67) - *n_fr* = 1 * (8000, 0.70) - *n_fr* = 1 * **n_p = 2 (Orange Line):** Starts at approximately 0.5 at 0 tokens, rises to around 0.65 at 1000 tokens, and plateaus around 0.68-0.72 for higher token counts. Data points for *n_fr* = 3 are overlaid on this line. * (0, 0.5) - *n_fr* = 3 * (1000, 0.65) - *n_fr* = 3 * (4000, 0.68) - *n_fr* = 3 * (8000, 0.72) - *n_fr* = 3 * **n_p = 5 (Light Blue Line):** Starts at approximately 0.55 at 0 tokens, rises to around 0.70 at 1000 tokens, and plateaus around 0.72-0.75 for higher token counts. Data points for *n_fr* = 5 are overlaid on this line. * (0, 0.55) - *n_fr* = 5 * (1000, 0.70) - *n_fr* = 5 * (4000, 0.73) - *n_fr* = 5 * (8000, 0.75) - *n_fr* = 5 * **n_p = 10 (Cyan Line):** Starts at approximately 0.6 at 0 tokens, rises to around 0.75 at 1000 tokens, and plateaus around 0.77-0.80 for higher token counts. Data points for *n_fr* = 10 are overlaid on this line. * (0, 0.6) - *n_fr* = 10 * (1000, 0.75) - *n_fr* = 10 * (4000, 0.78) - *n_fr* = 10 * (8000, 0.80) - *n_fr* = 10 * **n_p = 25 (Purple Line):** Starts at approximately 0.65 at 0 tokens, rises to around 0.80 at 1000 tokens, and plateaus around 0.80-0.82 for higher token counts. All lines exhibit a similar trend: an initial increase in mean pass rate with increasing tokens generated, followed by a plateau. ### Key Observations * Higher values of *n_p* generally result in higher mean pass rates, especially at lower token counts. * The effect of *n_p* diminishes as the number of tokens generated increases; the lines converge at higher token counts. * The data points for different *n_fr* values closely follow the corresponding *n_p* lines, suggesting that *n_fr* has a less pronounced effect on the pass rate compared to *n_p*. * The pass rate appears to stabilize after approximately 2000-4000 tokens generated, regardless of the *n_p* value. ### Interpretation The chart suggests that the parameter *n_p* plays a significant role in determining the pass rate of a process that generates tokens. Increasing *n_p* initially improves the pass rate, but the benefit diminishes as the number of tokens generated increases. This could indicate that *n_p* influences the initial quality of the generated tokens, but its impact becomes less important as the process continues. The relatively small variation in pass rate across different *n_fr* values suggests that this parameter has a less substantial effect on the overall outcome. The convergence of the lines at higher token counts implies that there's a limit to how much the pass rate can be improved, regardless of the *n_p* setting. The plateau in pass rate after a certain number of tokens generated could be due to inherent limitations in the process or the model being used. Further investigation might be needed to understand the underlying reasons for this stabilization. The chart provides valuable insights for optimizing the parameters *n_p* and *n_fr* to achieve the desired pass rate for a given number of tokens generated.

## Scatter Plot with Trend Line: Mean Pass Rate vs. Mean Tokens Generated ### Overview This image is a scatter plot with an overlaid trend line, illustrating the relationship between the mean number of tokens generated (x-axis) and the mean pass rate (y-axis). The data is categorized by two parameters: `n_p` (represented by color) and `n_fr` (represented by marker shape). The plot suggests a logarithmic or saturating relationship where pass rate increases with token count but plateaus. ### Components/Axes * **X-Axis:** Labeled "Mean number of tokens generated". Scale ranges from 0 to 10,000 with major tick marks at 0, 2000, 4000, 6000, 8000, and 10000. * **Y-Axis:** Labeled "Mean pass rate". Scale ranges from 0.0 to 1.0 with major tick marks at 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. * **Legend (Bottom-Right Quadrant):** Contains two columns. * **Left Column (Color for `n_p`):** * Brown line: `n_p = 1` * Yellow line: `n_p = 2` * Teal line: `n_p = 5` * Light Blue line: `n_p = 10` * Dark Blue line: `n_p = 25` * **Right Column (Marker Shape for `n_fr`):** * Circle: `n_fr = 1` * Downward Triangle: `n_fr = 3` * Square: `n_fr = 5` * Upward Triangle: `n_fr = 10` * **Trend Line:** A single, thick, dark gray line runs through the data points, showing the overall trend. It starts steeply and flattens out. ### Detailed Analysis Data points are identified by matching the color (for `n_p`) and marker shape (for `n_fr`). Values are approximate based on visual inspection. **Data Series & Approximate Points (x, y):** 1. **`n_p = 1` (Brown):** * `n_fr = 1` (Circle): (~500, 0.46) * `n_fr = 3` (Down Triangle): (~800, 0.50) * `n_fr = 5` (Square): (~1200, 0.52) * `n_fr = 10` (Up Triangle): (~1800, 0.54) 2. **`n_p = 2` (Yellow):** * `n_fr = 1` (Circle): (~700, 0.53) * `n_fr = 3` (Down Triangle): (~1400, 0.58) * `n_fr = 5` (Square): (~1900, 0.60) * `n_fr = 10` (Up Triangle): (~3500, 0.62) 3. **`n_p = 5` (Teal):** * `n_fr = 1` (Circle): (~1600, 0.61) * `n_fr = 3` (Down Triangle): (~2700, 0.66) * `n_fr = 5` (Square): (~4000, 0.67) * `n_fr = 10` (Up Triangle): (~7500, 0.70) 4. **`n_p = 10` (Light Blue):** * `n_fr = 3` (Down Triangle): (~5000, 0.70) * `n_fr = 5` (Square): (~7500, 0.71) 5. **`n_p = 25` (Dark Blue):** * `n_fr = 1` (Circle): (~6500, 0.71) **Trend Line Behavior:** The gray trend line begins near (0, 0.40), rises sharply until approximately 2000 tokens (reaching ~0.60), then its slope decreases significantly, approaching a plateau near 0.66-0.67 as tokens approach 8000. ### Key Observations 1. **Positive Correlation:** For all series, the mean pass rate increases as the mean number of tokens generated increases. 2. **Diminishing Returns:** The rate of improvement slows dramatically. The most significant gains in pass rate occur within the first ~2000 tokens. Beyond ~4000 tokens, additional tokens yield very small increases in pass rate. 3. **Effect of `n_p`:** Higher values of `n_p` (warmer to cooler colors: brown -> yellow -> teal -> blue) are associated with higher pass rates for a given token count. The `n_p=25` (dark blue) point achieves the highest observed pass rate (~0.71). 4. **Effect of `n_fr`:** For a fixed `n_p`, increasing `n_fr` (different marker shapes) generally corresponds to a higher mean number of tokens generated and a slightly higher pass rate. This is most clearly seen in the `n_p=1` and `n_p=2` series. 5. **Data Sparsity:** The plot is sparse for high `n_p` values (`n_p=10, 25`) and high `n_fr` values, with only one or two data points each. ### Interpretation This chart likely visualizes the performance (pass rate) of a generative AI model or system against its output length (token count), under different configurations of two parameters, `n_p` and `n_fr`. * **Core Finding:** There is a fundamental trade-off or relationship where generating more content (tokens) is associated with a higher probability of success (pass rate), but with severe diminishing returns. The system reaches near-optimal performance after generating a few thousand tokens. * **Parameter Insights:** `n_p` appears to be a more impactful parameter for boosting the maximum achievable pass rate than `n_fr`. `n_fr` seems to control a trade-off between output length and performance within a given `n_p` setting. * **Practical Implication:** The data suggests that for this system, allocating resources to generate beyond 4000-6000 tokens provides minimal performance benefit. Optimal efficiency might be found at the "knee" of the curve, around 2000-4000 tokens. The highest performance ceiling is set by the `n_p` parameter. * **Anomaly/Note:** The single dark blue circle (`n_p=25, n_fr=1`) at (~6500, 0.71) is an outlier in terms of parameter combination but follows the general trend, confirming that even with high `n_p`, the saturating behavior holds.

## Heatmap: Mean Passage Rate ### Overview The heatmap illustrates the mean passage rate of different models as the mean number of tokens generated increases. The color intensity represents the rate, with darker shades indicating higher rates. ### Components/Axes - **X-axis**: Mean number of tokens generated - **Y-axis**: Mean passage rate - **Legend**: Different models with corresponding colors and symbols ### Detailed Analysis or ### Content Details The heatmap shows a general trend where the mean passage rate increases with the mean number of tokens generated. Each model has a distinct color and symbol, indicating different parameters (n_p and n_fr). The models are as follows: - **n_p = 1**: Dark red, filled circle - **n_p = 2**: Dark orange, filled triangle - **n_p = 5**: Dark green, filled square - **n_p = 10**: Dark blue, filled diamond - **n_p = 25**: Dark purple, filled pentagon ### Key Observations - **n_p = 1**: The model with the highest mean passage rate, especially noticeable at higher token counts. - **n_p = 2**: Shows a moderate increase in passage rate. - **n_p = 5**: Exhibits a steady increase in passage rate. - **n_p = 10**: Shows a slight increase in passage rate. - **n_p = 25**: The model with the lowest mean passage rate, especially noticeable at lower token counts. ### Interpretation The data suggests that as the mean number of tokens generated increases, the mean passage rate also increases for all models. The model with n_p = 1 consistently shows the highest passage rate, indicating it might be more efficient or better at handling larger token counts. The model with n_p = 2 shows a moderate improvement, while n_p = 5 and n_p = 10 show steady increases. The model with n_p = 25 shows the lowest passage rate, which might indicate it is less efficient or better at handling smaller token counts. This information is crucial for selecting the most appropriate model for a given task based on the expected token count.

## Line Graph: Relationship Between Token Generation and Mean Pass Rate ### Overview The image depicts a line graph with a shaded confidence interval, plotting the relationship between the mean number of tokens generated (x-axis) and the mean pass rate (y-axis). Data points in various colors and shapes represent different parameter configurations (np and nfr values). The graph shows a general upward trend in pass rate with increasing token generation, followed by a plateau. ### Components/Axes - **X-axis**: "Mean number of tokens generated" (0 to 10,000, linear scale) - **Y-axis**: "Mean pass rate" (0.0 to 1.0, linear scale) - **Legend**: Located in the bottom-right corner, mapping colors/shapes to parameters: - **np values** (number of parameters): - np=1 (red line) - np=2 (orange line) - np=5 (teal line) - np=10 (blue line) - np=25 (dark blue line) - **nfr values** (number of function rules): - nfr=1 (red circle) - nfr=3 (orange triangle) - nfr=5 (teal square) - nfr=10 (blue triangle) ### Detailed Analysis 1. **Main Line (Black)**: - Starts at ~0.4 (y-axis) when x=0. - Rises steeply to ~0.65 at x=8,000. - Plateaus at ~0.65–0.70 beyond x=8,000. - Shaded area (confidence interval) widens at lower x-values (e.g., 0.55–0.75 at x=8,000) and narrows as x increases. 2. **Data Series**: - **np=1 (Red Line)**: - Data points: (1,000, 0.45), (2,000, 0.55), (4,000, 0.60), (6,000, 0.63), (8,000, 0.65). - **np=2 (Orange Line)**: - Data points: (1,000, 0.50), (2,000, 0.58), (4,000, 0.62), (6,000, 0.65), (8,000, 0.67). - **np=5 (Teal Line)**: - Data points: (2,000, 0.60), (4,000, 0.65), (6,000, 0.68), (8,000, 0.70). - **np=10 (Blue Line)**: - Data points: (4,000, 0.65), (6,000, 0.70), (8,000, 0.72). - **np=25 (Dark Blue Line)**: - Data points: (6,000, 0.70), (8,000, 0.72). - **nfr Values**: - nfr=1 (Red Circles): (1,000, 0.45), (2,000, 0.55), (4,000, 0.60). - nfr=3 (Orange Triangles): (2,000, 0.58), (4,000, 0.62), (6,000, 0.65). - nfr=5 (Teal Squares): (4,000, 0.65), (6,000, 0.68), (8,000, 0.70). - nfr=10 (Blue Triangles): (6,000, 0.70), (8,000, 0.72). ### Key Observations - **Trend**: Pass rate increases with token generation, but the rate of improvement slows after ~8,000 tokens. - **np Impact**: Higher np values achieve higher pass rates (e.g., np=25 reaches 0.72 vs. np=1 at 0.65). - **nfr Impact**: Higher nfr values correlate with higher pass rates for the same np (e.g., nfr=10 at 0.72 vs. nfr=1 at 0.45 for np=1). - **Confidence Interval**: The shaded area suggests greater uncertainty in pass rate estimates at lower token counts. ### Interpretation The data demonstrates a clear positive correlation between token generation and mean pass rate, with diminishing returns at higher token counts. Increasing np (model complexity) and nfr (rule diversity) both improve performance, but np has a more pronounced effect. The confidence interval narrowing at higher token counts indicates more reliable estimates as data volume grows. The plateau at ~0.7 suggests a performance ceiling under the tested conditions. The overlap between np and nfr data points implies that both parameters contribute synergistically to the outcome, though np appears to dominate.