## Line Chart: AlphaEvolve Performance ### Overview The image presents two line charts comparing the performance of AlphaEvolve using different compute resources. The top chart shows performance (Best Score, where lower is better) over time in hours, while the bottom chart shows performance against total CPU-hours. Both charts include lines representing 2 CPU, 5 CPU, 10 CPU, and 20 CPU configurations, along with horizontal lines indicating the "Previous SOTA" (State of the Art) score and the "AlphaEvolve Best" score. Shaded regions around each CPU line represent the variance or uncertainty in the performance. ### Components/Axes **Top Chart:** * **Title:** AlphaEvolve Performance by Compute Resources * **X-axis:** Time Passed (Hours), ranging from 0 to 40. * **Y-axis:** Best Score (Lower is Better), ranging from 1.5000 to 1.5200. * **Legend:** Located in the top-right corner. * 2 CPU (Mean) - Brown line * 5 CPU (Mean) - Blue line * 10 CPU (Mean) - Orange line * 20 CPU (Mean) - Green line * Previous SOTA (1.5098) - Red dashed line * AlphaEvolve Best (1.5032) - Blue dotted line **Bottom Chart:** * **Title:** AlphaEvolve Performance vs. Total CPU-Hours * **X-axis:** Total CPU-Hours (Time Passed x Number of CPUs), ranging from 0 to 1000. * **Y-axis:** Best Score (Lower is Better), ranging from 1.5000 to 1.5200. * **Legend:** Located in the top-right corner, identical to the top chart. * 2 CPU (Mean) - Brown line * 5 CPU (Mean) - Blue line * 10 CPU (Mean) - Orange line * 20 CPU (Mean) - Green line * Previous SOTA (1.5098) - Red dashed line * AlphaEvolve Best (1.5032) - Blue dotted line ### Detailed Analysis **Top Chart (Performance vs. Time):** * **2 CPU (Mean) - Brown:** Starts at approximately 1.519 and decreases rapidly initially, then plateaus around 1.508 after 20 hours. * **5 CPU (Mean) - Blue:** Starts at approximately 1.518 and decreases rapidly, then plateaus around 1.507 after 20 hours. * **10 CPU (Mean) - Orange:** Starts at approximately 1.516 and decreases rapidly, then plateaus around 1.507 after 20 hours. * **20 CPU (Mean) - Green:** Starts at approximately 1.514 and decreases rapidly, then plateaus around 1.507 after 20 hours. * **Previous SOTA (1.5098) - Red Dashed:** A horizontal line at 1.5098. * **AlphaEvolve Best (1.5032) - Blue Dotted:** A horizontal line at 1.5032. **Bottom Chart (Performance vs. CPU-Hours):** * **2 CPU (Mean) - Brown:** Starts at approximately 1.519 and decreases rapidly initially, then plateaus around 1.508 after 400 CPU-Hours. * **5 CPU (Mean) - Blue:** Starts at approximately 1.518 and decreases rapidly, then plateaus around 1.507 after 400 CPU-Hours. * **10 CPU (Mean) - Orange:** Starts at approximately 1.516 and decreases rapidly, then plateaus around 1.507 after 400 CPU-Hours. * **20 CPU (Mean) - Green:** Starts at approximately 1.514 and decreases rapidly, then plateaus around 1.507 after 400 CPU-Hours. * **Previous SOTA (1.5098) - Red Dashed:** A horizontal line at 1.5098. * **AlphaEvolve Best (1.5032) - Blue Dotted:** A horizontal line at 1.5032. ### Key Observations * All CPU configurations show a rapid initial improvement in the Best Score, followed by a plateau. * Higher CPU counts (20 CPU) generally achieve slightly better initial scores. * The performance plateaus around the same Best Score (approximately 1.507) for all CPU configurations. * AlphaEvolve Best (1.5032) is significantly better than the Previous SOTA (1.5098). ### Interpretation The charts demonstrate that increasing compute resources (more CPUs) leads to a slightly better initial performance for AlphaEvolve. However, the performance improvement diminishes over time, and all configurations eventually plateau at a similar Best Score. The "AlphaEvolve Best" score indicates a significant improvement over the "Previous SOTA," suggesting that AlphaEvolve, regardless of the CPU configuration, can achieve superior results. The CPU-Hours chart suggests that there's a point of diminishing returns; after a certain number of CPU-hours, increasing the total compute doesn't significantly improve the best score.

## Line Chart: AlphaEvolve Performance ### Overview The image presents two line charts illustrating the performance of AlphaEvolve, a system or algorithm, under varying compute resource conditions. The first chart plots "Best Score" against "Time Passed (Hours)", while the second plots "Best Score" against "Total CPU-Hours". Both charts include performance comparisons against a "Previous SOTA" (State of the Art) and the "AlphaEvolve Best" score. ### Components/Axes **Chart 1: AlphaEvolve Performance by Compute Resources** * **X-axis:** Time Passed (Hours), ranging from 0 to approximately 45 hours. * **Y-axis:** Best Score (Lower is Better), ranging from 1.5000 to 1.5200. * **Legend (Top-Right):** * 2 CPU (Mean) - Orange Line * 5 CPU (Mean) - Blue Line * 10 CPU (Mean) - Light Green Line * 20 CPU (Mean) - Yellow Line * Previous SOTA (1.5098) - Black Dotted Line * AlphaEvolve Best (1.5032) - Gray Dotted Line **Chart 2: AlphaEvolve Performance vs. Total CPU-Hours** * **X-axis:** Total CPU-Hours (Time Passed x Number of CPUs), ranging from 0 to approximately 1000. * **Y-axis:** Best Score (Lower is Better), ranging from 1.5000 to 1.5200. * **Legend (Top-Right):** Identical to Chart 1. ### Detailed Analysis or Content Details **Chart 1: AlphaEvolve Performance by Compute Resources** * **2 CPU (Orange):** Starts at approximately 1.5185 and decreases to approximately 1.5060 over 45 hours. The line exhibits a steep initial decline, followed by a flattening trend. * **5 CPU (Blue):** Starts at approximately 1.5175 and decreases to approximately 1.5050 over 45 hours. Similar to the 2 CPU line, it shows a rapid initial decrease and then plateaus. * **10 CPU (Light Green):** Starts at approximately 1.5160 and decreases to approximately 1.5040 over 45 hours. The decline is less pronounced than the 2 and 5 CPU lines. * **20 CPU (Yellow):** Starts at approximately 1.5150 and decreases to approximately 1.5030 over 45 hours. This line shows the most gradual decline. * **Previous SOTA (Black Dotted):** A horizontal line at 1.5098. * **AlphaEvolve Best (Gray Dotted):** A horizontal line at 1.5032. **Chart 2: AlphaEvolve Performance vs. Total CPU-Hours** * **2 CPU (Orange):** Starts at approximately 1.5185 and decreases to approximately 1.5060 at 1000 CPU-Hours. * **5 CPU (Blue):** Starts at approximately 1.5175 and decreases to approximately 1.5050 at 1000 CPU-Hours. * **10 CPU (Light Green):** Starts at approximately 1.5160 and decreases to approximately 1.5040 at 1000 CPU-Hours. * **20 CPU (Yellow):** Starts at approximately 1.5150 and decreases to approximately 1.5030 at 1000 CPU-Hours. * **Previous SOTA (Black Dotted):** A horizontal line at 1.5098. * **AlphaEvolve Best (Gray Dotted):** A horizontal line at 1.5032. ### Key Observations * In both charts, increasing CPU resources leads to a more gradual performance improvement (less steep decline in "Best Score"). * The 2 CPU configuration shows the most significant initial improvement, but also appears to plateau earlier. * The 20 CPU configuration exhibits the slowest improvement rate, but consistently outperforms the other configurations over longer durations. * All configurations surpass the "Previous SOTA" score. * The 20 CPU configuration approaches the "AlphaEvolve Best" score. * The lines converge as time/CPU-hours increase, suggesting diminishing returns from additional compute resources. ### Interpretation These charts demonstrate the scaling behavior of the AlphaEvolve algorithm with respect to compute resources. The initial rapid improvement observed across all CPU configurations suggests that the algorithm benefits significantly from increased parallelism in the early stages of execution. However, the flattening of the curves indicates that the benefits of adding more CPUs diminish over time, likely due to factors such as communication overhead or inherent limitations in the algorithm's parallelizability. The fact that all configurations outperform the "Previous SOTA" suggests that AlphaEvolve represents a substantial advancement in the field. The convergence of the lines towards the "AlphaEvolve Best" score implies that the optimal performance is achievable with sufficient compute resources and time. The choice of CPU configuration represents a trade-off between initial speed and ultimate performance. A lower CPU count (e.g., 2) might be preferable for quick initial results, while a higher CPU count (e.g., 20) could be more suitable for achieving the best possible score over a longer period. The data suggests that the algorithm is compute-bound, meaning its performance is primarily limited by the available processing power.

## Line Charts: AlphaEvolve Performance Analysis ### Overview The image contains two vertically stacked line charts analyzing the performance of a system called "AlphaEvolve." Both charts plot the "Best Score" (where a lower value indicates better performance) against different measures of computational resource usage. The charts compare performance across four different CPU allocations (2, 5, 10, and 20 CPUs) and include two benchmark reference lines. ### Components/Axes **Common Elements (Both Charts):** * **Y-Axis:** Label: "Best Score (Lower is Better)". Scale: Linear, ranging from 1.5000 to 1.5200, with major ticks at 0.0025 intervals (1.5000, 1.5025, 1.5050, 1.5075, 1.5100, 1.5125, 1.5150, 1.5175, 1.5200). * **Legend (Top-Right of each plot):** * `2 CPU (Mean)`: Solid purple line with a light purple shaded confidence interval. * `5 CPU (Mean)`: Solid blue line with a light blue shaded confidence interval. * `10 CPU (Mean)`: Solid orange line with a light orange shaded confidence interval. * `20 CPU (Mean)`: Solid green line with a light green shaded confidence interval. * `Previous SOTA (1.5098)`: Red dashed horizontal line. * `AlphaEvolve Best (1.5032)`: Blue dotted horizontal line. * **Reference Lines:** * The red dashed "Previous SOTA" line is fixed at y = 1.5098. * The blue dotted "AlphaEvolve Best" line is fixed at y = 1.5032. **Chart 1 (Top):** * **Title:** "AlphaEvolve Performance by Compute Resources" * **X-Axis:** Label: "Time Passed (Hours)". Scale: Linear, from 0 to 40 hours, with major ticks at 0, 10, 20, 30, 40. **Chart 2 (Bottom):** * **Title:** "AlphaEvolve Performance vs. Total CPU-Hours" * **X-Axis:** Label: "Total CPU-Hours (Time Passed × Number of CPUs)". Scale: Linear, from 0 to 1000 CPU-hours, with major ticks at 0, 200, 400, 600, 800, 1000. ### Detailed Analysis **Chart 1: Performance vs. Time** * **Trend Verification:** All four CPU configuration lines show a steep downward slope (improving score) initially, which gradually flattens over time. The lines for higher CPU counts (20, 10) descend more rapidly and reach lower scores sooner than those for lower CPU counts (5, 2). * **Data Points & Relationships:** * At Time ≈ 0, all lines start near a score of 1.5200. * The **20 CPU (green)** line crosses below the "Previous SOTA" (1.5098) line at approximately 2-3 hours. It approaches and nearly converges with the "AlphaEvolve Best" (1.5032) line by the 40-hour mark, ending at an approximate score of 1.5035. * The **10 CPU (orange)** line crosses below "Previous SOTA" at around 5-6 hours. By 40 hours, it reaches an approximate score of 1.5070. * The **5 CPU (blue)** line crosses below "Previous SOTA" at around 10-12 hours. By 40 hours, it reaches an approximate score of 1.5085. * The **2 CPU (purple)** line crosses below "Previous SOTA" at around 20-22 hours. By 40 hours, it reaches an approximate score of 1.5100. * **Uncertainty (Shaded Areas):** The shaded confidence intervals are widest at the beginning (high uncertainty) and narrow significantly over time for all series. The 2 CPU series maintains the widest interval throughout. **Chart 2: Performance vs. Total CPU-Hours** * **Trend Verification:** When plotted against total computational work (CPU-hours), the performance curves for different CPU allocations become much closer together. All lines still show a downward trend, but the advantage of higher parallelism is less pronounced. * **Data Points & Relationships:** * The x-axis now represents the product of time and CPU count. * The **20 CPU (green)** line, which used the most total resources, extends to nearly 1000 CPU-hours and achieves the best final score (~1.5035). * The **10 CPU (orange)** line extends to about 500 CPU-hours (40 hrs * 10 CPUs) with a final score of ~1.5070. * The **5 CPU (blue)** line extends to about 200 CPU-hours (40 hrs * 5 CPUs) with a final score of ~1.5085. * The **2 CPU (purple)** line extends to about 80 CPU-hours (40 hrs * 2 CPUs) with a final score of ~1.5100. * All lines cross the "Previous SOTA" threshold within the first 100-150 total CPU-hours. ### Key Observations 1. **Diminishing Returns with Parallelism:** While more CPUs lead to faster wall-clock time improvement (Chart 1), the efficiency per unit of total compute decreases. Achieving the same score with 20 CPUs requires disproportionately more total CPU-hours than with fewer CPUs. 2. **Convergence to a Limit:** All configurations appear to be converging towards the "AlphaEvolve Best" score of 1.5032, but at vastly different rates. The 20 CPU setup is closest to this apparent performance limit. 3. **Reduced Variability Over Time:** The narrowing shaded regions indicate that the system's performance becomes more consistent and predictable as it runs longer, regardless of the CPU allocation. 4. **Benchmark Context:** The "Previous SOTA" (1.5098) is surpassed by all tested configurations given sufficient time, but the "AlphaEvolve Best" (1.5032) represents a significantly more challenging target that only the highest-resource setup approaches closely. ### Interpretation The data demonstrates a classic trade-off in parallel computing for optimization tasks. **AlphaEvolve** benefits significantly from increased parallel resources (more CPUs), which dramatically reduces the *time to solution*. However, this speedup comes at the cost of reduced *computational efficiency*; the total work (CPU-hours) required to reach a given performance level increases with parallelism. The charts suggest that the "Previous SOTA" benchmark of 1.5098 is relatively easy to surpass with this method, while the "AlphaEvolve Best" of 1.5032 represents a much higher barrier, likely requiring either extensive wall-clock time or a large investment in parallel resources. The narrowing confidence intervals imply the algorithm stabilizes and converges reliably. For a project manager, this data is crucial for resource allocation: choosing between a quick result with many CPUs or a more compute-efficient result with fewer CPUs over a longer period. The performance ceiling (around 1.5032) may indicate a fundamental limit of the current algorithm or problem representation.

## Line Chart: AlphaEvolve Performance by Compute Resources ### Overview The image contains two line charts comparing AlphaEvolve's performance across different CPU configurations. The top chart plots performance against time passed (hours), while the bottom chart plots performance against total CPU-hours (time × CPUs). Both charts use "Best Score (Lower is Better)" as the y-axis metric. ### Components/Axes **Top Chart (Time Passed):** - **X-axis**: Time Passed (Hours) [0, 10, 20, 30, 40] - **Y-axis**: Best Score (Lower is Better) [1.5000, 1.5005, 1.5010, 1.5015, 1.5020, 1.5025, 1.5030, 1.5035, 1.5040, 1.5045, 1.5050] - **Legend**: - 2 CPU (Mean): Purple - 5 CPU (Mean): Blue - 10 CPU (Mean): Orange - 20 CPU (Mean): Green - Previous SOTA (1.5098): Red dashed - AlphaEvolve Best (1.5032): Gray dotted **Bottom Chart (Total CPU-Hours):** - **X-axis**: Total CPU-Hours (Time Passed × Number of CPUs) [0, 200, 400, 600, 800] - **Y-axis**: Best Score (Lower is Better) [1.5000, 1.5005, 1.5010, 1.5015, 1.5020, 1.5025, 1.5030, 1.5035, 1.5040, 1.5045, 1.5050] - **Legend**: Same as top chart ### Detailed Analysis **Top Chart Trends:** 1. **2 CPU (Purple)**: Starts at ~1.5045, decreases sharply to ~1.5015 by 10 hours, then plateaus. 2. **5 CPU (Blue)**: Begins at ~1.5035, drops to ~1.5010 by 10 hours, stabilizes. 3. **10 CPU (Orange)**: Starts at ~1.5025, falls to ~1.5008 by 10 hours, remains flat. 4. **20 CPU (Green)**: Begins at ~1.5020, decreases to ~1.5005 by 10 hours, maintains lowest score. 5. **Previous SOTA (Red dashed)**: Horizontal line at ~1.5098. 6. **AlphaEvolve Best (Gray dotted)**: Horizontal line at ~1.5032. **Bottom Chart Trends:** 1. **2 CPU (Purple)**: Starts at ~1.5045, drops to ~1.5015 at 200 CPU-hours, then plateaus. 2. **5 CPU (Blue)**: Begins at ~1.5035, falls to ~1.5010 at 200 CPU-hours, stabilizes. 3. **10 CPU (Orange)**: Starts at ~1.5025, decreases to ~1.5008 at 200 CPU-hours, remains flat. 4. **20 CPU (Green)**: Begins at ~1.5020, drops to ~1.5005 at 200 CPU-hours, maintains lowest score. 5. **Previous SOTA (Red dashed)**: Horizontal line at ~1.5098. 6. **AlphaEvolve Best (Gray dotted)**: Horizontal line at ~1.5032. ### Key Observations 1. **Performance Scaling**: Higher CPU configurations (20 CPU) achieve better scores faster than lower configurations. 2. **Confidence Intervals**: Shaded regions (95% CI) narrow significantly after ~10 hours/time or 200 CPU-hours, indicating stabilized performance estimates. 3. **AlphaEvolve Advantage**: The gray dotted line (1.5032) is consistently below the red dashed line (1.5098), demonstrating superior performance over previous SOTA. 4. **Diminishing Returns**: Performance improvements plateau after ~10 hours/time or 200 CPU-hours for all configurations. ### Interpretation The data demonstrates that AlphaEvolve's performance improves with increased compute resources, with 20 CPU configurations achieving the best scores. The convergence of all CPU lines toward the AlphaEvolve Best line (1.5032) suggests that resource allocation directly impacts optimization quality. The narrowing confidence intervals over time/CPU-hours indicate that early performance estimates are less reliable, but stabilize with prolonged computation. Notably, AlphaEvolve outperforms the Previous SOTA (1.5098) by ~0.0066 in best score, representing a statistically significant improvement. The charts imply that while more CPUs yield better results, the marginal gains diminish after a certain threshold (200 CPU-hours), suggesting potential cost-efficiency tradeoffs for practitioners.