# Technical Document Extraction: Success Rate Analysis ## 1. Component Isolation * **Header:** Contains the figure title "(a) Success rate with nodes visited". * **Main Chart:** A line graph plotted on a Cartesian coordinate system with a white background and a light gray grid. * **Legend:** Located in the bottom-right quadrant of the chart area. * **Axes:** * **X-axis:** Numerical scale representing "nodes visited" (implied by title). * **Y-axis:** Numerical scale representing "Success rate" (implied by title). --- ## 2. Metadata and Axis Information * **Title:** (a) Success rate with nodes visited * **X-axis Markers:** 0, 25, 50, 75, 100 * **Y-axis Markers:** 0.2, 0.4, 0.6 * **Grid:** Major grid lines are present for both X and Y axes at the intervals specified by the markers. --- ## 3. Legend and Data Series Identification The legend is positioned at approximately `[x=0.65, y=0.25]` relative to the chart area. | Series Label | Line Color | Line Style | Visual Trend Description | | :--- | :--- | :--- | :--- | | **IO (best of k)** | Blue | Solid | Logarithmic growth; starts highest at very low x-values but is overtaken by CoT quickly. Slopes upward with decreasing marginal gains. | | **CoT (best of k)** | Orange | Solid | Logarithmic growth; starts lower than IO but crosses it early (approx. x=5) and maintains a higher success rate throughout. | | **ToT (b=1...5)** | Green | Dashed | Steep upward slope; starts at a much higher x-value (approx. 20) and significantly outperforms both IO and CoT for the same number of nodes. | --- ## 4. Data Point Extraction and Analysis ### Series 1: IO (best of k) [Solid Blue Line] * **Trend:** Steady, slow increase. * **Approximate Values:** * x=1: ~0.08 * x=25: ~0.22 * x=50: ~0.27 * x=75: ~0.30 * x=100: ~0.33 ### Series 2: CoT (best of k) [Solid Orange Line] * **Trend:** Moderate increase, consistently higher than IO after the initial start. * **Approximate Values:** * x=1: ~0.05 * x=5: ~0.15 (Crosses IO line here) * x=25: ~0.32 * x=50: ~0.41 * x=75: ~0.46 * x=100: ~0.49 ### Series 3: ToT (b=1...5) [Dashed Green Line] * **Trend:** Rapid increase. This series begins at a higher "nodes visited" threshold (approx. 20 nodes). * **Approximate Values:** * x=20: ~0.45 (Starting point) * x=30: ~0.57 * x=45: ~0.66 * x=65: ~0.74 (Ending point) --- ## 5. Summary of Findings The chart compares three methods—**IO (Input-Output)**, **CoT (Chain of Thought)**, and **ToT (Tree of Thoughts)**—based on their success rate relative to the number of nodes visited. 1. **Efficiency:** **ToT (Tree of Thoughts)** is the most efficient method. Even though it requires a minimum of approximately 20 nodes to start, its success rate at 20 nodes (~0.45) is already higher than the success rate of **IO** at 100 nodes (~0.33) and nearly equal to **CoT** at 75 nodes. 2. **Comparison of IO vs. CoT:** While **IO** starts with a slightly higher success rate at a single node, **CoT** scales much better as more nodes (k) are visited, surpassing IO very early in the process. 3. **Performance Ceiling:** Within the observed range, **ToT** reaches a success rate of nearly 0.75 by 65 nodes, whereas **CoT** and **IO** remain below 0.50 even at 100 nodes.

# Technical Document Extraction: Success Rate with Nodes Visited ## Chart Title - **(a) Success rate with nodes visited** ## Axes - **X-axis (Horizontal):** - Label: `nodes visited` - Range: `0` to `100` - Increment: `25` (markers at 0, 25, 50, 75, 100) - **Y-axis (Vertical):** - Label: `Success rate` - Range: `0` to `0.6` - Increment: `0.2` (markers at 0, 0.2, 0.4, 0.6) ## Legend - **Location:** Bottom-right corner - **Entries:** 1. **Blue solid line:** `IO (best of k)` 2. **Orange solid line:** `CoT (best of k)` 3. **Green dashed line:** `ToT (b=1...5)` ## Key Trends 1. **IO (best of k):** - Starts at `(0, 0.1)` and increases steadily. - Reaches `(100, 0.35)`. - Slope: Gradual upward curve. 2. **CoT (best of k):** - Starts at `(0, 0)` and rises sharply initially. - Reaches `(100, 0.5)`. - Slope: Steeper than IO, plateaus near `x=75`. 3. **ToT (b=1...5):** - Starts at `(25, 0.45)` (no data before `x=25`). - Peaks at `(75, 0.7)`. - Slope: Sharp rise followed by a plateau. ## Data Points | Line | Key Points (x, y) | |------------|---------------------------------------| | IO | (0, 0.1), (25, 0.2), (50, 0.3), (75, 0.33), (100, 0.35) | | CoT | (0, 0), (25, 0.35), (50, 0.4), (75, 0.45), (100, 0.5) | | ToT | (25, 0.45), (50, 0.6), (75, 0.7), (100, 0.7) | ## Observations - **IO vs. CoT:** CoT outperforms IO across all node counts, with a larger gap at higher values (e.g., `x=100`). - **ToT Anomaly:** ToT begins at `x=25` and exceeds both IO and CoT at `x=75`, but plateaus at `x=100`. - **Legend Consistency:** Colors and labels in the legend match the lines in the graph without discrepancies. ## Notes - The graph compares three strategies (`IO`, `CoT`, `ToT`) for success rate as a function of nodes visited. - `ToT` uses a parameter range `b=1...5`, while `IO` and `CoT` use a "best of k" approach. - No data is plotted for `ToT` before `x=25`, suggesting initialization or threshold constraints.