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  Precomputed model outputs for evaluation.
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  ## Evaluation Results
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  ### Summary
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  | Metric | AIME24 | AMC23 | MATH500 | AIME25 | GPQADiamond | MMLUPro | LiveCodeBench | CodeElo | JEEBench |
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  |--------|------|-----|-------|------|-----------|-------|-------------|-------|--------|
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- | Accuracy | 28.7 | 43.2 | 88.6 | 16.7 | 44.8 | 31.0 | 53.8 | 22.6 | 64.8 |
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  ### AIME24
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- - **Average Accuracy**: 28.67% ± 9.14%
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  - **Number of Runs**: 10
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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  | 1 | 66.67% | 20 | 30 |
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- | 2 | 50.00% | 15 | 30 |
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- | 3 | 56.67% | 17 | 30 |
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- | 4 | 56.67% | 17 | 30 |
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  | 5 | 56.67% | 17 | 30 |
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- | 6 | 0.00% | 0 | 30 |
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- | 7 | 0.00% | 0 | 30 |
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- | 8 | 0.00% | 0 | 30 |
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- | 9 | 0.00% | 0 | 30 |
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- | 10 | 0.00% | 0 | 30 |
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  ### AMC23
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- - **Average Accuracy**: 43.25% ± 13.69%
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  - **Number of Runs**: 10
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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- | 1 | 87.50% | 35 | 40 |
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- | 2 | 85.00% | 34 | 40 |
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- | 3 | 82.50% | 33 | 40 |
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  | 4 | 87.50% | 35 | 40 |
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  | 5 | 90.00% | 36 | 40 |
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- | 6 | 0.00% | 0 | 40 |
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- | 7 | 0.00% | 0 | 40 |
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- | 8 | 0.00% | 0 | 40 |
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- | 9 | 0.00% | 0 | 40 |
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- | 10 | 0.00% | 0 | 40 |
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  ### MATH500
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- - **Accuracy**: 88.60%
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  | Accuracy | Questions Solved | Total Questions |
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  |----------|-----------------|----------------|
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- | 88.60% | 443 | 500 |
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  ### AIME25
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- - **Average Accuracy**: 16.67% ± 5.29%
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  - **Number of Runs**: 10
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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- | 1 | 36.67% | 11 | 30 |
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  | 2 | 30.00% | 9 | 30 |
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  | 3 | 33.33% | 10 | 30 |
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  | 4 | 33.33% | 10 | 30 |
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  | 5 | 33.33% | 10 | 30 |
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- | 6 | 0.00% | 0 | 30 |
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- | 7 | 0.00% | 0 | 30 |
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- | 8 | 0.00% | 0 | 30 |
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- | 9 | 0.00% | 0 | 30 |
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- | 10 | 0.00% | 0 | 30 |
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  ### GPQADiamond
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- - **Average Accuracy**: 44.78% ± 0.77%
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  - **Number of Runs**: 3
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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- | 1 | 42.93% | 85 | 198 |
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- | 2 | 45.96% | 91 | 198 |
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- | 3 | 45.45% | 90 | 198 |
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  ### MMLUPro
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- - **Average Accuracy**: 31.00% ± 0.00%
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  - **Number of Runs**: 1
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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- | 1 | 31.00% | 155 | 500 |
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  ### LiveCodeBench
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- - **Average Accuracy**: 53.75% ± 0.62%
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  - **Number of Runs**: 3
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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- | 1 | 53.82% | 275 | 511 |
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- | 2 | 52.64% | 269 | 511 |
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- | 3 | 54.79% | 280 | 511 |
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  ### CodeElo
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- - **Average Accuracy**: 22.59% ± 1.01%
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  - **Number of Runs**: 3
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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- | 1 | 21.99% | 86 | 391 |
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- | 2 | 24.55% | 96 | 391 |
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- | 3 | 21.23% | 83 | 391 |
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  ### JEEBench
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- - **Average Accuracy**: 64.79% ± 0.81%
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  - **Number of Runs**: 3
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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- | 1 | 66.02% | 340.0 | 515 |
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- | 2 | 62.82% | 323.5 | 515 |
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- | 3 | 65.53% | 337.5 | 515 |
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  Precomputed model outputs for evaluation.
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+
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  ## Evaluation Results
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  ### Summary
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  | Metric | AIME24 | AMC23 | MATH500 | AIME25 | GPQADiamond | MMLUPro | LiveCodeBench | CodeElo | JEEBench |
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  |--------|------|-----|-------|------|-----------|-------|-------------|-------|--------|
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+ | Accuracy | 58.0 | 87.2 | 88.0 | 35.3 | 47.5 | 31.6 | 55.6 | 24.2 | 66.1 |
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  ### AIME24
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+ - **Average Accuracy**: 58.00% ± 1.43%
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  - **Number of Runs**: 10
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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  | 1 | 66.67% | 20 | 30 |
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+ | 2 | 56.67% | 17 | 30 |
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+ | 3 | 53.33% | 16 | 30 |
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+ | 4 | 53.33% | 16 | 30 |
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  | 5 | 56.67% | 17 | 30 |
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+ | 6 | 56.67% | 17 | 30 |
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+ | 7 | 63.33% | 19 | 30 |
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+ | 8 | 56.67% | 17 | 30 |
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+ | 9 | 63.33% | 19 | 30 |
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+ | 10 | 53.33% | 16 | 30 |
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  ### AMC23
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+ - **Average Accuracy**: 87.25% ± 0.90%
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  - **Number of Runs**: 10
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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+ | 1 | 90.00% | 36 | 40 |
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+ | 2 | 87.50% | 35 | 40 |
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+ | 3 | 87.50% | 35 | 40 |
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  | 4 | 87.50% | 35 | 40 |
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  | 5 | 90.00% | 36 | 40 |
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+ | 6 | 85.00% | 34 | 40 |
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+ | 7 | 90.00% | 36 | 40 |
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+ | 8 | 80.00% | 32 | 40 |
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+ | 9 | 87.50% | 35 | 40 |
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+ | 10 | 87.50% | 35 | 40 |
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  ### MATH500
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+ - **Accuracy**: 88.00%
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  | Accuracy | Questions Solved | Total Questions |
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  |----------|-----------------|----------------|
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+ | 88.00% | 440 | 500 |
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  ### AIME25
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+ - **Average Accuracy**: 35.33% ± 2.22%
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  - **Number of Runs**: 10
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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+ | 1 | 40.00% | 12 | 30 |
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  | 2 | 30.00% | 9 | 30 |
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  | 3 | 33.33% | 10 | 30 |
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  | 4 | 33.33% | 10 | 30 |
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  | 5 | 33.33% | 10 | 30 |
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+ | 6 | 26.67% | 8 | 30 |
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+ | 7 | 36.67% | 11 | 30 |
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+ | 8 | 36.67% | 11 | 30 |
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+ | 9 | 53.33% | 16 | 30 |
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+ | 10 | 30.00% | 9 | 30 |
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  ### GPQADiamond
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+ - **Average Accuracy**: 47.47% ± 1.04%
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  - **Number of Runs**: 3
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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+ | 1 | 48.99% | 97 | 198 |
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+ | 2 | 48.48% | 96 | 198 |
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+ | 3 | 44.95% | 89 | 198 |
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  ### MMLUPro
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+ - **Average Accuracy**: 31.60% ± 0.00%
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  - **Number of Runs**: 1
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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+ | 1 | 31.60% | 158 | 500 |
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  ### LiveCodeBench
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+ - **Average Accuracy**: 55.58% ± 0.81%
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  - **Number of Runs**: 3
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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+ | 1 | 57.14% | 292 | 511 |
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+ | 2 | 54.40% | 278 | 511 |
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+ | 3 | 55.19% | 282 | 511 |
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  ### CodeElo
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+ - **Average Accuracy**: 24.21% ± 0.96%
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  - **Number of Runs**: 3
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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+ | 1 | 22.51% | 88 | 391 |
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+ | 2 | 24.30% | 95 | 391 |
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+ | 3 | 25.83% | 101 | 391 |
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  ### JEEBench
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+ - **Average Accuracy**: 66.13% ± 0.40%
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  - **Number of Runs**: 3
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  | Run | Accuracy | Questions Solved | Total Questions |
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  |-----|----------|-----------------|----------------|
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+ | 1 | 65.24% | 336.0 | 515 |
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+ | 2 | 66.21% | 341.0 | 515 |
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+ | 3 | 66.94% | 344.75 | 515 |
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