| # Math Benchmarks |
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| Mathematical optimization and algorithm evolution problems. |
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| ## Problems |
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| ### Signal processing & geometry (from SkyDiscover demos) |
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| - [signal_processing](signal_processing/) — Real-time adaptive filtering for non-stationary time series |
| - [circle_packing](circle_packing/) — Pack 26 circles in a unit square to maximize sum of radii (AlphaEvolve B.12) |
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| ### AlphaEvolve mathematical problems |
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| 12 problems from [AlphaEvolve Appendices A and B](https://storage.googleapis.com/deepmind-media/DeepMind.com/Blog/alphaevolve-a-gemini-powered-coding-agent-for-designing-advanced-algorithms/AlphaEvolve.pdf). All evaluators are normalized to **maximize** the target metric. |
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| **Appendix A:** |
| - [matmul](matmul/) — Faster algorithm for matrix multiplication (A) |
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| **Appendix B:** |
| 1. [first_autocorr_ineq](first_autocorr_ineq/) — Upper bound on autoconvolution constant (B.1) |
| 2. [second_autocorr_ineq](second_autocorr_ineq/) — Lower bound on autoconvolution norm constant (B.2) |
| 3. [third_autocorr_ineq](third_autocorr_ineq/) — Upper bound on absolute autoconvolution constant (B.3) |
| 4. [uncertainty_ineq](uncertainty_ineq/) — Upper bound on Fourier uncertainty constant (B.4) |
| 5. [erdos_min_overlap](erdos_min_overlap/) — Upper bound on Erdos minimum overlap constant (B.5) |
| 6. [sums_diffs_finite_sets](sums_diffs_finite_sets/) — Lower bound on sums/differences of finite sets (B.6) |
| 7. [hexagon_packing](hexagon_packing/) — Pack unit hexagons in a regular hexagon, n=11,12 (B.7) |
| 8. [minimizing_max_min_dist](minimizing_max_min_dist/) — Minimize max/min distance ratio, n=16 d=2 and n=14 d=3 (B.8) |
| 9. [heilbronn_triangle](heilbronn_triangle/) — Heilbronn problem for triangles, n=11 (B.9) |
| 10. [heilbronn_convex](heilbronn_convex/) — Heilbronn problem for convex regions, n=13,14 (B.10) |
| 11. [circle_packing_rect](circle_packing_rect/) — Pack circles in a rectangle of perimeter 4 (B.13) |
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| ## Run |
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| ```bash |
| uv run skydiscover-run \ |
| benchmarks/math/signal_processing/initial_program.py \ |
| benchmarks/math/signal_processing/evaluator.py \ |
| -c benchmarks/math/signal_processing/config.yaml \ |
| -s [your_algorithm] \ |
| -i 100 |
| ``` |
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| Each problem directory contains `initial_program.py`, `evaluator.py`, and either `config.yaml` or per-search configs. Some multi-variant problems have numbered subdirectories (e.g., `heilbronn_convex/13/`, `hexagon_packing/11/`). |
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