capacity_SOH ≈ 0.913 − 0.352 · tanh( cycle^((temperature/cycle)^0.485) )

I understand this fits the data, but exponents should be dimensionless, what is temperature/cycle?

What happens if you give the system not only the semi-mayor axis but also the semi-minor axis?

Have you tried with only the 6 planets Kepler know? (I don't expect this to change the result too much.)

Have you tired with noisy data?

For simple problems as Kepler's law, a quick detour on Desmos will show a perfect fit for power law instantly. In general, there are many important criteria for a better curve fitting (for ex. independent, normal distributed residuals), not just R, so I hope the author has/will incorporate them into the search to create a more robust result.

GP_ELITE is a symbolic regression engine in pure Python: given (X, y) data, it searches for a readable mathematical formula linking them, instead of a black-box model.

To show what that means concretely: I gave it nothing but the 8 planets' distance from the Sun and orbital period — 8 data points — and asked for a formula. It returned:

T = a · sqrt(a) (i.e. a^1.5), R² = 1.000000

That's Kepler's Third Law (T² ∝ a³), which took Kepler ~10 years to find in 1618. GP_ELITE found it in ~3 seconds. Reproducible: examples/kepler_demo.py.

v0.2.0 (this week) added the parts that make it reliable: Levenberg-Marquardt constant fitting (constants come back at machine precision — Coulomb's q1·q2/(4πεr²) is recovered exactly), multi-restart with a merged candidate archive, a Pareto front output (the full complexity ↔ accuracy staircase, not just one champion), and a guarded forecasting mode for extrapolating trends beyond your data without the usual GP blow-ups.

Pure Python/NumPy — pip install gp-elite, no compiler, no Julia.

Target Audience

Anyone with small experimental datasets (≤10 variables, 100–5000 points) who wants to understand a relationship, not just predict it: lab engineers, scientists, students. One concrete use case that drove development: battery degradation (SOH) forecasting — the guarded mode gives you an honest bracket of scenarios (a Pareto front from a conservative straight line to richer bounded laws) instead of one overconfident curve. Production-usable for that niche (built-in hold-out validation, regression-tested); not aimed at large-scale ML.

Comparison

vs gplearn (the established pure-Python option): I ran both on the same frozen benchmark — 15 Feynman physics equations, identical data and splits, generous budget for gplearn. Exact symbolic recovery (machine precision): GP_ELITE 10/15 (67%) vs gplearn 6/15 (40%). gplearn recovers the constant-free formulas and stalls as soon as a ½ or a 4π appears (no real constant optimization); LM fitting is what closes that gap. Every number is reproducible: PYTHONHASHSEED=0 python benchmarks/feynman_bench.py 0 15 and benchmarks/duel.py in the repo.

vs PySR / Operon (the state of the art): they are stronger on speed and scale, and I'm not claiming otherwise — but they require a Julia or C++ toolchain. GP_ELITE's whole point is zero barrier: pip install and go.

vs neural nets / gradient boosting: those win on raw accuracy for large data, but give you a black box — GP_ELITE gives you the actual equation.

Honest limits: weak on chaotic targets (tested on Collatz), degrades past ~6 variables with decoy features, and pure Python costs wall-time on big data.

Code (MIT): https://github.com/ariel95500-create/gp-elite