I am interested in training a genetic algorithm to find polynomial solutions to arbitrary input data. But when I tried this several years ago, the discovered polynomial solution was inevitably way more verbose than necessary; attempting to discover Newton's law of gravitation (F=Gmm/rr) for example led to an equation that had 20-30 characters in both the numerator and denominator.
So I am looking for an algorithm or method or transform for simplifying an overly verbose polynomial into something that is notationally simpler yet similarly valued. I realize that such a simplification algorithm doesn't know anything about the input domain and thus cannot judge correctness per se, but it seems like there must be such simplification approaches out there.
Have you tried calculating splines instead of polynomials? There are many different types of spline interpolations, you'd have to see which one suits you best. But in any case you'll be left with low degree polynomials (that don't go all over the place as a high degree polynomial does).
It would help if you'd share an example of what your inputs and outputs should look like!