While benchmarking a language prototype, I realized that I had a superlinear implementation of a test program, but wasn't sure if it was quadratic or cubic. I stayed up too late and wrote half a page of very messy Python which appears to try some finite-difference method for empirically approximating complexity from the benchmark results.
I'm still trying to reverse-engineer what Past Corbin did, but before I go too much further, can finite-difference methods even do this? I only know formal methods for complexity analysis, and I've never heard of algorithms for doing it automatically other than type systems or other syntactic analysis.