Hm. They were looking for conservation laws, threw out all trivial equations and kept the next set they found. Weren't they in fact building an engine to find what they knew was there? Isn't this just a program to fit coefficients? When did they stop running data thru their engine - when it found the "right" equations?
Not at all. Coefficient fitting is when you know what output you want, and you have a lot of inputs, and you have some idea of the functional form. In this case, they didn't say "I want to predict the position of the pendulum based on time given these initial conditions." They just said "here is a bunch of data" and it came back with useful equations.
