If you want to find new math functions or variants. I wonder if its possible to train a machine learning function to plot something like small matrices. Those correspond to different math functions. Then solve with that function a problem. Then look what matrix image it generated and what the closest math functions are. I thought it is an interesting idea. Coming up with variant functions.
Ex. a function that is a probability 0.9, 0.1 between sin(x) and cos(x)
Ex. a function that is a probability 0.9, 0.1 between sin(x) and cos(x)