I have two variables, call them $x$ and $y$, that can possess any arbitrary positive integer value. I have an automated process that produces an output based on these variables. I do not, however, know precisely how that output is being derived.
I can execute this process an arbitrary number of times and record the results, forming a table of $x$ and $y$ values with their resulting outputs. What I lack is a method for using such a table to obtain the performed function. Does such a thing exist? It has been a long time since I've dealt with math of this abstract nature and much of my vocabulary for dealing with it is rusty in the extreme.
I've noted some cyclicity in the nature of the results (the output is 4 when x and y are both $2^n+1$ for an arbitrary number $n$, frex) but am struggling with generalizing that and other observed cyclicities into a general function that encompasses all possible $x,y$ values.