Which algorithm generator based on input and output data are you currently using?

Question

Algorithms

Principle: at the input of the generator, your input and output data (several proven reference options) and at the output - you get a single conversion formula for all standards or 2-3 formulas for a step-by-step algorithm for converting the input data into the desired result.

Answer 1

In general terms, when you need to find a function of any kind (presumably the shortest) - the problem is not solved. We need artificial intelligence here. Real, not machine learning.
But, if we limit the class of admissible formulas, then there is a solution - for example, among polynomials for n given standards, you can always find a polynomial of degree n-1, which will pass through these points. This is if you have input and output data - one number each.
Here you can solve a system of n linear equations (denote the coefficients of the polynomial as unknown, substitute the known values ​​of x and y for all standards, use the Gauss method).
If you have several output numbers - solve the interpolation problem separately for each output parameter. If there are several input variables, also choose the type of polynomial that depends on all input variables and has at least n coefficients. But here the equations may become linearly dependent and there may be no solution. Then add more terms/coefficients.
Formally, the problem will be solved, but there is no practical sense in this at all. The formulas will be huge and scary.