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How can I do a blind installation in a list of pairs of x, y values ​​if I don't know the form f (x) = y?

If I have a function f (x) = y, I don’t know the form, and if I have a long list of pairs of x and y values ​​(potentially thousands of them), is there a program / package / library that will generate potential forms f (x)?

Obviously, there is a lot of ambiguity for the possible forms of any f (x), so something that gives many non-trivial unique answers (in abbreviated terms) would be ideal, but something that could give at least one answer would be good .

If x and y are obtained from observational data (i.e., experimental results), are there programs that can create approximate forms f (x)? On the other hand, if you know in advance that there is a completely deterministic connection between x and y (as with the input and output of the pseudo random number generator), are there programs that can create exact forms f (x)?

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http://en.wikipedia.org/wiki/Polynomial_interpolation

Some lists may also correspond to other types of functions, such as exponential, sinusoidal, and many others. It is impossible to find the “simplest” matching function, but the best thing you can do is list the common ones, such as exponential, sinusoidal, etc., And if none of them match, interpolate the polynomial.

I do not know any software that can do this for you.

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