> But it seems like a good strategy would be to test one number, guess assuming constant, test a second, guess assuming linear, test a third, guess assuming fir

> But it seems like a good strategy would be to test one number, guess assuming constant, test a second, guess assuming linear, test a third, guess assuming first order polynomial, and so on. You are still implicitly assuming that the function is continuous. There are a lot of nowhere-continuous functions, e.g. the sawtooth function. Or more interestingly, Conway's base13 function, which takes on every real number in every interval. Also what about continuous non-polynomials? e.g. exponentials, logarithms, sine/cosine etc.?