Quote:

If you're mapping (-infinity, +infinity) monotonically into (-1,1) or [-1,1] using doubles, you're going to have either significant regions of slope zero, or multiple inflection 'points'. That's what you get when approximating functions' behavior, no matter what the function is. Suppose I wrote

Sigmoid functions are functions mapping the real line into a subset (a,b) of the real line; infinity is not part of the domain.

Do you intend to ignore these, and the other points about floating point numbers? Fuzzy math will make correct entries wrong. I don't think anyone will want to participate if the contest judge - I hate the term - doesn't know what he's doing.