Fast sigmoid algorithm

Question

The sigmoid function is defined as

I found that using the C built-in function exp() to calculate the value of f(x) is slow. Is th

Answer 1

Using Eureqa to search for approximations to sigmoid I found 1/(1 + 0.3678749025^x) approximates it. It's pretty close, just gets rid of one operation with the negation of x.

Some of the other functions shown here are interesting, but is the power operation really that slow? I tested it and it actually did faster than addition, but that could just be a fluke. If so it should be just as fast or faster as all the others.

EDIT:0.5 + 0.5*tanh(0.5*x) and less accurate, 0.5 + 0.5*tanh(n) also works. And you could just get rid of the constants if you don't care about getting it between the range [0,1] like sigmoid. But it assumes that tanh is faster.