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
People here are mostly concerned about how fast one function is relative to another and create micro benchmark to see whether f1(x) runs 0.0001 ms faster than f2(x). The big problem is that this is mostly irrelevant, because what matters is how fast your network learns with your activation function trying to minimize your cost function.
As of current theory, rectifier function and softplus
compared to sigmoid function or similar activation functions, allow for faster and effective training of deep neural architectures on large and complex datasets.
So I suggest to throw away micro-optimization, and take a look at which function allows faster learning (also taking looking at various other cost function).