A Few of My Favorite Sigmoids (2018)

My favorite way to reasonably accurately approximate other sigmoids (including tanh and erf) is to pre-process the input through a low-order, odd polynomial. I’ve presented an argument that tanh is the best sigmoid function for digital music applications, though others are usable, and a function based on reciprocal square root behaves similarly and is faster. I’ve also presented implementations of tanh and erf sigmoid functions which are reasonably accurate numerically, high quality for audio applications, and faster than other commonly used implementations.

Source: raphlinus.github.io