Approximating Hyperbolic Tangent
by jtomschroeder on 4/22/2026, 11:46:38 PM
https://jtomschroeder.com/blog/approximating-tanh/
Comments
by: raphlinus
A different approach, refining the square root based sigmoid with a polynomial, is in my blog post "a few of my favorite sigmoids" [1]. I'm not sure which is faster without benchmarking, but I'm pretty sure its worst case error is better than any of the fast approximations.<p>[1]: <a href="https://raphlinus.github.io/audio/2018/09/05/sigmoid.html" rel="nofollow">https://raphlinus.github.io/audio/2018/09/05/sigmoid.html</a>
4/23/2026, 1:07:52 AM
by: agalunar
There’s an analysis of the Schraudolph approximation of the exponential function (along with an improvement upon it) that someone might find interesting at <a href="https://typ.dev/attention#affine-cast" rel="nofollow">https://typ.dev/attention#affine-cast</a>
4/23/2026, 12:52:53 AM
by: mjcohen
Looks interesting. Should start with a definition of the Hyperbolic Tangent. It is only about 2/3 of the way that the definition occurs in a discussion of computing exp(x).
4/23/2026, 12:31:18 AM