I did something similar for tanh once, though I found I could get to 1 ulp. Part of the motivation was that I could get 10x faster than libc. However, I then t

I did something similar for tanh once, though I found I could get to 1 ulp. Part of the motivation was that I could get 10x faster than libc. However, I then tried on my FreeBSD and could only get 4x faster. After a lot of head scratching and puzzling it turned out there was a bug in the version of libc on my linux box that slowed things down. It kind of took the wind out of the achievement, but it was still a great learning experience.