[nickcw]

Interesting reading about the difficulties with arctan.

There is a better series for arctan than the Taylor series which converges for all x. You can see it here in the accelerated series section

https://en.wikipedia.org/wiki/Arctangent_series

I wrote about it in my calculating pi blog some time ago

https://www.craig-wood.com/nick/articles/pi-machin/

It also takes fewer operations which is nice.

I thought it was invented by Euler but the Wikipedia article says Newton invented it and Euler popularized it.