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 he

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 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/ 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.