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.

You can't call it Ivy! That's an emacs package!

I genuinely can't tell if this is serious or not (or if the fact that it's impossible to tell is itself the point)

By definition, they can not be implemented. You can approximate them to some finite precision but you can not really implement them.

The typical computer algebra system (https://en.wikipedia.org/wiki/Computer_algebra_system) implements trigonometric functions just fine (with varying levels of sophistication)

They can be implemented, but what you cannot always do is compute their values in a finite number.

Let me know when you find infinite amount of time on your hands to wait for the calculation.

Damn, blogspot still exists! And it doesn't render well in my mobile, a product of simpler times.

Super interesting. Thank you.