missed optimization: acos(1-x) -> 2 * asin(sqrt(x/2)) [on 0 <= x < 0.5?]

[jepler]

Source: personal investigation in 2014, inspiration from freebsd math library

http://herbie.uwplse.org/demo/8a0cc529ad30320a1d61220a6aefb0d36298cb3c.4ba6b6e49c51088fa31e3dbc4e15bf82b3c31626/graph.html

[pavpanchekha]

Huh, that's an interesting rewrite, thanks for the suggestion. I'll think about how best to add this.

(Herbie has a list of rewrite rules it knows about, and I could add this directly, but I'm thinking about whether there's maybe some way to break this down into simpler steps that could be useful elsewhere.)

[pavpanchekha]

Herbie still doesn't handle this one well, and frankly we have no clear plans to make Herbie much better at trig, so I'm going to add this to our benchmark suite (#521) and close this issue.

[jepler]

That's fine! I reported this while kicking the tires of herbie but it's not actually vexing me in my real life.