Thanks for pushing this, I've never gone beyond "zero" shotting the prompt (is it still called zero shot with search?)

As a curiosity, it looks like r and q are only ever used as r/q, and therefore a sqrt could be saved by computing rq = sqrt((rxrx + ryry) / (qxqx + qyqy)). The if q < 1e-10 is also perhaps not necessary, since this would imply that the ellipse is degenerate. My method won't work in that case anyway.

For the other sqrt, maybe try std::hypot

Finally, for your test set, could you had some highly eccentric cases such as a=1 and b=100

Thanks for the investigation:)

Edit: BTW, the sin/cos renormalize trick is the same as what tx,ty are doing. It was pointed out to me by another SO member. My original implementation used trig functions

Nice, that worked. It's even faster.

                 yours  yours+opt  claude
  ---------------------------------------
  Time (ns)        40.9      36.4    38.7
  sqrt/iter           3         2       1
  Instructions      207       187     241

https://gist.github.com/achille/23680e9100db87565a8e67038797...