[0xfaded]

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

[achille]

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

Edit: it looks like the claude algorithm fails at high eccentricities. Gave chatgpt pro more context and it worked for 30min and only made marginal improvement on yours, by doing 2 steps then taking a third local step.

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

[0xfaded]

Haha nice, hanging in there by a thread