thanks for sharing that, it was simple, neat, elegant.

this sent me down a rabbit hole -- I asked a few models to solve that same problem, then followed up with a request to optimize it so it runs more efficiently.

chatgpt & gemini's solutions were buggy, but claude solved it, and actually found a solution that is even more efficient. It only needs to compute sqrt once per iteration. It's more complex however.

                   yours  claude
  ------------------------------
  Time (ns/call)    40.5   38.3
  sqrt per iter        3      1
  Accuracy        4.8e-7 4.8e-7

  // Rotate (c,s) by angle dt, then renormalize to unit circle
  float nc = c + dt*s, ns = s - dt*c;
  float len = sqrt(nc*nc + ns*ns);
  c = nc/len; s = ns/len;

p.s: it seems like Gemini has disabled the ability to share chats can anyone else confirm this?

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