thanks for sharing that, it was simple, neat, elegant. this sent me down a rabbit hole -- I asked...

achille • last Sunday at 4:29 AM • 1 reply • view on HN

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

Claude's trick: instead of calling sin/cos each iteration, it rotates the existing (cos,sin) pair by the small Newton step and renormalizes:

  // 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;

See: https://gist.github.com/achille/d1eadf82aa54056b9ded7706e8f5...

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

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0xfaded • last Sunday at 5:06 AM

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:)

alt Hacker News

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