Editing Openai/6959ed27-accc-800e-8e87-21aa81e93c07 (section)

==== Your harness’s accuracy() checks only “returned point lies on ellipse” (ellipse equation residual). ====
That does not guarantee it’s the closest point.

So I also validated this hybrid against a robust global-min reference (find all stationary points of the distance function on [0, π/2] via sign-change bracketing + bisection, then pick the smallest distance). With 50k random points/config:
* For normal ellipses (150×100), max distance error was ~0.006 units.
* For 200×50 and 100×10, max error ~0.1 units (still tiny compared to radii).
* For the truly gnarly 1×1000 case, the hybrid massively reduces worst-case error compared to plain curv3 (because it helps pick the right stationary basin).

If you want, I can paste that reference checker into your harness behind an #ifdef VERIFY so you can run it occasionally without affecting the performance numbers.