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

==== I wired this into your v2 harness style and ran it with: ====

g++ -O3 -march=native -ffast-math -std=c++17

Results (median of runs, 50k pts per config):

<syntaxhighlight>Moderate (150, 100)
  optimized (curv3):   51.6 ns/call
  rotation (claude):   41.9 ns/call
  curv2+newt1 (new):   41.8 ns/call

High ecc (200, 50)
  optimized (curv3):   54.2 ns/call
  rotation (claude):   42.0 ns/call
  curv2+newt1 (new):   41.8 ns/call

Very high (100, 10)
  optimized (curv3):   54.1 ns/call
  rotation (claude):   42.0 ns/call
  curv2+newt1 (new):   41.9 ns/call

Extreme (1, 1000)
  optimized (curv3):   52.5 ns/call
  rotation (claude):   49.7 ns/call
  curv2+newt1 (new):   49.5 ns/call

</syntaxhighlight>

So:
* vs 0xfaded curv3+opt: ~19–23% faster on the normal configs here.
* vs Claude rotation: basically a tie in most configs here, but the hybrid is consistently not worse and often a hair better.

(Your environment will absolutely shift the ns numbers; the point is the shape of the result: this hybrid removes one full curvature iteration and replaces it with a cheaper correction.)