A comparison with one of the many SIMD-mathlibraries would have been fairer than with plain libm. Long time ago I wrote such a dual-platform library for the PS3 (cell-processor) and x86 architecture (outdated, but still available here [1]). Depending on how standard libm implements atan2f, a speedup of 3x to 15x is achieved, without sacrifying accuracy.

1. https://webuser.hs-furtwangen.de/~dersch/libsimdmath.pdf