Thanks for the interesting writeup. I wonder if it is because glibc has a less-optimized atan2f (for floats). The double version seems quite involved in glibc anyway:

https://sourceware.org/git/?p=glibc.git;a=blob;f=sysdeps/iee...

...where the atan2f version ends up calling atan, which doesn't seem as sophisticated:

https://sourceware.org/git/?p=glibc.git;a=blob;f=sysdeps/iee...