Another reference, from 2016, in which I report on comparing the rsqrt and rcp instructions between Intel and AMD processors is https://github.com/jeff-arnold/math_routines/blob/main/rsqrt_rcp/docs/rsqrt_rcp.pdf.

See also https://members.loria.fr/PZimmermann/papers/accuracy.pdf which is a (continuing) study of the accuracy of various implementations of math library functions. In particular, the last paragraph of the introduction is relevant to the original question; it also mentions my report above.