I looked into this issue with rsqrt (and with rcp as well) between Intel and AMD processors in connection with CERN some years ago (2016). An unpublished report can be found at [1].

TL;DR: The same (very small) executables gave different results when run on Intel and AMD processors because the rsqrt and rcp instructions produced slightly different outputs on the two systems.

[1]: https://github.com/jeff-arnold/math_routines/blob/main/rsqrt....