Steven D'Aprano <steve+python@pearwood.info> added the comment:
sin(1<<500) is correctly computed as 0.42925739234242827
py> math.sin(1<<500) 0.9996230490249484 Wolfram Alpha says it is 0.429257392342428277735329299112473759079115476327819897... https://www.wolframalpha.com/input/?i=sin%282^500%29&assumption=%22TrigRD%22+-%3E+%22R%22
Some text could be added (which I am happy to produce) that explains what backward error means
You could start by telling us here what you mean by backward error. Are you talking about this? https://en.wikipedia.org/wiki/Numerical_stability#Stability_in_numerical_lin... ---------- nosy: +steven.daprano _______________________________________ Python tracker <report@bugs.python.org> <https://bugs.python.org/issue35880> _______________________________________