Curiously, early Intel 386 processors had a bug where 32-bit multiplies were genuinely nondeterministic: some answers would depend on the voltage, frequency, temperature, and manufacturing conditions. The problem was essentially analog, a layout issue, where the signal didn't always have enough margin. (This is unrelated to the famous Pentium FDIV bug.) Until Intel got the problem fixed, they would stamp bad chips with "16 BIT S/W ONLY", while good chips were labeled "ΣΣ".

What I mean is that the same code running on different hardware/os may not always give the same answer. It’ll be close, but you can’t always expect bit for bit identical.

They're always deterministic, just as long as physics is.