> If it doesn't matter, then high precision rarely matters either. Once you have results with unknown noise in them, and you do a few operations on those, the noise compounds, at approximately sqrt(N) bits for N steps of computation (rough estimate, it certainly depends on algorithm selection, compiler nuances, stability of problem, etc.). So high precision degrades quickly when doing any work without using a reproducible and understood rounding mode.
This isn't really true for any of the numerous numerical algorithms that satisfy backwards error bounds; there you would always prefer to have a well-rounded arithmetic at higher precision, if reproducibility is not required.
> Any rounding method works works for reproducibility
Only if you round _correctly_ in that direction.
> Banker's rounding is generally better for doing computation than the usual correctly rounded.
Banker's rounding _is_ the default IEEE 754 rounding mode.
This isn't really true for any of the numerous numerical algorithms that satisfy backwards error bounds; there you would always prefer to have a well-rounded arithmetic at higher precision, if reproducibility is not required.
> Any rounding method works works for reproducibility
Only if you round _correctly_ in that direction.
> Banker's rounding is generally better for doing computation than the usual correctly rounded.
Banker's rounding _is_ the default IEEE 754 rounding mode.