> The math library for Bob Morris's variable-precision desk calculator used backward error analysis to determine the precision necessary at each step to attain the user-specified precision of the result. I wonder if compilers could do this today? If you can bound values for floating point operations, you might be able to replace them with fixed point equivalents and get a big speedup. You might also be able to replac…
https://dl.acm.org/doi/10.1145/2911981
Is a nice overview.