[tialaramex]

Herbie - the tool which exists today - is excellent, but the perhaps more significant insight is that this could and should in principle be baked into compilers.

That is, a future language should let you say here's a real expression, and I want you to give me an approximation in my 64-bit floating point representation, and here's the parameters for accuracy and performance. What do those parameters look like? Herbie's existing UI might help us somewhat but it's definitely up for experimentation.

Compare regular expression handling - you are not expected in any popular language today to manually translate the expression into an FSM and then run the FSM, that's all done for you, you just write down the expression, real arithmetic could be the same.