My hope for the future is that Herbie's approach can evolve to a point where the person writing the software doesn't directly write FPU operations, any more than you'd manually work out all the best ways to optimise integer arithmetic. You write what you meant and the compiler figures out how to deliver that with FPU instructions. The parameters are more complicated for the second operation, but it's surely tractable.

"I want to calculate function F(x) here, I care about 0 <= x <= 4.0, inside those limits we need +/- 0.1% accuracy, for other values I don't care, and I want you to go as fast as possible within those parameters".