[LiamPowell]

I have a suspicion that the accuracy number is the mean of accuracies over all valid floats in the range (or something approximating that), which is going to be weighted towards zero where the accuracy is higher, and perhaps where sqrt near 1 has some artefacts.

[pavpanchekha]

It is, there's a page in the documentation about how errors are defined. Let me also add: Herbie generally gives the most accurate option it found first, and then the other stuff might be useful for speed (0.5x is way faster than two square roots and a divide!) but it's not as accurate

[Rexxar]

The input should be the range and the distribution of probability on this range. Intuitively we have a tendency to assume an uniform probability for range [-1, 1] which is not the case if we check every doubles.