Re:Herbie: Automatically Improving Floating Point Accuracy
by pavpanchekha on Friday August 07, 2020 @11:38AM
(#24083037)
That's right, the implicit distribution is uniform over floating-point values, so for example about a quarter of samples are between -1e-150 and 1e-150.
Also this is a bit of a special case because it's easy to show that x - x^2 / 2 is within 10^-15 of the true value provided abs(x) is within 10^-6 or so, so it's easy to figure out how good Herbie is doing.