A conversation with Jeffrey Sarnoff on the Herbie mailing list raised a very interesting small example of how floating-point error can occur. This example is extreme, but I thought it would be interesting to work through. The program is this: sqrt(x^2). Non-compositional error Run it through Herbie and Herbie will tell you that this expression is fairly inaccurate: approximately 29.1 bits of error, with the problems occurring for very large and very small inputs.1 [1 Herbie suggests the more ...
