Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[\frac{\left|x - y\right|}{\left|y\right|}\]
↓
\[\frac{\left|x - y\right|}{\left|y\right|}\]
\frac{\left|x - y\right|}{\left|y\right|}
↓
\frac{\left|x - y\right|}{\left|y\right|}
double f(double x, double y) {
        double r135926 = x;
        double r135927 = y;
        double r135928 = r135926 - r135927;
        double r135929 = fabs(r135928);
        double r135930 = fabs(r135927);
        double r135931 = r135929 / r135930;
        return r135931;
}
↓
double f(double x, double y) {
        double r135932 = x;
        double r135933 = y;
        double r135934 = r135932 - r135933;
        double r135935 = fabs(r135934);
        double r135936 = fabs(r135933);
        double r135937 = r135935 / r135936;
        return r135937;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{\left|x - y\right|}{\left|y\right|}\]

  2. Final simplification0.0

    \[\leadsto \frac{\left|x - y\right|}{\left|y\right|}\]

Reproduce

herbie shell --seed 2020021 +o rules:numerics
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))