Average Error: 0.0 → 0.0
Time: 1.7s
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 r80922 = x;
        double r80923 = y;
        double r80924 = r80922 - r80923;
        double r80925 = fabs(r80924);
        double r80926 = fabs(r80923);
        double r80927 = r80925 / r80926;
        return r80927;
}
↓
double f(double x, double y) {
        double r80928 = x;
        double r80929 = y;
        double r80930 = r80928 - r80929;
        double r80931 = fabs(r80930);
        double r80932 = fabs(r80929);
        double r80933 = r80931 / r80932;
        return r80933;
}

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 2020036 +o rules:numerics
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))