Average Error: 0.0 → 0.0
Time: 3.8s
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 r163067 = x;
        double r163068 = y;
        double r163069 = r163067 - r163068;
        double r163070 = fabs(r163069);
        double r163071 = fabs(r163068);
        double r163072 = r163070 / r163071;
        return r163072;
}
↓
double f(double x, double y) {
        double r163073 = x;
        double r163074 = y;
        double r163075 = r163073 - r163074;
        double r163076 = fabs(r163075);
        double r163077 = fabs(r163074);
        double r163078 = r163076 / r163077;
        return r163078;
}

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 2020057 +o rules:numerics
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))