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 r116121 = x;
        double r116122 = y;
        double r116123 = r116121 - r116122;
        double r116124 = fabs(r116123);
        double r116125 = fabs(r116122);
        double r116126 = r116124 / r116125;
        return r116126;
}
↓
double f(double x, double y) {
        double r116127 = x;
        double r116128 = y;
        double r116129 = r116127 - r116128;
        double r116130 = fabs(r116129);
        double r116131 = fabs(r116128);
        double r116132 = r116130 / r116131;
        return r116132;
}

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 2020062 +o rules:numerics
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))