Average Error: 0.0 → 0.0
Time: 1.3s
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 r99828 = x;
        double r99829 = y;
        double r99830 = r99828 - r99829;
        double r99831 = fabs(r99830);
        double r99832 = fabs(r99829);
        double r99833 = r99831 / r99832;
        return r99833;
}
↓
double f(double x, double y) {
        double r99834 = x;
        double r99835 = y;
        double r99836 = r99834 - r99835;
        double r99837 = fabs(r99836);
        double r99838 = fabs(r99835);
        double r99839 = r99837 / r99838;
        return r99839;
}

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 2020047 +o rules:numerics
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))