Average Error: 0.0 → 0.0
Time: 2.4s
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 r128631 = x;
        double r128632 = y;
        double r128633 = r128631 - r128632;
        double r128634 = fabs(r128633);
        double r128635 = fabs(r128632);
        double r128636 = r128634 / r128635;
        return r128636;
}
↓
double f(double x, double y) {
        double r128637 = x;
        double r128638 = y;
        double r128639 = r128637 - r128638;
        double r128640 = fabs(r128639);
        double r128641 = fabs(r128638);
        double r128642 = r128640 / r128641;
        return r128642;
}

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 2019353 +o rules:numerics
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))