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 r116605 = x;
        double r116606 = y;
        double r116607 = r116605 - r116606;
        double r116608 = fabs(r116607);
        double r116609 = fabs(r116606);
        double r116610 = r116608 / r116609;
        return r116610;
}
↓
double f(double x, double y) {
        double r116611 = x;
        double r116612 = y;
        double r116613 = r116611 - r116612;
        double r116614 = fabs(r116613);
        double r116615 = fabs(r116612);
        double r116616 = r116614 / r116615;
        return r116616;
}

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 2020056 +o rules:numerics
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))