Average Error: 0.0 → 0.0
Time: 13.6s
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 r128515 = x;
        double r128516 = y;
        double r128517 = r128515 - r128516;
        double r128518 = fabs(r128517);
        double r128519 = fabs(r128516);
        double r128520 = r128518 / r128519;
        return r128520;
}
↓
double f(double x, double y) {
        double r128521 = x;
        double r128522 = y;
        double r128523 = r128521 - r128522;
        double r128524 = fabs(r128523);
        double r128525 = fabs(r128522);
        double r128526 = r128524 / r128525;
        return r128526;
}

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 2020045 +o rules:numerics
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))