Average Error: 0.0 → 0.0
Time: 988.0ms
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 r98906 = x;
        double r98907 = y;
        double r98908 = r98906 - r98907;
        double r98909 = fabs(r98908);
        double r98910 = fabs(r98907);
        double r98911 = r98909 / r98910;
        return r98911;
}
↓
double f(double x, double y) {
        double r98912 = x;
        double r98913 = y;
        double r98914 = r98912 - r98913;
        double r98915 = fabs(r98914);
        double r98916 = fabs(r98913);
        double r98917 = r98915 / r98916;
        return r98917;
}

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 2020002 +o rules:numerics
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))