Average Error: 0.0 → 0.0
Time: 12.9s
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 r142032 = x;
        double r142033 = y;
        double r142034 = r142032 - r142033;
        double r142035 = fabs(r142034);
        double r142036 = fabs(r142033);
        double r142037 = r142035 / r142036;
        return r142037;
}
↓
double f(double x, double y) {
        double r142038 = x;
        double r142039 = y;
        double r142040 = r142038 - r142039;
        double r142041 = fabs(r142040);
        double r142042 = fabs(r142039);
        double r142043 = r142041 / r142042;
        return r142043;
}

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)))