Average Error: 0.0 → 0.0
Time: 4.5s
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 r539 = x;
        double r540 = y;
        double r541 = r539 - r540;
        double r542 = fabs(r541);
        double r543 = fabs(r540);
        double r544 = r542 / r543;
        return r544;
}
↓
double f(double x, double y) {
        double r545 = x;
        double r546 = y;
        double r547 = r545 - r546;
        double r548 = fabs(r547);
        double r549 = fabs(r546);
        double r550 = r548 / r549;
        return r550;
}

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 2020025 +o rules:numerics
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))