Average Error: 0.0 → 0.0
Time: 1.8s
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 r106387 = x;
        double r106388 = y;
        double r106389 = r106387 - r106388;
        double r106390 = fabs(r106389);
        double r106391 = fabs(r106388);
        double r106392 = r106390 / r106391;
        return r106392;
}
↓
double f(double x, double y) {
        double r106393 = x;
        double r106394 = y;
        double r106395 = r106393 - r106394;
        double r106396 = fabs(r106395);
        double r106397 = fabs(r106394);
        double r106398 = r106396 / r106397;
        return r106398;
}

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 2020100 +o rules:numerics
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))