Average Error: 0.0 → 0.0
Time: 6.5s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{x}{y + x} - \frac{y}{y + x}\]
\frac{x - y}{x + y}
↓
\frac{x}{y + x} - \frac{y}{y + x}
double f(double x, double y) {
        double r612792 = x;
        double r612793 = y;
        double r612794 = r612792 - r612793;
        double r612795 = r612792 + r612793;
        double r612796 = r612794 / r612795;
        return r612796;
}
↓
double f(double x, double y) {
        double r612797 = x;
        double r612798 = y;
        double r612799 = r612798 + r612797;
        double r612800 = r612797 / r612799;
        double r612801 = r612798 / r612799;
        double r612802 = r612800 - r612801;
        return r612802;
}

Error

Bits error versus x

Bits error versus y

Try it out

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Results

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Target

Original0.0
Target0.0
Herbie0.0
\[\frac{x}{x + y} - \frac{y}{x + y}\]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{x + y}\]
  2. Using strategy rm

  3. Applied div-sub0.0

    \[\leadsto \color{blue}{\frac{x}{x + y} - \frac{y}{x + y}}\]

  4. Final simplification0.0

    \[\leadsto \frac{x}{y + x} - \frac{y}{y + x}\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"

  :herbie-target
  (- (/ x (+ x y)) (/ y (+ x y)))

  (/ (- x y) (+ x y)))