Average Error: 0.0 → 0.0
Time: 1.9s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{x}{x + y} - \frac{y}{x + y}\]
\frac{x - y}{x + y}
↓
\frac{x}{x + y} - \frac{y}{x + y}
double f(double x, double y) {
        double r779906 = x;
        double r779907 = y;
        double r779908 = r779906 - r779907;
        double r779909 = r779906 + r779907;
        double r779910 = r779908 / r779909;
        return r779910;
}
↓
double f(double x, double y) {
        double r779911 = x;
        double r779912 = y;
        double r779913 = r779911 + r779912;
        double r779914 = r779911 / r779913;
        double r779915 = r779912 / r779913;
        double r779916 = r779914 - r779915;
        return r779916;
}

Error

Bits error versus x

Bits error versus y

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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

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

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

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