Average Error: 0.0 → 0.0
Time: 3.0s
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 r4891 = x;
        double r4892 = y;
        double r4893 = r4891 - r4892;
        double r4894 = r4891 + r4892;
        double r4895 = r4893 / r4894;
        return r4895;
}
↓
double f(double x, double y) {
        double r4896 = x;
        double r4897 = y;
        double r4898 = r4896 + r4897;
        double r4899 = r4896 / r4898;
        double r4900 = r4897 / r4898;
        double r4901 = r4899 - r4900;
        return r4901;
}

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

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

Reproduce

herbie shell --seed 2020025 
(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)))