Average Error: 0.0 → 0.0
Time: 2.7s
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 r1033968 = x;
        double r1033969 = y;
        double r1033970 = r1033968 - r1033969;
        double r1033971 = r1033968 + r1033969;
        double r1033972 = r1033970 / r1033971;
        return r1033972;
}
↓
double f(double x, double y) {
        double r1033973 = x;
        double r1033974 = y;
        double r1033975 = r1033973 + r1033974;
        double r1033976 = r1033973 / r1033975;
        double r1033977 = r1033974 / r1033975;
        double r1033978 = r1033976 - r1033977;
        return r1033978;
}

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 2019353 
(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)))