Average Error: 0.0 → 0.0
Time: 2.4s
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 r828114 = x;
        double r828115 = y;
        double r828116 = r828114 - r828115;
        double r828117 = r828114 + r828115;
        double r828118 = r828116 / r828117;
        return r828118;
}
↓
double f(double x, double y) {
        double r828119 = x;
        double r828120 = y;
        double r828121 = r828119 + r828120;
        double r828122 = r828119 / r828121;
        double r828123 = r828120 / r828121;
        double r828124 = r828122 - r828123;
        return r828124;
}

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 2020081 
(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)))