Average Error: 0.0 → 0.0
Time: 11.6s
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 r657127 = x;
        double r657128 = y;
        double r657129 = r657127 - r657128;
        double r657130 = r657127 + r657128;
        double r657131 = r657129 / r657130;
        return r657131;
}
↓
double f(double x, double y) {
        double r657132 = x;
        double r657133 = y;
        double r657134 = r657132 + r657133;
        double r657135 = r657132 / r657134;
        double r657136 = r657133 / r657134;
        double r657137 = r657135 - r657136;
        return r657137;
}

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 2019212 
(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)))