Average Error: 0.0 → 0.2
Time: 2.4s
Precision: 64
\[\frac{x - y}{2 - \left(x + y\right)}\]
↓
\[\frac{1}{2 - \left(x + y\right)} \cdot \left(x - y\right)\]
\frac{x - y}{2 - \left(x + y\right)}
↓
\frac{1}{2 - \left(x + y\right)} \cdot \left(x - y\right)
double f(double x, double y) {
        double r930821 = x;
        double r930822 = y;
        double r930823 = r930821 - r930822;
        double r930824 = 2.0;
        double r930825 = r930821 + r930822;
        double r930826 = r930824 - r930825;
        double r930827 = r930823 / r930826;
        return r930827;
}
↓
double f(double x, double y) {
        double r930828 = 1.0;
        double r930829 = 2.0;
        double r930830 = x;
        double r930831 = y;
        double r930832 = r930830 + r930831;
        double r930833 = r930829 - r930832;
        double r930834 = r930828 / r930833;
        double r930835 = r930830 - r930831;
        double r930836 = r930834 * r930835;
        return r930836;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.0
Target0.0
Herbie0.2
\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}\]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{2 - \left(x + y\right)}\]
  2. Using strategy rm

  3. Applied div-sub0.0

    \[\leadsto \color{blue}{\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}}\]
  4. Using strategy rm

  5. Applied div-inv0.1

    \[\leadsto \frac{x}{2 - \left(x + y\right)} - \color{blue}{y \cdot \frac{1}{2 - \left(x + y\right)}}\]

  6. Applied div-inv0.2

    \[\leadsto \color{blue}{x \cdot \frac{1}{2 - \left(x + y\right)}} - y \cdot \frac{1}{2 - \left(x + y\right)}\]

  7. Applied distribute-rgt-out--0.2

    \[\leadsto \color{blue}{\frac{1}{2 - \left(x + y\right)} \cdot \left(x - y\right)}\]

  8. Final simplification0.2

    \[\leadsto \frac{1}{2 - \left(x + y\right)} \cdot \left(x - y\right)\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2 (+ x y))) (/ y (- 2 (+ x y))))

  (/ (- x y) (- 2 (+ x y))))