Average Error: 0.0 → 0.1
Time: 14.2s
Precision: 64
\[\frac{x - y}{2 - \left(x + y\right)}\]
↓
\[\frac{1}{\frac{2}{x} - \left(1 + \frac{y}{x}\right)} - \frac{y}{2 - \left(x + y\right)}\]
\frac{x - y}{2 - \left(x + y\right)}
↓
\frac{1}{\frac{2}{x} - \left(1 + \frac{y}{x}\right)} - \frac{y}{2 - \left(x + y\right)}
double f(double x, double y) {
        double r506680 = x;
        double r506681 = y;
        double r506682 = r506680 - r506681;
        double r506683 = 2.0;
        double r506684 = r506680 + r506681;
        double r506685 = r506683 - r506684;
        double r506686 = r506682 / r506685;
        return r506686;
}
↓
double f(double x, double y) {
        double r506687 = 1.0;
        double r506688 = 2.0;
        double r506689 = x;
        double r506690 = r506688 / r506689;
        double r506691 = y;
        double r506692 = r506691 / r506689;
        double r506693 = r506687 + r506692;
        double r506694 = r506690 - r506693;
        double r506695 = r506687 / r506694;
        double r506696 = r506689 + r506691;
        double r506697 = r506688 - r506696;
        double r506698 = r506691 / r506697;
        double r506699 = r506695 - r506698;
        return r506699;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.0
Target0.0
Herbie0.1
\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}\]

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 clear-num0.0

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

  6. Taylor expanded around 0 0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 
(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))))