Average Error: 0.0 → 0.1
Time: 14.9s
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 r556761 = x;
        double r556762 = y;
        double r556763 = r556761 - r556762;
        double r556764 = 2.0;
        double r556765 = r556761 + r556762;
        double r556766 = r556764 - r556765;
        double r556767 = r556763 / r556766;
        return r556767;
}
↓
double f(double x, double y) {
        double r556768 = 1.0;
        double r556769 = 2.0;
        double r556770 = x;
        double r556771 = r556769 / r556770;
        double r556772 = y;
        double r556773 = r556772 / r556770;
        double r556774 = r556768 + r556773;
        double r556775 = r556771 - r556774;
        double r556776 = r556768 / r556775;
        double r556777 = r556770 + r556772;
        double r556778 = r556769 - r556777;
        double r556779 = r556772 / r556778;
        double r556780 = r556776 - r556779;
        return r556780;
}

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))))