Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\sqrt[3]{{\left(\frac{x}{x + y}\right)}^{3}} - \frac{y}{x + y}\]
\frac{x - y}{x + y}
↓
\sqrt[3]{{\left(\frac{x}{x + y}\right)}^{3}} - \frac{y}{x + y}
double f(double x, double y) {
        double r775843 = x;
        double r775844 = y;
        double r775845 = r775843 - r775844;
        double r775846 = r775843 + r775844;
        double r775847 = r775845 / r775846;
        return r775847;
}
↓
double f(double x, double y) {
        double r775848 = x;
        double r775849 = y;
        double r775850 = r775848 + r775849;
        double r775851 = r775848 / r775850;
        double r775852 = 3.0;
        double r775853 = pow(r775851, r775852);
        double r775854 = cbrt(r775853);
        double r775855 = r775849 / r775850;
        double r775856 = r775854 - r775855;
        return r775856;
}

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. Using strategy rm

  5. Applied add-cbrt-cube24.4

    \[\leadsto \frac{x}{\color{blue}{\sqrt[3]{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(x + y\right)}}} - \frac{y}{x + y}\]

  6. Applied add-cbrt-cube28.2

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(x \cdot x\right) \cdot x}}}{\sqrt[3]{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(x + y\right)}} - \frac{y}{x + y}\]

  7. Applied cbrt-undiv28.2

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(x \cdot x\right) \cdot x}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(x + y\right)}}} - \frac{y}{x + y}\]

  8. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{x}{x + y}\right)}^{3}}} - \frac{y}{x + y}\]

  9. Final simplification0.0

    \[\leadsto \sqrt[3]{{\left(\frac{x}{x + y}\right)}^{3}} - \frac{y}{x + y}\]

Reproduce

herbie shell --seed 2020064 
(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)))