Average Error: 0.0 → 0.0
Time: 4.4s
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 r812072 = x;
        double r812073 = y;
        double r812074 = r812072 - r812073;
        double r812075 = r812072 + r812073;
        double r812076 = r812074 / r812075;
        return r812076;
}
↓
double f(double x, double y) {
        double r812077 = x;
        double r812078 = y;
        double r812079 = r812077 + r812078;
        double r812080 = r812077 / r812079;
        double r812081 = 3.0;
        double r812082 = pow(r812080, r812081);
        double r812083 = cbrt(r812082);
        double r812084 = r812078 / r812079;
        double r812085 = r812083 - r812084;
        return r812085;
}

Error

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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-cube23.6

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

  6. Applied add-cbrt-cube27.4

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

  7. Applied cbrt-undiv27.4

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

  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 2020089 +o rules:numerics
(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)))