Average Error: 0.0 → 0.0
Time: 15.7s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\sqrt[3]{\left(\frac{x - y}{x + y} \cdot \frac{x - y}{x + y}\right) \cdot \frac{x - y}{x + y}}\]
\frac{x - y}{x + y}
↓
\sqrt[3]{\left(\frac{x - y}{x + y} \cdot \frac{x - y}{x + y}\right) \cdot \frac{x - y}{x + y}}
double f(double x, double y) {
        double r127320142 = x;
        double r127320143 = y;
        double r127320144 = r127320142 - r127320143;
        double r127320145 = r127320142 + r127320143;
        double r127320146 = r127320144 / r127320145;
        return r127320146;
}
↓
double f(double x, double y) {
        double r127320147 = x;
        double r127320148 = y;
        double r127320149 = r127320147 - r127320148;
        double r127320150 = r127320147 + r127320148;
        double r127320151 = r127320149 / r127320150;
        double r127320152 = r127320151 * r127320151;
        double r127320153 = r127320152 * r127320151;
        double r127320154 = cbrt(r127320153);
        return r127320154;
}

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 add-cbrt-cube41.5

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

  4. Applied add-cbrt-cube42.3

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

  5. Applied cbrt-undiv42.3

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019173 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"

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

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