Average Error: 0.0 → 1.3
Time: 14.8s
Precision: 64
\[\frac{x - y}{2 - \left(x + y\right)}\]
↓
\[\frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{\frac{2 - \left(x + y\right)}{\sqrt[3]{x - y}}}\]
\frac{x - y}{2 - \left(x + y\right)}
↓
\frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{\frac{2 - \left(x + y\right)}{\sqrt[3]{x - y}}}
double f(double x, double y) {
        double r556773 = x;
        double r556774 = y;
        double r556775 = r556773 - r556774;
        double r556776 = 2.0;
        double r556777 = r556773 + r556774;
        double r556778 = r556776 - r556777;
        double r556779 = r556775 / r556778;
        return r556779;
}
↓
double f(double x, double y) {
        double r556780 = x;
        double r556781 = y;
        double r556782 = r556780 - r556781;
        double r556783 = cbrt(r556782);
        double r556784 = r556783 * r556783;
        double r556785 = 2.0;
        double r556786 = r556780 + r556781;
        double r556787 = r556785 - r556786;
        double r556788 = r556787 / r556783;
        double r556789 = r556784 / r556788;
        return r556789;
}

Error

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Bits error versus y

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Results

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Target

Original0.0
Target0.0
Herbie1.3
\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}\]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{2 - \left(x + y\right)}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.3

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}}{2 - \left(x + y\right)}\]

  4. Applied associate-/l*1.3

    \[\leadsto \color{blue}{\frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{\frac{2 - \left(x + y\right)}{\sqrt[3]{x - y}}}}\]

  5. Final simplification1.3

    \[\leadsto \frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{\frac{2 - \left(x + y\right)}{\sqrt[3]{x - y}}}\]

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(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))))