Average Error: 0.0 → 0.0
Time: 6.3s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\sqrt[3]{{\left(\frac{x - y}{x + y}\right)}^{3}}\]
\frac{x - y}{x + y}
↓
\sqrt[3]{{\left(\frac{x - y}{x + y}\right)}^{3}}
double f(double x, double y) {
        double r1098757 = x;
        double r1098758 = y;
        double r1098759 = r1098757 - r1098758;
        double r1098760 = r1098757 + r1098758;
        double r1098761 = r1098759 / r1098760;
        return r1098761;
}
↓
double f(double x, double y) {
        double r1098762 = x;
        double r1098763 = y;
        double r1098764 = r1098762 - r1098763;
        double r1098765 = r1098762 + r1098763;
        double r1098766 = r1098764 / r1098765;
        double r1098767 = 3.0;
        double r1098768 = pow(r1098766, r1098767);
        double r1098769 = cbrt(r1098768);
        return r1098769;
}

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-cube41.4

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

  4. Applied add-cbrt-cube42.2

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

  5. Applied cbrt-undiv42.2

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 
(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)))