Average Error: 0.0 → 0.0
Time: 6.2s
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 r520394 = x;
        double r520395 = y;
        double r520396 = r520394 - r520395;
        double r520397 = r520394 + r520395;
        double r520398 = r520396 / r520397;
        return r520398;
}
↓
double f(double x, double y) {
        double r520399 = x;
        double r520400 = y;
        double r520401 = r520399 - r520400;
        double r520402 = r520399 + r520400;
        double r520403 = r520401 / r520402;
        double r520404 = 3.0;
        double r520405 = pow(r520403, r520404);
        double r520406 = cbrt(r520405);
        return r520406;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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)))