Average Error: 0.0 → 0.0
Time: 11.4s
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 r266006 = x;
        double r266007 = y;
        double r266008 = r266006 + r266007;
        double r266009 = r266006 - r266007;
        double r266010 = r266008 / r266009;
        return r266010;
}
↓
double f(double x, double y) {
        double r266011 = x;
        double r266012 = y;
        double r266013 = r266011 + r266012;
        double r266014 = r266011 - r266012;
        double r266015 = r266013 / r266014;
        double r266016 = 3.0;
        double r266017 = pow(r266015, r266016);
        double r266018 = cbrt(r266017);
        return r266018;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{1}{\frac{x}{x + y} - \frac{y}{x + y}}\]

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

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (/ 1 (- (/ x (+ x y)) (/ y (+ x y))))

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