Average Error: 0.0 → 0.0
Time: 5.5s
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 r551308 = x;
        double r551309 = y;
        double r551310 = r551308 + r551309;
        double r551311 = r551308 - r551309;
        double r551312 = r551310 / r551311;
        return r551312;
}
↓
double f(double x, double y) {
        double r551313 = x;
        double r551314 = y;
        double r551315 = r551313 + r551314;
        double r551316 = r551313 - r551314;
        double r551317 = r551315 / r551316;
        double r551318 = 3.0;
        double r551319 = pow(r551317, r551318);
        double r551320 = cbrt(r551319);
        return r551320;
}

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 2019350 
(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)))