Average Error: 0.0 → 0.0
Time: 3.0s
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 r560978 = x;
        double r560979 = y;
        double r560980 = r560978 + r560979;
        double r560981 = r560978 - r560979;
        double r560982 = r560980 / r560981;
        return r560982;
}
↓
double f(double x, double y) {
        double r560983 = x;
        double r560984 = y;
        double r560985 = r560983 + r560984;
        double r560986 = r560983 - r560984;
        double r560987 = r560985 / r560986;
        double r560988 = 3.0;
        double r560989 = pow(r560987, r560988);
        double r560990 = cbrt(r560989);
        return r560990;
}

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
\[\frac{1}{\frac{x}{x + y} - \frac{y}{x + y}}\]

Derivation

  1. Initial program 0.0

    \[\frac{x + y}{x - y}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube42.1

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

  4. Applied add-cbrt-cube43.0

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

  5. Applied cbrt-undiv43.0

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

  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 2020002 +o rules:numerics
(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)))