Average Error: 0.0 → 0.1
Time: 4.0s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\left(\sqrt[3]{\sqrt[3]{{\left(\frac{x + y}{x - y}\right)}^{3}}} \cdot \sqrt[3]{\frac{x + y}{x - y}}\right) \cdot \sqrt[3]{\frac{x + y}{x - y}}\]
\frac{x + y}{x - y}
↓
\left(\sqrt[3]{\sqrt[3]{{\left(\frac{x + y}{x - y}\right)}^{3}}} \cdot \sqrt[3]{\frac{x + y}{x - y}}\right) \cdot \sqrt[3]{\frac{x + y}{x - y}}
double f(double x, double y) {
        double r531019 = x;
        double r531020 = y;
        double r531021 = r531019 + r531020;
        double r531022 = r531019 - r531020;
        double r531023 = r531021 / r531022;
        return r531023;
}
↓
double f(double x, double y) {
        double r531024 = x;
        double r531025 = y;
        double r531026 = r531024 + r531025;
        double r531027 = r531024 - r531025;
        double r531028 = r531026 / r531027;
        double r531029 = 3.0;
        double r531030 = pow(r531028, r531029);
        double r531031 = cbrt(r531030);
        double r531032 = cbrt(r531031);
        double r531033 = cbrt(r531028);
        double r531034 = r531032 * r531033;
        double r531035 = r531034 * r531033;
        return r531035;
}

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

Derivation

  1. Initial program 0.0

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

  3. Applied add-cube-cbrt0.1

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

  5. Applied add-cbrt-cube41.6

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

  6. Applied add-cbrt-cube42.6

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

  7. Applied cbrt-undiv42.6

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020039 
(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)))