Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\sqrt[3]{\frac{1}{{\left(\frac{x - y}{x + y}\right)}^{3}}}\]
\frac{x + y}{x - y}
↓
\sqrt[3]{\frac{1}{{\left(\frac{x - y}{x + y}\right)}^{3}}}
double f(double x, double y) {
        double r516489 = x;
        double r516490 = y;
        double r516491 = r516489 + r516490;
        double r516492 = r516489 - r516490;
        double r516493 = r516491 / r516492;
        return r516493;
}
↓
double f(double x, double y) {
        double r516494 = 1.0;
        double r516495 = x;
        double r516496 = y;
        double r516497 = r516495 - r516496;
        double r516498 = r516495 + r516496;
        double r516499 = r516497 / r516498;
        double r516500 = 3.0;
        double r516501 = pow(r516499, r516500);
        double r516502 = r516494 / r516501;
        double r516503 = cbrt(r516502);
        return r516503;
}

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-cube40.9

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

  4. Applied add-cbrt-cube41.7

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

  5. Applied cbrt-undiv41.7

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

  6. Simplified0.0

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

  8. Applied clear-num0.0

    \[\leadsto \sqrt[3]{{\color{blue}{\left(\frac{1}{\frac{x - y}{x + y}}\right)}}^{3}}\]
  9. Using strategy rm

  10. Applied cube-div0.0

    \[\leadsto \sqrt[3]{\color{blue}{\frac{{1}^{3}}{{\left(\frac{x - y}{x + y}\right)}^{3}}}}\]

  11. Simplified0.0

    \[\leadsto \sqrt[3]{\frac{\color{blue}{1}}{{\left(\frac{x - y}{x + y}\right)}^{3}}}\]

  12. Final simplification0.0

    \[\leadsto \sqrt[3]{\frac{1}{{\left(\frac{x - y}{x + y}\right)}^{3}}}\]

Reproduce

herbie shell --seed 2020027 +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)))