Average Error: 0.0 → 0.1
Time: 13.5s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\sqrt[3]{\frac{y + x}{x - y}} \cdot \left(\sqrt[3]{\frac{y + x}{x - y}} \cdot \sqrt[3]{\frac{y + x}{x - y}}\right)\]
\frac{x + y}{x - y}
↓
\sqrt[3]{\frac{y + x}{x - y}} \cdot \left(\sqrt[3]{\frac{y + x}{x - y}} \cdot \sqrt[3]{\frac{y + x}{x - y}}\right)
double f(double x, double y) {
        double r23212575 = x;
        double r23212576 = y;
        double r23212577 = r23212575 + r23212576;
        double r23212578 = r23212575 - r23212576;
        double r23212579 = r23212577 / r23212578;
        return r23212579;
}
↓
double f(double x, double y) {
        double r23212580 = y;
        double r23212581 = x;
        double r23212582 = r23212580 + r23212581;
        double r23212583 = r23212581 - r23212580;
        double r23212584 = r23212582 / r23212583;
        double r23212585 = cbrt(r23212584);
        double r23212586 = r23212585 * r23212585;
        double r23212587 = r23212585 * r23212586;
        return r23212587;
}

Error

Bits error versus x

Bits error versus y

Try it out

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"

  :herbie-target
  (/ 1.0 (- (/ x (+ x y)) (/ y (+ x y))))

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