Average Error: 0.0 → 0.1
Time: 14.3s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\left(\sqrt[3]{\frac{x + y}{x - y}} \cdot \sqrt[3]{\frac{x + y}{x - y}}\right) \cdot \sqrt[3]{\frac{x + y}{x - y}}\]
\frac{x + y}{x - y}
↓
\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}}
double f(double x, double y) {
        double r310288 = x;
        double r310289 = y;
        double r310290 = r310288 + r310289;
        double r310291 = r310288 - r310289;
        double r310292 = r310290 / r310291;
        return r310292;
}
↓
double f(double x, double y) {
        double r310293 = x;
        double r310294 = y;
        double r310295 = r310293 + r310294;
        double r310296 = r310293 - r310294;
        double r310297 = r310295 / r310296;
        double r310298 = cbrt(r310297);
        double r310299 = r310298 * r310298;
        double r310300 = r310299 * r310298;
        return r310300;
}

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

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

Reproduce

herbie shell --seed 2019325 +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)))