Average Error: 0.0 → 0.1
Time: 3.5s
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 r544112 = x;
        double r544113 = y;
        double r544114 = r544112 + r544113;
        double r544115 = r544112 - r544113;
        double r544116 = r544114 / r544115;
        return r544116;
}
↓
double f(double x, double y) {
        double r544117 = x;
        double r544118 = y;
        double r544119 = r544117 + r544118;
        double r544120 = r544117 - r544118;
        double r544121 = r544119 / r544120;
        double r544122 = cbrt(r544121);
        double r544123 = r544122 * r544122;
        double r544124 = r544123 * r544122;
        return r544124;
}

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 2020001 
(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)))