Average Error: 0.0 → 0.1
Time: 3.7s
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 r475133 = x;
        double r475134 = y;
        double r475135 = r475133 + r475134;
        double r475136 = r475133 - r475134;
        double r475137 = r475135 / r475136;
        return r475137;
}
↓
double f(double x, double y) {
        double r475138 = x;
        double r475139 = y;
        double r475140 = r475138 + r475139;
        double r475141 = r475138 - r475139;
        double r475142 = r475140 / r475141;
        double r475143 = cbrt(r475142);
        double r475144 = r475143 * r475143;
        double r475145 = r475144 * r475143;
        return r475145;
}

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 +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)))