Average Error: 0.0 → 0.0
Time: 9.8s
Precision: 64
\[\frac{x + y}{x - y}\]
\[\sqrt[3]{\frac{x + y}{x - y} \cdot \left(\frac{x + y}{x - y} \cdot \frac{x + y}{x - y}\right)}\]
\frac{x + y}{x - y}
\sqrt[3]{\frac{x + y}{x - y} \cdot \left(\frac{x + y}{x - y} \cdot \frac{x + y}{x - y}\right)}
double f(double x, double y) {
        double r7545169 = x;
        double r7545170 = y;
        double r7545171 = r7545169 + r7545170;
        double r7545172 = r7545169 - r7545170;
        double r7545173 = r7545171 / r7545172;
        return r7545173;
}

double f(double x, double y) {
        double r7545174 = x;
        double r7545175 = y;
        double r7545176 = r7545174 + r7545175;
        double r7545177 = r7545174 - r7545175;
        double r7545178 = r7545176 / r7545177;
        double r7545179 = r7545178 * r7545178;
        double r7545180 = r7545178 * r7545179;
        double r7545181 = cbrt(r7545180);
        return r7545181;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{x + y}{x - y}\]
  2. Using strategy rm
  3. Applied add-cbrt-cube41.3

    \[\leadsto \frac{x + y}{\color{blue}{\sqrt[3]{\left(\left(x - y\right) \cdot \left(x - y\right)\right) \cdot \left(x - y\right)}}}\]
  4. Applied add-cbrt-cube41.6

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(x + y\right)}}}{\sqrt[3]{\left(\left(x - y\right) \cdot \left(x - y\right)\right) \cdot \left(x - y\right)}}\]
  5. Applied cbrt-undiv41.6

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(x + y\right)}{\left(\left(x - y\right) \cdot \left(x - y\right)\right) \cdot \left(x - y\right)}}}\]
  6. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{\left(\frac{x + y}{x - y} \cdot \frac{x + y}{x - y}\right) \cdot \frac{x + y}{x - y}}}\]
  7. Final simplification0.0

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

Reproduce

herbie shell --seed 1 
(FPCore (x y)
  :name "(x+y)/(x-y)"
  (/ (+ x y) (- x y)))