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;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.0

$\frac{x + y}{x - y}$
2. Using strategy rm

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

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