Average Error: 0.1 → 0.1
Time: 10.1s
Precision: 64
$\frac{x}{x - y} \cdot \frac{x}{x - y}$
$\frac{\frac{x}{x - y}}{1 - \frac{y}{x}}$
\frac{x}{x - y} \cdot \frac{x}{x - y}
\frac{\frac{x}{x - y}}{1 - \frac{y}{x}}
double f(double x, double y) {
double r1416470 = x;
double r1416471 = y;
double r1416472 = r1416470 - r1416471;
double r1416473 = r1416470 / r1416472;
double r1416474 = r1416473 * r1416473;
return r1416474;
}


double f(double x, double y) {
double r1416475 = x;
double r1416476 = y;
double r1416477 = r1416475 - r1416476;
double r1416478 = r1416475 / r1416477;
double r1416479 = 1.0;
double r1416480 = r1416476 / r1416475;
double r1416481 = r1416479 - r1416480;
double r1416482 = r1416478 / r1416481;
return r1416482;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.1

$\frac{x}{x - y} \cdot \frac{x}{x - y}$
2. Using strategy rm
3. Applied clear-num0.1

$\leadsto \frac{x}{x - y} \cdot \color{blue}{\frac{1}{\frac{x - y}{x}}}$
4. Using strategy rm
5. Applied pow10.1

$\leadsto \frac{x}{x - y} \cdot \color{blue}{{\left(\frac{1}{\frac{x - y}{x}}\right)}^{1}}$
6. Applied pow10.1

$\leadsto \color{blue}{{\left(\frac{x}{x - y}\right)}^{1}} \cdot {\left(\frac{1}{\frac{x - y}{x}}\right)}^{1}$
7. Applied pow-prod-down0.1

$\leadsto \color{blue}{{\left(\frac{x}{x - y} \cdot \frac{1}{\frac{x - y}{x}}\right)}^{1}}$
8. Simplified0.1

$\leadsto {\color{blue}{\left(\frac{\frac{x}{x - y}}{1 - \frac{y}{x}}\right)}}^{1}$
9. Final simplification0.1

$\leadsto \frac{\frac{x}{x - y}}{1 - \frac{y}{x}}$

# Reproduce

herbie shell --seed 1
(FPCore (x y)
:name "(x/(x-y))*(x/(x-y))"
:precision binary64
(* (/ x (- x y)) (/ x (- x y))))