Average Error: 14.7 → 1.1
Time: 11.1s
Precision: 64
$\sqrt{\frac{x}{y}}$
$\left|\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right| \cdot \sqrt{\frac{\sqrt[3]{x}}{\sqrt[3]{y}}}$
\sqrt{\frac{x}{y}}
\left|\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right| \cdot \sqrt{\frac{\sqrt[3]{x}}{\sqrt[3]{y}}}
double f(double x, double y) {
double r8457873 = x;
double r8457874 = y;
double r8457875 = r8457873 / r8457874;
double r8457876 = sqrt(r8457875);
return r8457876;
}


double f(double x, double y) {
double r8457877 = x;
double r8457878 = cbrt(r8457877);
double r8457879 = y;
double r8457880 = cbrt(r8457879);
double r8457881 = r8457878 / r8457880;
double r8457882 = fabs(r8457881);
double r8457883 = sqrt(r8457881);
double r8457884 = r8457882 * r8457883;
return r8457884;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 14.7

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

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

$\leadsto \sqrt{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}$
5. Applied times-frac15.4

$\leadsto \sqrt{\color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}}}$
6. Applied sqrt-prod4.3

$\leadsto \color{blue}{\sqrt{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \sqrt{\frac{\sqrt[3]{x}}{\sqrt[3]{y}}}}$
7. Simplified1.1

$\leadsto \color{blue}{\left|\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right|} \cdot \sqrt{\frac{\sqrt[3]{x}}{\sqrt[3]{y}}}$
8. Final simplification1.1

$\leadsto \left|\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right| \cdot \sqrt{\frac{\sqrt[3]{x}}{\sqrt[3]{y}}}$

# Reproduce

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