Average Error: 12.3 → 0
Time: 16.2s
Precision: 64
$\frac{1}{\frac{\left(x \cdot x\right) \cdot 1}{\sqrt{x}}}$
${x}^{\frac{-3}{2}}$
\frac{1}{\frac{\left(x \cdot x\right) \cdot 1}{\sqrt{x}}}
{x}^{\frac{-3}{2}}
double f(double x) {
double r421319 = 1.0;
double r421320 = x;
double r421321 = r421320 * r421320;
double r421322 = r421321 * r421319;
double r421323 = sqrt(r421320);
double r421324 = r421322 / r421323;
double r421325 = r421319 / r421324;
return r421325;
}


double f(double x) {
double r421326 = x;
double r421327 = -1.5;
double r421328 = pow(r421326, r421327);
return r421328;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 12.3

$\frac{1}{\frac{\left(x \cdot x\right) \cdot 1}{\sqrt{x}}}$
2. Simplified0.3

$\leadsto \color{blue}{\frac{\frac{\sqrt{x}}{x}}{x}}$
3. Using strategy rm
4. Applied pow10.3

$\leadsto \frac{\frac{\sqrt{x}}{x}}{\color{blue}{{x}^{1}}}$
5. Applied pow10.3

$\leadsto \frac{\frac{\sqrt{x}}{\color{blue}{{x}^{1}}}}{{x}^{1}}$
6. Applied pow1/20.3

$\leadsto \frac{\frac{\color{blue}{{x}^{\frac{1}{2}}}}{{x}^{1}}}{{x}^{1}}$
7. Applied pow-div0.2

$\leadsto \frac{\color{blue}{{x}^{\left(\frac{1}{2} - 1\right)}}}{{x}^{1}}$
8. Applied pow-div0

$\leadsto \color{blue}{{x}^{\left(\left(\frac{1}{2} - 1\right) - 1\right)}}$
9. Simplified0

$\leadsto {x}^{\color{blue}{\frac{-3}{2}}}$
10. Final simplification0

$\leadsto {x}^{\frac{-3}{2}}$

# Reproduce

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