Average Error: 0.0 → 0.0
Time: 52.0s
Precision: 64
$\frac{1}{{\left(\cosh x\right)}^{2}}$
$\frac{1}{\cosh x} \cdot \frac{1}{\cosh x}$
\frac{1}{{\left(\cosh x\right)}^{2}}
\frac{1}{\cosh x} \cdot \frac{1}{\cosh x}
double f(double x) {
double r17124497 = 1.0;
double r17124498 = x;
double r17124499 = cosh(r17124498);
double r17124500 = 2.0;
double r17124501 = pow(r17124499, r17124500);
double r17124502 = r17124497 / r17124501;
return r17124502;
}


double f(double x) {
double r17124503 = 1.0;
double r17124504 = x;
double r17124505 = cosh(r17124504);
double r17124506 = r17124503 / r17124505;
double r17124507 = r17124506 * r17124506;
return r17124507;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.0

$\frac{1}{{\left(\cosh x\right)}^{2}}$
2. Simplified0.0

$\leadsto \color{blue}{\frac{1}{\cosh x \cdot \cosh x}}$
3. Using strategy rm

$\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\cosh x \cdot \cosh x}$
5. Applied times-frac0.0

$\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\cosh x} \cdot \frac{\sqrt[3]{1}}{\cosh x}}$
6. Simplified0.0

$\leadsto \color{blue}{\frac{1}{\cosh x}} \cdot \frac{\sqrt[3]{1}}{\cosh x}$
7. Simplified0.0

$\leadsto \frac{1}{\cosh x} \cdot \color{blue}{\frac{1}{\cosh x}}$
8. Final simplification0.0

$\leadsto \frac{1}{\cosh x} \cdot \frac{1}{\cosh x}$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "1/pow(cosh(x),2)"
(/ 1 (pow (cosh x) 2)))