Average Error: 58.0 → 0.3
Time: 52.7s
Precision: 64
$\cosh \left(x + 1\right) - \cosh 1$
$\left(\left(\sinh \left(\frac{x}{2}\right) \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)}\right) \cdot \left(\sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)} \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)}\right)\right) \cdot 2$
\cosh \left(x + 1\right) - \cosh 1
\left(\left(\sinh \left(\frac{x}{2}\right) \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)}\right) \cdot \left(\sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)} \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)}\right)\right) \cdot 2
double f(double x) {
double r33240509 = x;
double r33240510 = 1.0;
double r33240511 = r33240509 + r33240510;
double r33240512 = cosh(r33240511);
double r33240513 = cosh(r33240510);
double r33240514 = r33240512 - r33240513;
return r33240514;
}


double f(double x) {
double r33240515 = x;
double r33240516 = 2.0;
double r33240517 = r33240515 / r33240516;
double r33240518 = sinh(r33240517);
double r33240519 = 1.0;
double r33240520 = r33240519 + r33240515;
double r33240521 = r33240519 + r33240520;
double r33240522 = r33240521 / r33240516;
double r33240523 = sinh(r33240522);
double r33240524 = cbrt(r33240523);
double r33240525 = r33240518 * r33240524;
double r33240526 = r33240524 * r33240524;
double r33240527 = r33240525 * r33240526;
double r33240528 = r33240527 * r33240516;
return r33240528;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 58.0

$\cosh \left(x + 1\right) - \cosh 1$
2. Using strategy rm
3. Applied diff-cosh58.0

$\leadsto \color{blue}{2 \cdot \left(\sinh \left(\frac{\left(x + 1\right) + 1}{2}\right) \cdot \sinh \left(\frac{\left(x + 1\right) - 1}{2}\right)\right)}$
4. Simplified0.4

$\leadsto 2 \cdot \color{blue}{\left(\sinh \left(\frac{1 + \left(x + 1\right)}{2}\right) \cdot \sinh \left(\frac{x}{2}\right)\right)}$
5. Using strategy rm

$\leadsto 2 \cdot \left(\color{blue}{\left(\left(\sqrt[3]{\sinh \left(\frac{1 + \left(x + 1\right)}{2}\right)} \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(x + 1\right)}{2}\right)}\right) \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(x + 1\right)}{2}\right)}\right)} \cdot \sinh \left(\frac{x}{2}\right)\right)$
7. Applied associate-*l*0.3

$\leadsto 2 \cdot \color{blue}{\left(\left(\sqrt[3]{\sinh \left(\frac{1 + \left(x + 1\right)}{2}\right)} \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(x + 1\right)}{2}\right)}\right) \cdot \left(\sqrt[3]{\sinh \left(\frac{1 + \left(x + 1\right)}{2}\right)} \cdot \sinh \left(\frac{x}{2}\right)\right)\right)}$
8. Final simplification0.3

$\leadsto \left(\left(\sinh \left(\frac{x}{2}\right) \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)}\right) \cdot \left(\sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)} \cdot \sqrt[3]{\sinh \left(\frac{1 + \left(1 + x\right)}{2}\right)}\right)\right) \cdot 2$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "cosh(x+1)-cosh(1)"
(- (cosh (+ x 1.0)) (cosh 1.0)))