Average Error: 2.7 → 2.7
Time: 30.7s
Precision: 64
${\left(\sin \left(2 \cdot \cos \left(\sqrt{x}\right)\right)\right)}^{e}$
${\left(\sin \left(2 \cdot \sqrt[3]{{\left(\cos \left(\sqrt{x}\right)\right)}^{3}}\right)\right)}^{e}$
{\left(\sin \left(2 \cdot \cos \left(\sqrt{x}\right)\right)\right)}^{e}
{\left(\sin \left(2 \cdot \sqrt[3]{{\left(\cos \left(\sqrt{x}\right)\right)}^{3}}\right)\right)}^{e}
double f(double x) {
double r207856 = 2.0;
double r207857 = x;
double r207858 = sqrt(r207857);
double r207859 = cos(r207858);
double r207860 = r207856 * r207859;
double r207861 = sin(r207860);
double r207862 = exp(1.0);
double r207863 = pow(r207861, r207862);
return r207863;
}


double f(double x) {
double r207864 = 2.0;
double r207865 = x;
double r207866 = sqrt(r207865);
double r207867 = cos(r207866);
double r207868 = 3.0;
double r207869 = pow(r207867, r207868);
double r207870 = cbrt(r207869);
double r207871 = r207864 * r207870;
double r207872 = sin(r207871);
double r207873 = exp(1.0);
double r207874 = pow(r207872, r207873);
return r207874;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 2.7

${\left(\sin \left(2 \cdot \cos \left(\sqrt{x}\right)\right)\right)}^{e}$
2. Using strategy rm

$\leadsto {\left(\sin \left(2 \cdot \color{blue}{\sqrt[3]{\left(\cos \left(\sqrt{x}\right) \cdot \cos \left(\sqrt{x}\right)\right) \cdot \cos \left(\sqrt{x}\right)}}\right)\right)}^{e}$
4. Simplified2.7

$\leadsto {\left(\sin \left(2 \cdot \sqrt[3]{\color{blue}{{\left(\cos \left(\sqrt{x}\right)\right)}^{3}}}\right)\right)}^{e}$
5. Final simplification2.7

$\leadsto {\left(\sin \left(2 \cdot \sqrt[3]{{\left(\cos \left(\sqrt{x}\right)\right)}^{3}}\right)\right)}^{e}$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "pow(sin(2*cos(sqrt(x))), E)"
:precision binary64
(pow (sin (* 2 (cos (sqrt x)))) E))