Average Error: 9.7 → 9.8
Time: 46.6s
Precision: 64
${\left(\tan x\right)}^{\left(\sin \left({x}^{\left(\sqrt{\cos x}\right)}\right)\right)}$
${\left(\tan x\right)}^{\left(\sin \left({x}^{\left(\sqrt[3]{{\left(\sqrt{\cos x}\right)}^{3}}\right)}\right)\right)}$
{\left(\tan x\right)}^{\left(\sin \left({x}^{\left(\sqrt{\cos x}\right)}\right)\right)}
{\left(\tan x\right)}^{\left(\sin \left({x}^{\left(\sqrt[3]{{\left(\sqrt{\cos x}\right)}^{3}}\right)}\right)\right)}
double f(double x) {
double r660133 = x;
double r660134 = tan(r660133);
double r660135 = cos(r660133);
double r660136 = sqrt(r660135);
double r660137 = pow(r660133, r660136);
double r660138 = sin(r660137);
double r660139 = pow(r660134, r660138);
return r660139;
}


double f(double x) {
double r660140 = x;
double r660141 = tan(r660140);
double r660142 = cos(r660140);
double r660143 = sqrt(r660142);
double r660144 = 3.0;
double r660145 = pow(r660143, r660144);
double r660146 = cbrt(r660145);
double r660147 = pow(r660140, r660146);
double r660148 = sin(r660147);
double r660149 = pow(r660141, r660148);
return r660149;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 9.7

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

$\leadsto {\left(\tan x\right)}^{\left(\sin \left({x}^{\color{blue}{\left(\sqrt[3]{\left(\sqrt{\cos x} \cdot \sqrt{\cos x}\right) \cdot \sqrt{\cos x}}\right)}}\right)\right)}$
4. Simplified9.8

$\leadsto {\left(\tan x\right)}^{\left(\sin \left({x}^{\left(\sqrt[3]{\color{blue}{{\left(\sqrt{\cos x}\right)}^{3}}}\right)}\right)\right)}$
5. Final simplification9.8

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

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "pow(tan(x), sin(x^sqrt(cos(x))))"
:precision binary64
(pow (tan x) (sin (pow x (sqrt (cos x))))))