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;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

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
  3. Applied add-cbrt-cube9.8

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