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;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

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
  3. Applied add-cbrt-cube2.7

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