Average Error: 30.1 → 30.2
Time: 17.3s
Precision: 64
\[\cos \left({x}^{2}\right)\]
\[\left(\sqrt[3]{\cos \left({x}^{2}\right)} \cdot \sqrt[3]{\cos \left({x}^{2}\right)}\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{\cos \left({x}^{2}\right)}} \cdot \sqrt[3]{\sqrt[3]{\cos \left({x}^{2}\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos \left({x}^{2}\right)}}\right)\]
\cos \left({x}^{2}\right)
\left(\sqrt[3]{\cos \left({x}^{2}\right)} \cdot \sqrt[3]{\cos \left({x}^{2}\right)}\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{\cos \left({x}^{2}\right)}} \cdot \sqrt[3]{\sqrt[3]{\cos \left({x}^{2}\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos \left({x}^{2}\right)}}\right)
double f(double x) {
        double r646778 = x;
        double r646779 = 2.0;
        double r646780 = pow(r646778, r646779);
        double r646781 = cos(r646780);
        return r646781;
}

double f(double x) {
        double r646782 = x;
        double r646783 = 2.0;
        double r646784 = pow(r646782, r646783);
        double r646785 = cos(r646784);
        double r646786 = cbrt(r646785);
        double r646787 = r646786 * r646786;
        double r646788 = cbrt(r646786);
        double r646789 = r646788 * r646788;
        double r646790 = r646789 * r646788;
        double r646791 = r646787 * r646790;
        return r646791;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.1

    \[\cos \left({x}^{2}\right)\]
  2. Using strategy rm
  3. Applied add-cube-cbrt30.2

    \[\leadsto \color{blue}{\left(\sqrt[3]{\cos \left({x}^{2}\right)} \cdot \sqrt[3]{\cos \left({x}^{2}\right)}\right) \cdot \sqrt[3]{\cos \left({x}^{2}\right)}}\]
  4. Using strategy rm
  5. Applied add-cube-cbrt30.2

    \[\leadsto \left(\sqrt[3]{\cos \left({x}^{2}\right)} \cdot \sqrt[3]{\cos \left({x}^{2}\right)}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{\cos \left({x}^{2}\right)}} \cdot \sqrt[3]{\sqrt[3]{\cos \left({x}^{2}\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos \left({x}^{2}\right)}}\right)}\]
  6. Final simplification30.2

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

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "cos(x^2)"
  :precision binary64
  (cos (pow x 2)))