Average Error: 0.5 → 0.7
Time: 17.4s
Precision: 64
\[{\left(1 + \log x\right)}^{2}\]
\[{\left(\left(1 + 2 \cdot \log \left(\sqrt[3]{{x}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)\right) + \log \left(\sqrt[3]{x}\right)\right)}^{2}\]
{\left(1 + \log x\right)}^{2}
{\left(\left(1 + 2 \cdot \log \left(\sqrt[3]{{x}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)\right) + \log \left(\sqrt[3]{x}\right)\right)}^{2}
double f(double x) {
        double r926779 = 1.0;
        double r926780 = x;
        double r926781 = log(r926780);
        double r926782 = r926779 + r926781;
        double r926783 = 2.0;
        double r926784 = pow(r926782, r926783);
        return r926784;
}

double f(double x) {
        double r926785 = 1.0;
        double r926786 = 2.0;
        double r926787 = x;
        double r926788 = 0.6666666666666666;
        double r926789 = pow(r926787, r926788);
        double r926790 = cbrt(r926789);
        double r926791 = cbrt(r926787);
        double r926792 = cbrt(r926791);
        double r926793 = r926790 * r926792;
        double r926794 = log(r926793);
        double r926795 = r926786 * r926794;
        double r926796 = r926785 + r926795;
        double r926797 = log(r926791);
        double r926798 = r926796 + r926797;
        double r926799 = 2.0;
        double r926800 = pow(r926798, r926799);
        return r926800;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[{\left(1 + \log x\right)}^{2}\]
  2. Using strategy rm
  3. Applied add-cube-cbrt0.5

    \[\leadsto {\left(1 + \log \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)}\right)}^{2}\]
  4. Applied log-prod0.7

    \[\leadsto {\left(1 + \color{blue}{\left(\log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right)\right)}\right)}^{2}\]
  5. Applied associate-+r+0.7

    \[\leadsto {\color{blue}{\left(\left(1 + \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right) + \log \left(\sqrt[3]{x}\right)\right)}}^{2}\]
  6. Simplified0.7

    \[\leadsto {\left(\color{blue}{\left(1 + 2 \cdot \log \left(\sqrt[3]{x}\right)\right)} + \log \left(\sqrt[3]{x}\right)\right)}^{2}\]
  7. Using strategy rm
  8. Applied add-cube-cbrt0.7

    \[\leadsto {\left(\left(1 + 2 \cdot \log \left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}\right)\right) + \log \left(\sqrt[3]{x}\right)\right)}^{2}\]
  9. Applied cbrt-prod0.7

    \[\leadsto {\left(\left(1 + 2 \cdot \log \color{blue}{\left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)}\right) + \log \left(\sqrt[3]{x}\right)\right)}^{2}\]
  10. Simplified0.7

    \[\leadsto {\left(\left(1 + 2 \cdot \log \left(\color{blue}{\sqrt[3]{{x}^{\frac{2}{3}}}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)\right) + \log \left(\sqrt[3]{x}\right)\right)}^{2}\]
  11. Final simplification0.7

    \[\leadsto {\left(\left(1 + 2 \cdot \log \left(\sqrt[3]{{x}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)\right) + \log \left(\sqrt[3]{x}\right)\right)}^{2}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "pow(1 + log(x), 2)"
  :precision binary64
  (pow (+ 1 (log x)) 2))