Average Error: 0.3 → 0.3
Time: 20.8s
Precision: 64
\[x \cdot \log x\]
↓
\[\log \left(\sqrt[3]{x}\right) \cdot \left(x + x\right) + \left(\log \left(\sqrt[3]{\sqrt[3]{x}}\right) \cdot x + \log \left(\sqrt[3]{{x}^{\frac{1}{3}} \cdot \sqrt[3]{x}}\right) \cdot x\right)\]
x \cdot \log x
↓
\log \left(\sqrt[3]{x}\right) \cdot \left(x + x\right) + \left(\log \left(\sqrt[3]{\sqrt[3]{x}}\right) \cdot x + \log \left(\sqrt[3]{{x}^{\frac{1}{3}} \cdot \sqrt[3]{x}}\right) \cdot x\right)
double f(double x) {
        double r940689 = x;
        double r940690 = log(r940689);
        double r940691 = r940689 * r940690;
        return r940691;
}
↓
double f(double x) {
        double r940692 = x;
        double r940693 = cbrt(r940692);
        double r940694 = log(r940693);
        double r940695 = r940692 + r940692;
        double r940696 = r940694 * r940695;
        double r940697 = cbrt(r940693);
        double r940698 = log(r940697);
        double r940699 = r940698 * r940692;
        double r940700 = 0.3333333333333333;
        double r940701 = pow(r940692, r940700);
        double r940702 = r940701 * r940693;
        double r940703 = cbrt(r940702);
        double r940704 = log(r940703);
        double r940705 = r940704 * r940692;
        double r940706 = r940699 + r940705;
        double r940707 = r940696 + r940706;
        return r940707;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[x \cdot \log x\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.3

    \[\leadsto x \cdot \log \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)}\]

  4. Applied log-prod0.4

    \[\leadsto x \cdot \color{blue}{\left(\log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right)\right)}\]

  5. Applied distribute-lft-in0.4

    \[\leadsto \color{blue}{x \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + x \cdot \log \left(\sqrt[3]{x}\right)}\]

  6. Simplified0.4

    \[\leadsto \color{blue}{\log \left(\sqrt[3]{x}\right) \cdot \left(x + x\right)} + x \cdot \log \left(\sqrt[3]{x}\right)\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.4

    \[\leadsto \log \left(\sqrt[3]{x}\right) \cdot \left(x + x\right) + x \cdot \log \left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}\right)\]

  9. Applied cbrt-prod0.4

    \[\leadsto \log \left(\sqrt[3]{x}\right) \cdot \left(x + x\right) + x \cdot \log \color{blue}{\left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)}\]

  10. Applied log-prod0.3

    \[\leadsto \log \left(\sqrt[3]{x}\right) \cdot \left(x + x\right) + x \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) + \log \left(\sqrt[3]{\sqrt[3]{x}}\right)\right)}\]

  11. Applied distribute-rgt-in0.3

    \[\leadsto \log \left(\sqrt[3]{x}\right) \cdot \left(x + x\right) + \color{blue}{\left(\log \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) \cdot x + \log \left(\sqrt[3]{\sqrt[3]{x}}\right) \cdot x\right)}\]
  12. Using strategy rm

  13. Applied pow1/30.3

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

  14. Final simplification0.3

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

Reproduce

herbie shell --seed 2019170 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  (* x (log x)))