Average Error: 0.3 → 0.3
Time: 10.0s
Precision: 64
\[x \cdot \log x\]
↓
\[\left(\log \left(\sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right)\right) \cdot x + \left(\left(\frac{1}{9} \cdot \log x\right) \cdot x + \left(\frac{1}{9} \cdot \log x\right) \cdot \left(x + x\right)\right)\]
x \cdot \log x
↓
\left(\log \left(\sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right)\right) \cdot x + \left(\left(\frac{1}{9} \cdot \log x\right) \cdot x + \left(\frac{1}{9} \cdot \log x\right) \cdot \left(x + x\right)\right)
double f(double x) {
        double r432562 = x;
        double r432563 = log(r432562);
        double r432564 = r432562 * r432563;
        return r432564;
}
↓
double f(double x) {
        double r432565 = x;
        double r432566 = cbrt(r432565);
        double r432567 = log(r432566);
        double r432568 = r432567 + r432567;
        double r432569 = r432568 * r432565;
        double r432570 = 0.1111111111111111;
        double r432571 = log(r432565);
        double r432572 = r432570 * r432571;
        double r432573 = r432572 * r432565;
        double r432574 = r432565 + r432565;
        double r432575 = r432572 * r432574;
        double r432576 = r432573 + r432575;
        double r432577 = r432569 + r432576;
        return r432577;
}

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

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

  8. Applied pow1/30.3

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

  10. Applied add-cube-cbrt0.3

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

  11. Applied unpow-prod-down0.3

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

  12. Applied log-prod0.3

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

  13. Applied distribute-lft-in0.3

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

  14. Simplified0.3

    \[\leadsto \left(\log \left(\sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right)\right) \cdot x + \left(\color{blue}{\left(\frac{1}{9} \cdot \log x\right) \cdot \left(x + x\right)} + x \cdot \log \left({\left(\sqrt[3]{x}\right)}^{\frac{1}{3}}\right)\right)\]

  15. Simplified0.3

    \[\leadsto \left(\log \left(\sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right)\right) \cdot x + \left(\left(\frac{1}{9} \cdot \log x\right) \cdot \left(x + x\right) + \color{blue}{\left(\frac{1}{9} \cdot \log x\right) \cdot x}\right)\]

  16. Final simplification0.3

    \[\leadsto \left(\log \left(\sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right)\right) \cdot x + \left(\left(\frac{1}{9} \cdot \log x\right) \cdot x + \left(\frac{1}{9} \cdot \log x\right) \cdot \left(x + x\right)\right)\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  (* x (log x)))