Average Error: 0.3 → 0.3
Time: 5.9s
Precision: 64
\[x \cdot \log x\]
↓
\[x \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) + \left(x \cdot \log \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{x}}\right)\right)\]
x \cdot \log x
↓
x \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) + \left(x \cdot \log \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{x}}\right)\right)
double f(double x) {
        double r37622 = x;
        double r37623 = log(r37622);
        double r37624 = r37622 * r37623;
        return r37624;
}
↓
double f(double x) {
        double r37625 = x;
        double r37626 = 2.0;
        double r37627 = cbrt(r37625);
        double r37628 = log(r37627);
        double r37629 = r37626 * r37628;
        double r37630 = r37625 * r37629;
        double r37631 = r37627 * r37627;
        double r37632 = cbrt(r37631);
        double r37633 = log(r37632);
        double r37634 = r37625 * r37633;
        double r37635 = cbrt(r37627);
        double r37636 = log(r37635);
        double r37637 = r37625 * r37636;
        double r37638 = r37634 + r37637;
        double r37639 = r37630 + r37638;
        return r37639;
}

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

    \[\leadsto \color{blue}{x \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right)} + x \cdot \log \left(\sqrt[3]{x}\right)\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.4

    \[\leadsto x \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) + x \cdot \log \left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}\right)\]

  9. Applied cbrt-prod0.4

    \[\leadsto x \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) + x \cdot \log \color{blue}{\left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)}\]

  10. Applied log-prod0.3

    \[\leadsto x \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) + x \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) + \log \left(\sqrt[3]{\sqrt[3]{x}}\right)\right)}\]

  11. Applied distribute-lft-in0.3

    \[\leadsto x \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) + \color{blue}{\left(x \cdot \log \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{x}}\right)\right)}\]

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2020024 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))