Average Error: 0.3 → 0.3
Time: 14.1s
Precision: 64
\[x \cdot \log x\]
↓
\[\left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) \cdot x + \log \left(\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{{x}^{\frac{2}{3}}}\right) \cdot x\]
x \cdot \log x
↓
\left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) \cdot x + \log \left(\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{{x}^{\frac{2}{3}}}\right) \cdot x
double f(double x) {
        double r43432 = x;
        double r43433 = log(r43432);
        double r43434 = r43432 * r43433;
        return r43434;
}
↓
double f(double x) {
        double r43435 = x;
        double r43436 = cbrt(r43435);
        double r43437 = log(r43436);
        double r43438 = 2.0;
        double r43439 = r43437 * r43438;
        double r43440 = r43439 * r43435;
        double r43441 = cbrt(r43436);
        double r43442 = 0.6666666666666666;
        double r43443 = pow(r43435, r43442);
        double r43444 = cbrt(r43443);
        double r43445 = r43441 * r43444;
        double r43446 = log(r43445);
        double r43447 = r43446 * r43435;
        double r43448 = r43440 + r43447;
        return r43448;
}

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. Simplified0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  (* x (log x)))