Average Error: 0.3 → 0.3
Time: 17.2s
Precision: 64
\[x \cdot \log x\]
↓
\[\left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) \cdot x + \log \left(\sqrt[3]{{x}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{x}}\right) \cdot x\]
x \cdot \log x
↓
\left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) \cdot x + \log \left(\sqrt[3]{{x}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{x}}\right) \cdot x
double f(double x) {
        double r36973 = x;
        double r36974 = log(r36973);
        double r36975 = r36973 * r36974;
        return r36975;
}
↓
double f(double x) {
        double r36976 = 2.0;
        double r36977 = x;
        double r36978 = cbrt(r36977);
        double r36979 = log(r36978);
        double r36980 = r36976 * r36979;
        double r36981 = r36980 * r36977;
        double r36982 = 0.6666666666666666;
        double r36983 = pow(r36977, r36982);
        double r36984 = cbrt(r36983);
        double r36985 = cbrt(r36978);
        double r36986 = r36984 * r36985;
        double r36987 = log(r36986);
        double r36988 = r36987 * r36977;
        double r36989 = r36981 + r36988;
        return r36989;
}

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

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

  7. Simplified0.4

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

  9. Applied add-cube-cbrt0.4

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

  10. Applied cbrt-prod0.4

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))