Average Error: 0.3 → 0.3
Time: 14.7s
Precision: 64
\[x \cdot \log x\]
↓
\[\left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) \cdot x + x \cdot \log \left({\left(\frac{1}{x}\right)}^{\frac{-1}{3}}\right)\]
x \cdot \log x
↓
\left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) \cdot x + x \cdot \log \left({\left(\frac{1}{x}\right)}^{\frac{-1}{3}}\right)
double f(double x) {
        double r46970 = x;
        double r46971 = log(r46970);
        double r46972 = r46970 * r46971;
        return r46972;
}
↓
double f(double x) {
        double r46973 = x;
        double r46974 = cbrt(r46973);
        double r46975 = log(r46974);
        double r46976 = 2.0;
        double r46977 = r46975 * r46976;
        double r46978 = r46977 * r46973;
        double r46979 = 1.0;
        double r46980 = r46979 / r46973;
        double r46981 = -0.3333333333333333;
        double r46982 = pow(r46980, r46981);
        double r46983 = log(r46982);
        double r46984 = r46973 * r46983;
        double r46985 = r46978 + r46984;
        return r46985;
}

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. Taylor expanded around inf 0.3

    \[\leadsto x \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) + x \cdot \log \color{blue}{\left({\left(\frac{1}{x}\right)}^{\frac{-1}{3}}\right)}\]

  8. Final simplification0.3

    \[\leadsto \left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) \cdot x + x \cdot \log \left({\left(\frac{1}{x}\right)}^{\frac{-1}{3}}\right)\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  (* x (log x)))