Average Error: 0.3 → 0.3
Time: 21.3s
Precision: 64
\[x \cdot \log x\]
↓
\[\log \left({x}^{\frac{1}{3}}\right) \cdot x + \log \left(\sqrt[3]{x}\right) \cdot \left(x + x\right)\]
x \cdot \log x
↓
\log \left({x}^{\frac{1}{3}}\right) \cdot x + \log \left(\sqrt[3]{x}\right) \cdot \left(x + x\right)
double f(double x) {
        double r867793 = x;
        double r867794 = log(r867793);
        double r867795 = r867793 * r867794;
        return r867795;
}
↓
double f(double x) {
        double r867796 = x;
        double r867797 = 0.3333333333333333;
        double r867798 = pow(r867796, r867797);
        double r867799 = log(r867798);
        double r867800 = r867799 * r867796;
        double r867801 = cbrt(r867796);
        double r867802 = log(r867801);
        double r867803 = r867796 + r867796;
        double r867804 = r867802 * r867803;
        double r867805 = r867800 + r867804;
        return r867805;
}

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-rgt-in0.4

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

  6. Simplified0.4

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

  8. Applied pow1/30.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  (* x (log x)))