Average Error: 0.3 → 0.3
Time: 18.1s
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 r43135 = x;
        double r43136 = log(r43135);
        double r43137 = r43135 * r43136;
        return r43137;
}
↓
double f(double x) {
        double r43138 = 2.0;
        double r43139 = x;
        double r43140 = cbrt(r43139);
        double r43141 = log(r43140);
        double r43142 = r43138 * r43141;
        double r43143 = r43142 * r43139;
        double r43144 = 0.6666666666666666;
        double r43145 = pow(r43139, r43144);
        double r43146 = cbrt(r43145);
        double r43147 = cbrt(r43140);
        double r43148 = r43146 * r43147;
        double r43149 = log(r43148);
        double r43150 = r43149 * r43139;
        double r43151 = r43143 + r43150;
        return r43151;
}

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 +o rules:numerics
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))