Average Error: 0.3 → 0.3
Time: 42.4s
Precision: 64
\[x \cdot \log x\]
↓
\[\log \left({x}^{\frac{1}{3}}\right) \cdot x + \left(x \cdot \log \left(\sqrt[3]{x}\right) + x \cdot \log \left(\sqrt[3]{x}\right)\right)\]
x \cdot \log x
↓
\log \left({x}^{\frac{1}{3}}\right) \cdot x + \left(x \cdot \log \left(\sqrt[3]{x}\right) + x \cdot \log \left(\sqrt[3]{x}\right)\right)
double f(double x) {
        double r962051 = x;
        double r962052 = log(r962051);
        double r962053 = r962051 * r962052;
        return r962053;
}
↓
double f(double x) {
        double r962054 = x;
        double r962055 = 0.3333333333333333;
        double r962056 = pow(r962054, r962055);
        double r962057 = log(r962056);
        double r962058 = r962057 * r962054;
        double r962059 = cbrt(r962054);
        double r962060 = log(r962059);
        double r962061 = r962054 * r962060;
        double r962062 = r962061 + r962061;
        double r962063 = r962058 + r962062;
        return r962063;
}

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

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

  7. Simplified0.4

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

  9. Applied pow1/30.3

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

  10. Final simplification0.3

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

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)))