Average Error: 0.3 → 0.3
Time: 17.4s
Precision: 64
\[x \cdot \log x\]
↓
\[\log \left({x}^{\frac{1}{3}}\right) \cdot x + \left(\log \left(\sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right)\right) \cdot x\]
x \cdot \log x
↓
\log \left({x}^{\frac{1}{3}}\right) \cdot x + \left(\log \left(\sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right)\right) \cdot x
double f(double x) {
        double r1081424 = x;
        double r1081425 = log(r1081424);
        double r1081426 = r1081424 * r1081425;
        return r1081426;
}
↓
double f(double x) {
        double r1081427 = x;
        double r1081428 = 0.3333333333333333;
        double r1081429 = pow(r1081427, r1081428);
        double r1081430 = log(r1081429);
        double r1081431 = r1081430 * r1081427;
        double r1081432 = cbrt(r1081427);
        double r1081433 = log(r1081432);
        double r1081434 = r1081433 + r1081433;
        double r1081435 = r1081434 * r1081427;
        double r1081436 = r1081431 + r1081435;
        return r1081436;
}

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

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

  8. Applied pow1/30.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  (* x (log x)))