Average Error: 0.3 → 0.3
Time: 15.6s
Precision: 64
\[x \cdot \log x\]
↓
\[x \cdot \log \left(\sqrt{x}\right) + x \cdot \log \left(\sqrt{x}\right)\]
x \cdot \log x
↓
x \cdot \log \left(\sqrt{x}\right) + x \cdot \log \left(\sqrt{x}\right)
double f(double x) {
        double r1143458 = x;
        double r1143459 = log(r1143458);
        double r1143460 = r1143458 * r1143459;
        return r1143460;
}
↓
double f(double x) {
        double r1143461 = x;
        double r1143462 = sqrt(r1143461);
        double r1143463 = log(r1143462);
        double r1143464 = r1143461 * r1143463;
        double r1143465 = r1143464 + r1143464;
        return r1143465;
}

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-sqr-sqrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-rgt-in0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019192 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  (* x (log x)))