Average Error: 0.3 → 0.3
Time: 4.4s
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 r34811 = x;
        double r34812 = log(r34811);
        double r34813 = r34811 * r34812;
        return r34813;
}
↓
double f(double x) {
        double r34814 = x;
        double r34815 = sqrt(r34814);
        double r34816 = log(r34815);
        double r34817 = r34814 * r34816;
        double r34818 = r34817 + r34817;
        return r34818;
}

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-lft-in0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020065 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))