Average Error: 0.3 → 0.3
Time: 4.3s
Precision: 64
\[x \cdot \log x\]
↓
\[\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right) + x \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right) + x \cdot \log \left(\sqrt{x}\right)\]
x \cdot \log x
↓
\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right) + x \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right) + x \cdot \log \left(\sqrt{x}\right)
double f(double x) {
        double r34784 = x;
        double r34785 = log(r34784);
        double r34786 = r34784 * r34785;
        return r34786;
}
↓
double f(double x) {
        double r34787 = x;
        double r34788 = 2.0;
        double r34789 = sqrt(r34787);
        double r34790 = cbrt(r34789);
        double r34791 = log(r34790);
        double r34792 = r34788 * r34791;
        double r34793 = r34787 * r34792;
        double r34794 = r34787 * r34791;
        double r34795 = r34793 + r34794;
        double r34796 = log(r34789);
        double r34797 = r34787 * r34796;
        double r34798 = r34795 + r34797;
        return r34798;
}

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. Using strategy rm

  7. Applied add-cube-cbrt0.3

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

  8. Applied log-prod0.3

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

  9. Applied distribute-lft-in0.3

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

  10. Simplified0.3

    \[\leadsto \left(\color{blue}{x \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right)} + x \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right) + x \cdot \log \left(\sqrt{x}\right)\]

  11. Final simplification0.3

    \[\leadsto \left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right) + x \cdot \log \left(\sqrt[3]{\sqrt{x}}\right)\right) + x \cdot \log \left(\sqrt{x}\right)\]

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))