Average Error: 0.3 → 0.3
Time: 5.9s
Precision: 64
\[x \cdot \log x\]
↓
\[x \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) + \left(x \cdot \log \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{x}}\right)\right)\]
x \cdot \log x
↓
x \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) + \left(x \cdot \log \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{x}}\right)\right)
double f(double x) {
        double r37842 = x;
        double r37843 = log(r37842);
        double r37844 = r37842 * r37843;
        return r37844;
}
↓
double f(double x) {
        double r37845 = x;
        double r37846 = 2.0;
        double r37847 = cbrt(r37845);
        double r37848 = log(r37847);
        double r37849 = r37846 * r37848;
        double r37850 = r37845 * r37849;
        double r37851 = r37847 * r37847;
        double r37852 = cbrt(r37851);
        double r37853 = log(r37852);
        double r37854 = r37845 * r37853;
        double r37855 = cbrt(r37847);
        double r37856 = log(r37855);
        double r37857 = r37845 * r37856;
        double r37858 = r37854 + r37857;
        double r37859 = r37850 + r37858;
        return r37859;
}

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

    \[\leadsto \color{blue}{x \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right)} + x \cdot \log \left(\sqrt[3]{x}\right)\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.4

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

  9. Applied cbrt-prod0.4

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

  10. Applied log-prod0.3

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

  11. Applied distribute-lft-in0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))