Average Error: 0.3 → 0.3
Time: 6.7s
Precision: 64
\[x \cdot \log x\]
↓
\[x \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) \cdot 2\right) + x \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{x}}\right) \cdot 2 + \log \left(\sqrt[3]{x}\right)\right)\]
x \cdot \log x
↓
x \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) \cdot 2\right) + x \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{x}}\right) \cdot 2 + \log \left(\sqrt[3]{x}\right)\right)
double f(double x) {
        double r50342 = x;
        double r50343 = log(r50342);
        double r50344 = r50342 * r50343;
        return r50344;
}
↓
double f(double x) {
        double r50345 = x;
        double r50346 = cbrt(r50345);
        double r50347 = r50346 * r50346;
        double r50348 = cbrt(r50347);
        double r50349 = log(r50348);
        double r50350 = 2.0;
        double r50351 = r50349 * r50350;
        double r50352 = r50345 * r50351;
        double r50353 = cbrt(r50346);
        double r50354 = log(r50353);
        double r50355 = r50354 * r50350;
        double r50356 = log(r50346);
        double r50357 = r50355 + r50356;
        double r50358 = r50345 * r50357;
        double r50359 = r50352 + r50358;
        return r50359;
}

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

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

  9. Applied cbrt-prod0.4

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

  10. Applied log-prod0.4

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

  11. Applied distribute-rgt-in0.4

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

  12. Applied distribute-lft-in0.3

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

  13. Applied associate-+l+0.4

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

  14. Simplified0.3

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

  15. Final simplification0.3

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))