Average Error: 0.3 → 0.4
Time: 7.4s
Precision: 64
\[x \cdot \log x\]
↓
\[x \cdot \left(\left(\log \left(\sqrt[3]{\sqrt[3]{x}}\right) \cdot 2 + \log \left(\sqrt[3]{x}\right)\right) + 2 \cdot \log \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right)\right)\]
x \cdot \log x
↓
x \cdot \left(\left(\log \left(\sqrt[3]{\sqrt[3]{x}}\right) \cdot 2 + \log \left(\sqrt[3]{x}\right)\right) + 2 \cdot \log \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right)\right)
double f(double x) {
        double r40359 = x;
        double r40360 = log(r40359);
        double r40361 = r40359 * r40360;
        return r40361;
}
↓
double f(double x) {
        double r40362 = x;
        double r40363 = cbrt(r40362);
        double r40364 = cbrt(r40363);
        double r40365 = log(r40364);
        double r40366 = 2.0;
        double r40367 = r40365 * r40366;
        double r40368 = log(r40363);
        double r40369 = r40367 + r40368;
        double r40370 = r40363 * r40363;
        double r40371 = cbrt(r40370);
        double r40372 = log(r40371);
        double r40373 = r40366 * r40372;
        double r40374 = r40369 + r40373;
        double r40375 = r40362 * r40374;
        return r40375;
}

Error

Bits error versus x

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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-lft-in0.4

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

  12. Applied distribute-rgt-in0.3

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

  13. Applied associate-+l+0.4

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

  14. Simplified0.3

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

  15. Final simplification0.4

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))