Average Error: 0.3 → 0.3
Time: 4.5s
Precision: 64
\[x \cdot \log x\]
↓
\[x \cdot \left(\log \left(\sqrt{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) + \log \left(\sqrt{\sqrt[3]{x}}\right)\right) + x \cdot \log \left(\sqrt{x}\right)\]
x \cdot \log x
↓
x \cdot \left(\log \left(\sqrt{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) + \log \left(\sqrt{\sqrt[3]{x}}\right)\right) + x \cdot \log \left(\sqrt{x}\right)
double f(double x) {
        double r33401 = x;
        double r33402 = log(r33401);
        double r33403 = r33401 * r33402;
        return r33403;
}
↓
double f(double x) {
        double r33404 = x;
        double r33405 = cbrt(r33404);
        double r33406 = r33405 * r33405;
        double r33407 = sqrt(r33406);
        double r33408 = log(r33407);
        double r33409 = sqrt(r33405);
        double r33410 = log(r33409);
        double r33411 = r33408 + r33410;
        double r33412 = r33404 * r33411;
        double r33413 = sqrt(r33404);
        double r33414 = log(r33413);
        double r33415 = r33404 * r33414;
        double r33416 = r33412 + r33415;
        return r33416;
}

Error

Bits error versus x

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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

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

  8. Applied sqrt-prod0.3

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

  9. Applied log-prod0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020002 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))