Average Error: 0.3 → 0.3
Time: 21.3s
Precision: 64
\[x \cdot \log x\]
↓
\[\log \left(\sqrt[3]{x}\right) \cdot \left(x + x\right) + \left(\log \left(\sqrt[3]{\sqrt[3]{x}}\right) \cdot x + \log \left(\sqrt[3]{{x}^{\frac{1}{3}} \cdot \sqrt[3]{x}}\right) \cdot x\right)\]
x \cdot \log x
↓
\log \left(\sqrt[3]{x}\right) \cdot \left(x + x\right) + \left(\log \left(\sqrt[3]{\sqrt[3]{x}}\right) \cdot x + \log \left(\sqrt[3]{{x}^{\frac{1}{3}} \cdot \sqrt[3]{x}}\right) \cdot x\right)
double f(double x) {
        double r1169428 = x;
        double r1169429 = log(r1169428);
        double r1169430 = r1169428 * r1169429;
        return r1169430;
}
↓
double f(double x) {
        double r1169431 = x;
        double r1169432 = cbrt(r1169431);
        double r1169433 = log(r1169432);
        double r1169434 = r1169431 + r1169431;
        double r1169435 = r1169433 * r1169434;
        double r1169436 = cbrt(r1169432);
        double r1169437 = log(r1169436);
        double r1169438 = r1169437 * r1169431;
        double r1169439 = 0.3333333333333333;
        double r1169440 = pow(r1169431, r1169439);
        double r1169441 = r1169440 * r1169432;
        double r1169442 = cbrt(r1169441);
        double r1169443 = log(r1169442);
        double r1169444 = r1169443 * r1169431;
        double r1169445 = r1169438 + r1169444;
        double r1169446 = r1169435 + r1169445;
        return r1169446;
}

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

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

  8. Applied add-cube-cbrt0.4

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

  9. Applied cbrt-prod0.4

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

  10. Applied log-prod0.3

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

  11. Applied distribute-lft-in0.3

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

  13. Applied pow1/30.3

    \[\leadsto \log \left(\sqrt[3]{x}\right) \cdot \left(x + x\right) + \left(x \cdot \log \left(\sqrt[3]{\sqrt[3]{x} \cdot \color{blue}{{x}^{\frac{1}{3}}}}\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{x}}\right)\right)\]

  14. Final simplification0.3

    \[\leadsto \log \left(\sqrt[3]{x}\right) \cdot \left(x + x\right) + \left(\log \left(\sqrt[3]{\sqrt[3]{x}}\right) \cdot x + \log \left(\sqrt[3]{{x}^{\frac{1}{3}} \cdot \sqrt[3]{x}}\right) \cdot x\right)\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  (* x (log x)))