Average Error: 0.3 → 0.3
Time: 18.6s
Precision: 64
\[x \cdot \log x\]
↓
\[\left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) \cdot x + \log \left(\sqrt[3]{{x}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{x}}\right) \cdot x\]
x \cdot \log x
↓
\left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) \cdot x + \log \left(\sqrt[3]{{x}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{x}}\right) \cdot x
double f(double x) {
        double r44268 = x;
        double r44269 = log(r44268);
        double r44270 = r44268 * r44269;
        return r44270;
}
↓
double f(double x) {
        double r44271 = 2.0;
        double r44272 = x;
        double r44273 = cbrt(r44272);
        double r44274 = log(r44273);
        double r44275 = r44271 * r44274;
        double r44276 = r44275 * r44272;
        double r44277 = 0.6666666666666666;
        double r44278 = pow(r44272, r44277);
        double r44279 = cbrt(r44278);
        double r44280 = cbrt(r44273);
        double r44281 = r44279 * r44280;
        double r44282 = log(r44281);
        double r44283 = r44282 * r44272;
        double r44284 = r44276 + r44283;
        return r44284;
}

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

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

  7. Simplified0.4

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

  9. Applied add-cube-cbrt0.4

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

  10. Applied cbrt-prod0.4

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))