Average Error: 0.3 → 0.4
Time: 13.3s
Precision: 64
\[x \cdot \log x\]
↓
\[x \cdot \left(\log \left(\sqrt[3]{x}\right) + \frac{2}{3} \cdot \log x\right)\]
x \cdot \log x
↓
x \cdot \left(\log \left(\sqrt[3]{x}\right) + \frac{2}{3} \cdot \log x\right)
double f(double x) {
        double r53088 = x;
        double r53089 = log(r53088);
        double r53090 = r53088 * r53089;
        return r53090;
}
↓
double f(double x) {
        double r53091 = x;
        double r53092 = cbrt(r53091);
        double r53093 = log(r53092);
        double r53094 = 0.6666666666666666;
        double r53095 = log(r53091);
        double r53096 = r53094 * r53095;
        double r53097 = r53093 + r53096;
        double r53098 = r53091 * r53097;
        return r53098;
}

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

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

  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. Taylor expanded around inf 0.3

    \[\leadsto \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right) \cdot x + \log \color{blue}{\left({\left(\frac{1}{x}\right)}^{\frac{-1}{3}}\right)} \cdot x\]
  9. Using strategy rm

  10. Applied distribute-rgt-out0.4

    \[\leadsto \color{blue}{x \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right) + \log \left({\left(\frac{1}{x}\right)}^{\frac{-1}{3}}\right)\right)}\]

  11. Simplified0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2019209 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))