Average Error: 0.3 → 0.4
Time: 6.1s
Precision: 64
\[x \cdot \log x\]
↓
\[x \cdot \left(2 \cdot \log \left({\left(\frac{1}{x}\right)}^{\frac{-1}{3}}\right)\right) + x \cdot \log \left(\sqrt[3]{x}\right)\]
x \cdot \log x
↓
x \cdot \left(2 \cdot \log \left({\left(\frac{1}{x}\right)}^{\frac{-1}{3}}\right)\right) + x \cdot \log \left(\sqrt[3]{x}\right)
double f(double x) {
        double r46090 = x;
        double r46091 = log(r46090);
        double r46092 = r46090 * r46091;
        return r46092;
}
↓
double f(double x) {
        double r46093 = x;
        double r46094 = 2.0;
        double r46095 = 1.0;
        double r46096 = r46095 / r46093;
        double r46097 = -0.3333333333333333;
        double r46098 = pow(r46096, r46097);
        double r46099 = log(r46098);
        double r46100 = r46094 * r46099;
        double r46101 = r46093 * r46100;
        double r46102 = cbrt(r46093);
        double r46103 = log(r46102);
        double r46104 = r46093 * r46103;
        double r46105 = r46101 + r46104;
        return r46105;
}

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

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

  7. Taylor expanded around inf 0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))