Average Error: 0.3 → 0.4
Time: 16.9s
Precision: 64
\[x \cdot \log x\]
↓
\[\log \left({x}^{\frac{1}{3}}\right) \cdot \left(x + x\right) + \log \left(\sqrt[3]{x}\right) \cdot x\]
x \cdot \log x
↓
\log \left({x}^{\frac{1}{3}}\right) \cdot \left(x + x\right) + \log \left(\sqrt[3]{x}\right) \cdot x
double f(double x) {
        double r57114 = x;
        double r57115 = log(r57114);
        double r57116 = r57114 * r57115;
        return r57116;
}
↓
double f(double x) {
        double r57117 = x;
        double r57118 = 0.3333333333333333;
        double r57119 = pow(r57117, r57118);
        double r57120 = log(r57119);
        double r57121 = r57117 + r57117;
        double r57122 = r57120 * r57121;
        double r57123 = cbrt(r57117);
        double r57124 = log(r57123);
        double r57125 = r57124 * r57117;
        double r57126 = r57122 + r57125;
        return r57126;
}

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 pow1/30.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  (* x (log x)))