Average Error: 0.3 → 0.3
Time: 10.1s
Precision: 64
\[x \cdot \log x\]
↓
\[\log \left(\sqrt[3]{x}\right) \cdot \left(x + x\right) + \left(\log \left(\sqrt[3]{\sqrt[3]{x}}\right) \cdot x + \log \left(\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right) \cdot x\right)\]
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]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right) \cdot x\right)
double f(double x) {
        double r350232 = x;
        double r350233 = log(r350232);
        double r350234 = r350232 * r350233;
        return r350234;
}
↓
double f(double x) {
        double r350235 = x;
        double r350236 = cbrt(r350235);
        double r350237 = log(r350236);
        double r350238 = r350235 + r350235;
        double r350239 = r350237 * r350238;
        double r350240 = cbrt(r350236);
        double r350241 = log(r350240);
        double r350242 = r350241 * r350235;
        double r350243 = r350240 * r350240;
        double r350244 = log(r350243);
        double r350245 = r350244 * r350235;
        double r350246 = r350242 + r350245;
        double r350247 = r350239 + r350246;
        return r350247;
}

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

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

  9. Applied log-prod0.3

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

  10. Applied distribute-rgt-in0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  (* x (log x)))