Average Error: 0.3 → 0.3
Time: 2.1s
Precision: binary64
\[x \cdot \log x\]
↓
\[x \cdot \left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) + \left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{x}}\right)\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{x}}\right)\right)\]
x \cdot \log x
↓
x \cdot \left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) + \left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{x}}\right)\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{x}}\right)\right)
(FPCore (x) :precision binary64 (* x (log x)))
↓
(FPCore (x)
 :precision binary64
 (+
  (* x (* (log (cbrt x)) 2.0))
  (+ (* x (* 2.0 (log (cbrt (cbrt x))))) (* x (log (cbrt (cbrt x)))))))
double code(double x) {
	return ((double) (x * ((double) log(x))));
}
↓
double code(double x) {
	return ((double) (((double) (x * ((double) (((double) log(((double) cbrt(x)))) * 2.0)))) + ((double) (((double) (x * ((double) (2.0 * ((double) log(((double) cbrt(((double) cbrt(x)))))))))) + ((double) (x * ((double) log(((double) cbrt(((double) cbrt(x))))))))))));
}

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

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

  8. Applied add-cube-cbrt0.4

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

  9. Applied log-prod0.3

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

  10. Applied distribute-lft-in0.3

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2020198 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))