Average Error: 0.3 → 0.3
Time: 2.7s
Precision: binary64
\[x \cdot \log x\]
↓
\[x \cdot \left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) + \left(x \cdot \log \left(\sqrt[3]{{x}^{0.6666666666666666}}\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{x}}\right)\right)\]
x \cdot \log x
↓
x \cdot \left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) + \left(x \cdot \log \left(\sqrt[3]{{x}^{0.6666666666666666}}\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 (log (cbrt (pow x 0.6666666666666666))))
   (* x (log (cbrt (cbrt x)))))))
double code(double x) {
	return x * log(x);
}
↓
double code(double x) {
	return (x * (log(cbrt(x)) * 2.0)) + ((x * log(cbrt(pow(x, 0.6666666666666666)))) + (x * log(cbrt(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-cbrt_binary64_4540.3

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

  4. Applied log-prod_binary64_5050.4

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

  5. Applied distribute-rgt-in_binary64_3690.4

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

  6. Simplified0.4

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

  7. Simplified0.4

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

  9. Applied add-cube-cbrt_binary64_4540.4

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

  10. Applied cbrt-prod_binary64_4500.4

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

  11. Applied log-prod_binary64_5050.3

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

  12. Applied distribute-rgt-in_binary64_3690.3

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

  13. Simplified0.3

    \[\leadsto x \cdot \left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) + \left(\color{blue}{x \cdot \log \left(\sqrt[3]{{x}^{0.6666666666666666}}\right)} + \log \left(\sqrt[3]{\sqrt[3]{x}}\right) \cdot x\right)\]

  14. Simplified0.3

    \[\leadsto x \cdot \left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) + \left(x \cdot \log \left(\sqrt[3]{{x}^{0.6666666666666666}}\right) + \color{blue}{x \cdot \log \left(\sqrt[3]{\sqrt[3]{x}}\right)}\right)\]

  15. Final simplification0.3

    \[\leadsto x \cdot \left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) + \left(x \cdot \log \left(\sqrt[3]{{x}^{0.6666666666666666}}\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{x}}\right)\right)\]

Reproduce

herbie shell --seed 2020355 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))