Average Error: 0.3 → 0.3
Time: 3.6s
Precision: 64
\[x \cdot \log x\]
↓
\[x \cdot \log \left(\sqrt{x}\right) + \left(x \cdot \log \left(\sqrt{\sqrt{x}}\right) + x \cdot \log \left(\sqrt{\sqrt{x}}\right)\right)\]
x \cdot \log x
↓
x \cdot \log \left(\sqrt{x}\right) + \left(x \cdot \log \left(\sqrt{\sqrt{x}}\right) + x \cdot \log \left(\sqrt{\sqrt{x}}\right)\right)
double code(double x) {
	return (x * log(x));
}
↓
double code(double x) {
	return ((x * log(sqrt(x))) + ((x * log(sqrt(sqrt(x)))) + (x * log(sqrt(sqrt(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-sqr-sqrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  7. Applied add-sqr-sqrt0.3

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

  8. Applied sqrt-prod0.3

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

  9. Applied log-prod0.3

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

  10. Applied distribute-lft-in0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2020058 +o rules:numerics
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))