Average Error: 0.3 → 0.3
Time: 2.6s
Precision: binary64
\[x \cdot \log x\]
↓
\[x \cdot \log \left(\sqrt{x}\right) + x \cdot \left(\log \left(\left|{x}^{0.3333333333333333}\right|\right) + \log \left(\sqrt{\sqrt[3]{x}}\right)\right)\]
x \cdot \log x
↓
x \cdot \log \left(\sqrt{x}\right) + x \cdot \left(\log \left(\left|{x}^{0.3333333333333333}\right|\right) + \log \left(\sqrt{\sqrt[3]{x}}\right)\right)
(FPCore (x) :precision binary64 (* x (log x)))
↓
(FPCore (x)
 :precision binary64
 (+
  (* x (log (sqrt x)))
  (* x (+ (log (fabs (pow x 0.3333333333333333))) (log (sqrt (cbrt x)))))))
double code(double x) {
	return x * log(x);
}
↓
double code(double x) {
	return (x * log(sqrt(x))) + (x * (log(fabs(pow(x, 0.3333333333333333))) + log(sqrt(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-sqr-sqrt_binary640.3

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

  4. Applied log-prod_binary640.3

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

  5. Applied distribute-rgt-in_binary640.3

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

  6. Simplified0.3

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

  7. Simplified0.3

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

  9. Applied add-cube-cbrt_binary640.3

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

  10. Applied sqrt-prod_binary640.3

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

  11. Applied log-prod_binary640.3

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

  12. Simplified0.3

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

  14. Applied pow1/3_binary640.3

    \[\leadsto x \cdot \log \left(\sqrt{x}\right) + x \cdot \left(\log \left(\left|\color{blue}{{x}^{0.3333333333333333}}\right|\right) + \log \left(\sqrt{\sqrt[3]{x}}\right)\right)\]

  15. Final simplification0.3

    \[\leadsto x \cdot \log \left(\sqrt{x}\right) + x \cdot \left(\log \left(\left|{x}^{0.3333333333333333}\right|\right) + \log \left(\sqrt{\sqrt[3]{x}}\right)\right)\]

Reproduce

herbie shell --seed 2020233 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))