Average Error: 0.3 → 0.3
Time: 4.5s
Precision: binary64
\[x \cdot \log x\]
↓
\[x \cdot \left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) + x \cdot \log \left({x}^{0.3333333333333333}\right)\]
x \cdot \log x
↓
x \cdot \left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) + x \cdot \log \left({x}^{0.3333333333333333}\right)
(FPCore (x) :precision binary64 (* x (log x)))
↓
(FPCore (x)
 :precision binary64
 (+ (* x (* (log (cbrt x)) 2.0)) (* x (log (pow x 0.3333333333333333)))))
double code(double x) {
	return x * log(x);
}
↓
double code(double x) {
	return (x * (log(cbrt(x)) * 2.0)) + (x * log(pow(x, 0.3333333333333333)));
}

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 pow1/3_binary64_5010.3

    \[\leadsto x \cdot \left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) + x \cdot \log \color{blue}{\left({x}^{0.3333333333333333}\right)}\]

  10. Final simplification0.3

    \[\leadsto x \cdot \left(\log \left(\sqrt[3]{x}\right) \cdot 2\right) + x \cdot \log \left({x}^{0.3333333333333333}\right)\]

Reproduce

herbie shell --seed 2021093 
(FPCore (x)
  :name "Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2"
  :precision binary64
  (* x (log x)))