Average Error: 0.4 → 0.4
Time: 8.3s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[1 \cdot {\left(\frac{\sqrt{k}}{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}\right)}^{\left(-1\right)}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
1 \cdot {\left(\frac{\sqrt{k}}{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}\right)}^{\left(-1\right)}
double code(double k, double n) {
	return ((1.0 / sqrt(k)) * pow(((2.0 * ((double) M_PI)) * n), ((1.0 - k) / 2.0)));
}
↓
double code(double k, double n) {
	return (1.0 * pow((sqrt(k) / pow(((2.0 * ((double) M_PI)) * n), ((1.0 - k) / 2.0))), -1.0));
}

Error

Bits error versus k

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
  2. Using strategy rm

  3. Applied div-inv0.4

    \[\leadsto \color{blue}{\left(1 \cdot \frac{1}{\sqrt{k}}\right)} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]

  4. Applied associate-*l*0.4

    \[\leadsto \color{blue}{1 \cdot \left(\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\right)}\]

  5. Simplified0.3

    \[\leadsto 1 \cdot \color{blue}{\frac{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}}\]
  6. Using strategy rm

  7. Applied clear-num0.4

    \[\leadsto 1 \cdot \color{blue}{\frac{1}{\frac{\sqrt{k}}{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}}}\]
  8. Using strategy rm

  9. Applied pow10.4

    \[\leadsto 1 \cdot \frac{1}{\color{blue}{{\left(\frac{\sqrt{k}}{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}\right)}^{1}}}\]

  10. Applied pow-flip0.4

    \[\leadsto 1 \cdot \color{blue}{{\left(\frac{\sqrt{k}}{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}\right)}^{\left(-1\right)}}\]

  11. Final simplification0.4

    \[\leadsto 1 \cdot {\left(\frac{\sqrt{k}}{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}\right)}^{\left(-1\right)}\]

Reproduce

herbie shell --seed 2020053 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))