Average Error: 0.5 → 0.6
Time: 14.2s
Precision: binary64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{\left(1 \cdot {\left(2 \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)}\right) \cdot {n}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{\left(1 \cdot {\left(2 \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)}\right) \cdot {n}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}
double code(double k, double n) {
	return ((double) (((double) (1.0 / ((double) sqrt(k)))) * ((double) pow(((double) (((double) (2.0 * ((double) M_PI))) * n)), ((double) (((double) (1.0 - k)) / 2.0))))));
}
↓
double code(double k, double n) {
	return ((double) (((double) (((double) (1.0 * ((double) pow(((double) (2.0 * ((double) M_PI))), ((double) (((double) (1.0 - k)) / 2.0)))))) * ((double) pow(n, ((double) (((double) (1.0 - k)) / 2.0)))))) / ((double) sqrt(k))));
}

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 0.5

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

  3. Applied unpow-prod-down0.6

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

  4. Applied associate-*r*0.7

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

  6. Applied associate-*l/0.6

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

  7. Applied associate-*l/0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2020148 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))