Average Error: 0.5 → 0.5
Time: 12.5s
Precision: binary64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)} \]
↓
\[\frac{{\left({\left(2 \cdot \left(n \cdot \pi\right)\right)}^{\left(1 - k\right)}\right)}^{0.5}}{\sqrt{k}} \]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{{\left({\left(2 \cdot \left(n \cdot \pi\right)\right)}^{\left(1 - k\right)}\right)}^{0.5}}{\sqrt{k}}

(FPCore (k n)
 :precision binary64
 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
↓
(FPCore (k n)
 :precision binary64
 (/ (pow (pow (* 2.0 (* n PI)) (- 1.0 k)) 0.5) (sqrt k)))
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 pow(pow((2.0 * (n * ((double) M_PI))), (1.0 - k)), 0.5) / 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. Simplified0.5

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

  4. Applied div-inv_binary640.5

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

  5. Applied pow-unpow_binary640.5

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

  6. Simplified0.5

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

  7. Final simplification0.5

    \[\leadsto \frac{{\left({\left(2 \cdot \left(n \cdot \pi\right)\right)}^{\left(1 - k\right)}\right)}^{0.5}}{\sqrt{k}} \]

Reproduce

herbie shell --seed 2021202 
(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))))