Average Error: 0.4 → 0.4
Time: 8.2s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
double f(double k, double n) {
        double r156719 = 1.0;
        double r156720 = k;
        double r156721 = sqrt(r156720);
        double r156722 = r156719 / r156721;
        double r156723 = 2.0;
        double r156724 = atan2(1.0, 0.0);
        double r156725 = r156723 * r156724;
        double r156726 = n;
        double r156727 = r156725 * r156726;
        double r156728 = r156719 - r156720;
        double r156729 = r156728 / r156723;
        double r156730 = pow(r156727, r156729);
        double r156731 = r156722 * r156730;
        return r156731;
}
↓
double f(double k, double n) {
        double r156732 = 1.0;
        double r156733 = k;
        double r156734 = sqrt(r156733);
        double r156735 = r156732 / r156734;
        double r156736 = 2.0;
        double r156737 = atan2(1.0, 0.0);
        double r156738 = r156736 * r156737;
        double r156739 = n;
        double r156740 = r156738 * r156739;
        double r156741 = r156732 - r156733;
        double r156742 = r156741 / r156736;
        double r156743 = pow(r156740, r156742);
        double r156744 = r156735 * r156743;
        return r156744;
}

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 sqr-pow0.5

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

  5. Applied pow-prod-up0.4

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

  6. Simplified0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019352 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))