Average Error: 0.4 → 0.4
Time: 27.4s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\sqrt{k}} \cdot {\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{1 - k}{2}\right)}\]
\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(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{1 - k}{2}\right)}
double f(double k, double n) {
        double r3381907 = 1.0;
        double r3381908 = k;
        double r3381909 = sqrt(r3381908);
        double r3381910 = r3381907 / r3381909;
        double r3381911 = 2.0;
        double r3381912 = atan2(1.0, 0.0);
        double r3381913 = r3381911 * r3381912;
        double r3381914 = n;
        double r3381915 = r3381913 * r3381914;
        double r3381916 = r3381907 - r3381908;
        double r3381917 = r3381916 / r3381911;
        double r3381918 = pow(r3381915, r3381917);
        double r3381919 = r3381910 * r3381918;
        return r3381919;
}
↓
double f(double k, double n) {
        double r3381920 = 1.0;
        double r3381921 = k;
        double r3381922 = sqrt(r3381921);
        double r3381923 = r3381920 / r3381922;
        double r3381924 = n;
        double r3381925 = 2.0;
        double r3381926 = atan2(1.0, 0.0);
        double r3381927 = r3381925 * r3381926;
        double r3381928 = r3381924 * r3381927;
        double r3381929 = r3381920 - r3381921;
        double r3381930 = r3381929 / r3381925;
        double r3381931 = pow(r3381928, r3381930);
        double r3381932 = r3381923 * r3381931;
        return r3381932;
}

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019163 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))