Average Error: 0.4 → 0.4
Time: 33.3s
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 r2990174 = 1.0;
        double r2990175 = k;
        double r2990176 = sqrt(r2990175);
        double r2990177 = r2990174 / r2990176;
        double r2990178 = 2.0;
        double r2990179 = atan2(1.0, 0.0);
        double r2990180 = r2990178 * r2990179;
        double r2990181 = n;
        double r2990182 = r2990180 * r2990181;
        double r2990183 = r2990174 - r2990175;
        double r2990184 = r2990183 / r2990178;
        double r2990185 = pow(r2990182, r2990184);
        double r2990186 = r2990177 * r2990185;
        return r2990186;
}
↓
double f(double k, double n) {
        double r2990187 = 1.0;
        double r2990188 = k;
        double r2990189 = sqrt(r2990188);
        double r2990190 = r2990187 / r2990189;
        double r2990191 = n;
        double r2990192 = 2.0;
        double r2990193 = atan2(1.0, 0.0);
        double r2990194 = r2990192 * r2990193;
        double r2990195 = r2990191 * r2990194;
        double r2990196 = r2990187 - r2990188;
        double r2990197 = r2990196 / r2990192;
        double r2990198 = pow(r2990195, r2990197);
        double r2990199 = r2990190 * r2990198;
        return r2990199;
}

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 2019146 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))