Average Error: 0.4 → 0.4
Time: 30.9s
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 r3170113 = 1.0;
        double r3170114 = k;
        double r3170115 = sqrt(r3170114);
        double r3170116 = r3170113 / r3170115;
        double r3170117 = 2.0;
        double r3170118 = atan2(1.0, 0.0);
        double r3170119 = r3170117 * r3170118;
        double r3170120 = n;
        double r3170121 = r3170119 * r3170120;
        double r3170122 = r3170113 - r3170114;
        double r3170123 = r3170122 / r3170117;
        double r3170124 = pow(r3170121, r3170123);
        double r3170125 = r3170116 * r3170124;
        return r3170125;
}
↓
double f(double k, double n) {
        double r3170126 = 1.0;
        double r3170127 = k;
        double r3170128 = sqrt(r3170127);
        double r3170129 = r3170126 / r3170128;
        double r3170130 = n;
        double r3170131 = 2.0;
        double r3170132 = atan2(1.0, 0.0);
        double r3170133 = r3170131 * r3170132;
        double r3170134 = r3170130 * r3170133;
        double r3170135 = r3170126 - r3170127;
        double r3170136 = r3170135 / r3170131;
        double r3170137 = pow(r3170134, r3170136);
        double r3170138 = r3170129 * r3170137;
        return r3170138;
}

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 2019134 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))