Average Error: 0.4 → 0.4
Time: 29.9s
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 r3919041 = 1.0;
        double r3919042 = k;
        double r3919043 = sqrt(r3919042);
        double r3919044 = r3919041 / r3919043;
        double r3919045 = 2.0;
        double r3919046 = atan2(1.0, 0.0);
        double r3919047 = r3919045 * r3919046;
        double r3919048 = n;
        double r3919049 = r3919047 * r3919048;
        double r3919050 = r3919041 - r3919042;
        double r3919051 = r3919050 / r3919045;
        double r3919052 = pow(r3919049, r3919051);
        double r3919053 = r3919044 * r3919052;
        return r3919053;
}
↓
double f(double k, double n) {
        double r3919054 = 1.0;
        double r3919055 = k;
        double r3919056 = sqrt(r3919055);
        double r3919057 = r3919054 / r3919056;
        double r3919058 = n;
        double r3919059 = 2.0;
        double r3919060 = atan2(1.0, 0.0);
        double r3919061 = r3919059 * r3919060;
        double r3919062 = r3919058 * r3919061;
        double r3919063 = r3919054 - r3919055;
        double r3919064 = r3919063 / r3919059;
        double r3919065 = pow(r3919062, r3919064);
        double r3919066 = r3919057 * r3919065;
        return r3919066;
}

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))))