Average Error: 0.4 → 0.4
Time: 31.1s
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 r2602576 = 1.0;
        double r2602577 = k;
        double r2602578 = sqrt(r2602577);
        double r2602579 = r2602576 / r2602578;
        double r2602580 = 2.0;
        double r2602581 = atan2(1.0, 0.0);
        double r2602582 = r2602580 * r2602581;
        double r2602583 = n;
        double r2602584 = r2602582 * r2602583;
        double r2602585 = r2602576 - r2602577;
        double r2602586 = r2602585 / r2602580;
        double r2602587 = pow(r2602584, r2602586);
        double r2602588 = r2602579 * r2602587;
        return r2602588;
}
↓
double f(double k, double n) {
        double r2602589 = 1.0;
        double r2602590 = k;
        double r2602591 = sqrt(r2602590);
        double r2602592 = r2602589 / r2602591;
        double r2602593 = n;
        double r2602594 = 2.0;
        double r2602595 = atan2(1.0, 0.0);
        double r2602596 = r2602594 * r2602595;
        double r2602597 = r2602593 * r2602596;
        double r2602598 = r2602589 - r2602590;
        double r2602599 = r2602598 / r2602594;
        double r2602600 = pow(r2602597, r2602599);
        double r2602601 = r2602592 * r2602600;
        return r2602601;
}

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 2019144 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))