Average Error: 0.4 → 0.3
Time: 23.4s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{{\left(\left(n \cdot 2\right) \cdot \pi\right)}^{\left(\frac{1}{2} - \frac{k}{2}\right)}}{\sqrt{k}}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{{\left(\left(n \cdot 2\right) \cdot \pi\right)}^{\left(\frac{1}{2} - \frac{k}{2}\right)}}{\sqrt{k}}
double f(double k, double n) {
        double r1944444 = 1.0;
        double r1944445 = k;
        double r1944446 = sqrt(r1944445);
        double r1944447 = r1944444 / r1944446;
        double r1944448 = 2.0;
        double r1944449 = atan2(1.0, 0.0);
        double r1944450 = r1944448 * r1944449;
        double r1944451 = n;
        double r1944452 = r1944450 * r1944451;
        double r1944453 = r1944444 - r1944445;
        double r1944454 = r1944453 / r1944448;
        double r1944455 = pow(r1944452, r1944454);
        double r1944456 = r1944447 * r1944455;
        return r1944456;
}
↓
double f(double k, double n) {
        double r1944457 = n;
        double r1944458 = 2.0;
        double r1944459 = r1944457 * r1944458;
        double r1944460 = atan2(1.0, 0.0);
        double r1944461 = r1944459 * r1944460;
        double r1944462 = 0.5;
        double r1944463 = k;
        double r1944464 = r1944463 / r1944458;
        double r1944465 = r1944462 - r1944464;
        double r1944466 = pow(r1944461, r1944465);
        double r1944467 = sqrt(r1944463);
        double r1944468 = r1944466 / r1944467;
        return r1944468;
}

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. Simplified0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2019154 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))