Average Error: 0.4 → 0.5
Time: 29.2s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\left(\frac{1}{\sqrt{k}} \cdot {\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{\frac{1 - k}{2}}{2}\right)}\right) \cdot {\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{\frac{1 - k}{2}}{2}\right)}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\left(\frac{1}{\sqrt{k}} \cdot {\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{\frac{1 - k}{2}}{2}\right)}\right) \cdot {\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{\frac{1 - k}{2}}{2}\right)}
double f(double k, double n) {
        double r4221426 = 1.0;
        double r4221427 = k;
        double r4221428 = sqrt(r4221427);
        double r4221429 = r4221426 / r4221428;
        double r4221430 = 2.0;
        double r4221431 = atan2(1.0, 0.0);
        double r4221432 = r4221430 * r4221431;
        double r4221433 = n;
        double r4221434 = r4221432 * r4221433;
        double r4221435 = r4221426 - r4221427;
        double r4221436 = r4221435 / r4221430;
        double r4221437 = pow(r4221434, r4221436);
        double r4221438 = r4221429 * r4221437;
        return r4221438;
}
↓
double f(double k, double n) {
        double r4221439 = 1.0;
        double r4221440 = k;
        double r4221441 = sqrt(r4221440);
        double r4221442 = r4221439 / r4221441;
        double r4221443 = n;
        double r4221444 = 2.0;
        double r4221445 = atan2(1.0, 0.0);
        double r4221446 = r4221444 * r4221445;
        double r4221447 = r4221443 * r4221446;
        double r4221448 = r4221439 - r4221440;
        double r4221449 = r4221448 / r4221444;
        double r4221450 = 2.0;
        double r4221451 = r4221449 / r4221450;
        double r4221452 = pow(r4221447, r4221451);
        double r4221453 = r4221442 * r4221452;
        double r4221454 = r4221453 * r4221452;
        return r4221454;
}

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. Using strategy rm

  3. Applied sqr-pow0.5

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

  4. Applied associate-*r*0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2019170 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))