Average Error: 0.4 → 0.4
Time: 31.5s
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 r5058347 = 1.0;
        double r5058348 = k;
        double r5058349 = sqrt(r5058348);
        double r5058350 = r5058347 / r5058349;
        double r5058351 = 2.0;
        double r5058352 = atan2(1.0, 0.0);
        double r5058353 = r5058351 * r5058352;
        double r5058354 = n;
        double r5058355 = r5058353 * r5058354;
        double r5058356 = r5058347 - r5058348;
        double r5058357 = r5058356 / r5058351;
        double r5058358 = pow(r5058355, r5058357);
        double r5058359 = r5058350 * r5058358;
        return r5058359;
}
↓
double f(double k, double n) {
        double r5058360 = 1.0;
        double r5058361 = k;
        double r5058362 = sqrt(r5058361);
        double r5058363 = r5058360 / r5058362;
        double r5058364 = n;
        double r5058365 = 2.0;
        double r5058366 = atan2(1.0, 0.0);
        double r5058367 = r5058365 * r5058366;
        double r5058368 = r5058364 * r5058367;
        double r5058369 = r5058360 - r5058361;
        double r5058370 = r5058369 / r5058365;
        double r5058371 = pow(r5058368, r5058370);
        double r5058372 = r5058363 * r5058371;
        return r5058372;
}

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 *-commutative0.4

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

  5. Applied *-commutative0.4

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

  6. 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 2019172 +o rules:numerics
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))