Average Error: 0.4 → 0.4
Time: 3.3m
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\frac{1}{\frac{{\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}}}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{1}{\frac{1}{\frac{{\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}}}
double f(double k, double n) {
        double r30741272 = 1.0;
        double r30741273 = k;
        double r30741274 = sqrt(r30741273);
        double r30741275 = r30741272 / r30741274;
        double r30741276 = 2.0;
        double r30741277 = atan2(1.0, 0.0);
        double r30741278 = r30741276 * r30741277;
        double r30741279 = n;
        double r30741280 = r30741278 * r30741279;
        double r30741281 = r30741272 - r30741273;
        double r30741282 = r30741281 / r30741276;
        double r30741283 = pow(r30741280, r30741282);
        double r30741284 = r30741275 * r30741283;
        return r30741284;
}
↓
double f(double k, double n) {
        double r30741285 = 1.0;
        double r30741286 = n;
        double r30741287 = 2.0;
        double r30741288 = atan2(1.0, 0.0);
        double r30741289 = r30741287 * r30741288;
        double r30741290 = r30741286 * r30741289;
        double r30741291 = k;
        double r30741292 = r30741285 - r30741291;
        double r30741293 = r30741292 / r30741287;
        double r30741294 = pow(r30741290, r30741293);
        double r30741295 = sqrt(r30741291);
        double r30741296 = r30741294 / r30741295;
        double r30741297 = r30741285 / r30741296;
        double r30741298 = r30741285 / r30741297;
        return r30741298;
}

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

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

  4. Applied clear-num0.4

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

  6. Applied *-un-lft-identity0.4

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

  7. Applied associate-/l*0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019124 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))