Average Error: 0.4 → 0.4
Time: 31.9s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
\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(\left(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
double f(double k, double n) {
        double r3163332 = 1.0;
        double r3163333 = k;
        double r3163334 = sqrt(r3163333);
        double r3163335 = r3163332 / r3163334;
        double r3163336 = 2.0;
        double r3163337 = atan2(1.0, 0.0);
        double r3163338 = r3163336 * r3163337;
        double r3163339 = n;
        double r3163340 = r3163338 * r3163339;
        double r3163341 = r3163332 - r3163333;
        double r3163342 = r3163341 / r3163336;
        double r3163343 = pow(r3163340, r3163342);
        double r3163344 = r3163335 * r3163343;
        return r3163344;
}
↓
double f(double k, double n) {
        double r3163345 = 1.0;
        double r3163346 = k;
        double r3163347 = sqrt(r3163346);
        double r3163348 = r3163345 / r3163347;
        double r3163349 = atan2(1.0, 0.0);
        double r3163350 = 2.0;
        double r3163351 = r3163349 * r3163350;
        double r3163352 = n;
        double r3163353 = r3163351 * r3163352;
        double r3163354 = r3163345 - r3163346;
        double r3163355 = r3163354 / r3163350;
        double r3163356 = pow(r3163353, r3163355);
        double r3163357 = r3163348 * r3163356;
        return r3163357;
}

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 div-inv0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))