Average Error: 0.4 → 0.4
Time: 25.6s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)} \cdot {k}^{\frac{-1}{2}}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)} \cdot {k}^{\frac{-1}{2}}
double f(double k, double n) {
        double r1758420 = 1.0;
        double r1758421 = k;
        double r1758422 = sqrt(r1758421);
        double r1758423 = r1758420 / r1758422;
        double r1758424 = 2.0;
        double r1758425 = atan2(1.0, 0.0);
        double r1758426 = r1758424 * r1758425;
        double r1758427 = n;
        double r1758428 = r1758426 * r1758427;
        double r1758429 = r1758420 - r1758421;
        double r1758430 = r1758429 / r1758424;
        double r1758431 = pow(r1758428, r1758430);
        double r1758432 = r1758423 * r1758431;
        return r1758432;
}
↓
double f(double k, double n) {
        double r1758433 = 2.0;
        double r1758434 = atan2(1.0, 0.0);
        double r1758435 = r1758433 * r1758434;
        double r1758436 = n;
        double r1758437 = r1758435 * r1758436;
        double r1758438 = 1.0;
        double r1758439 = k;
        double r1758440 = r1758438 - r1758439;
        double r1758441 = r1758440 / r1758433;
        double r1758442 = pow(r1758437, r1758441);
        double r1758443 = -0.5;
        double r1758444 = pow(r1758439, r1758443);
        double r1758445 = r1758442 * r1758444;
        return r1758445;
}

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 pow1/20.4

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

  4. Applied pow-flip0.4

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

  5. Simplified0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019152 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))