Average Error: 0.4 → 0.5
Time: 8.2s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\sqrt{k}} \cdot \left({\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{\frac{1 - k}{2}}{2}\right)} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{\frac{1 - k}{2}}{2}\right)}\right)\]
\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(\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)
double f(double k, double n) {
        double r128498 = 1.0;
        double r128499 = k;
        double r128500 = sqrt(r128499);
        double r128501 = r128498 / r128500;
        double r128502 = 2.0;
        double r128503 = atan2(1.0, 0.0);
        double r128504 = r128502 * r128503;
        double r128505 = n;
        double r128506 = r128504 * r128505;
        double r128507 = r128498 - r128499;
        double r128508 = r128507 / r128502;
        double r128509 = pow(r128506, r128508);
        double r128510 = r128501 * r128509;
        return r128510;
}
↓
double f(double k, double n) {
        double r128511 = 1.0;
        double r128512 = k;
        double r128513 = sqrt(r128512);
        double r128514 = r128511 / r128513;
        double r128515 = 2.0;
        double r128516 = atan2(1.0, 0.0);
        double r128517 = r128515 * r128516;
        double r128518 = n;
        double r128519 = r128517 * r128518;
        double r128520 = r128511 - r128512;
        double r128521 = r128520 / r128515;
        double r128522 = 2.0;
        double r128523 = r128521 / r128522;
        double r128524 = pow(r128519, r128523);
        double r128525 = r128524 * r128524;
        double r128526 = r128514 * r128525;
        return r128526;
}

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. Final simplification0.5

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

Reproduce

herbie shell --seed 2020056 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))