Average Error: 0.4 → 0.4
Time: 25.6s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(2 \cdot \frac{\frac{1 - k}{2}}{2}\right)} \cdot \frac{1}{\sqrt{k}}\]
\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(2 \cdot \frac{\frac{1 - k}{2}}{2}\right)} \cdot \frac{1}{\sqrt{k}}
double f(double k, double n) {
        double r83617 = 1.0;
        double r83618 = k;
        double r83619 = sqrt(r83618);
        double r83620 = r83617 / r83619;
        double r83621 = 2.0;
        double r83622 = atan2(1.0, 0.0);
        double r83623 = r83621 * r83622;
        double r83624 = n;
        double r83625 = r83623 * r83624;
        double r83626 = r83617 - r83618;
        double r83627 = r83626 / r83621;
        double r83628 = pow(r83625, r83627);
        double r83629 = r83620 * r83628;
        return r83629;
}
↓
double f(double k, double n) {
        double r83630 = 2.0;
        double r83631 = atan2(1.0, 0.0);
        double r83632 = r83630 * r83631;
        double r83633 = n;
        double r83634 = r83632 * r83633;
        double r83635 = 2.0;
        double r83636 = 1.0;
        double r83637 = k;
        double r83638 = r83636 - r83637;
        double r83639 = r83638 / r83630;
        double r83640 = r83639 / r83635;
        double r83641 = r83635 * r83640;
        double r83642 = pow(r83634, r83641);
        double r83643 = sqrt(r83637);
        double r83644 = r83636 / r83643;
        double r83645 = r83642 * r83644;
        return r83645;
}

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-pow0.4

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

  4. Applied associate-*r*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019297 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))