Average Error: 0.4 → 0.4
Time: 14.8s
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 r61626 = 1.0;
        double r61627 = k;
        double r61628 = sqrt(r61627);
        double r61629 = r61626 / r61628;
        double r61630 = 2.0;
        double r61631 = atan2(1.0, 0.0);
        double r61632 = r61630 * r61631;
        double r61633 = n;
        double r61634 = r61632 * r61633;
        double r61635 = r61626 - r61627;
        double r61636 = r61635 / r61630;
        double r61637 = pow(r61634, r61636);
        double r61638 = r61629 * r61637;
        return r61638;
}
↓
double f(double k, double n) {
        double r61639 = 2.0;
        double r61640 = atan2(1.0, 0.0);
        double r61641 = r61639 * r61640;
        double r61642 = n;
        double r61643 = r61641 * r61642;
        double r61644 = 2.0;
        double r61645 = 1.0;
        double r61646 = k;
        double r61647 = r61645 - r61646;
        double r61648 = r61647 / r61639;
        double r61649 = r61648 / r61644;
        double r61650 = r61644 * r61649;
        double r61651 = pow(r61643, r61650);
        double r61652 = sqrt(r61646);
        double r61653 = r61645 / r61652;
        double r61654 = r61651 * r61653;
        return r61654;
}

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 2019304 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))