Average Error: 0.4 → 0.5
Time: 8.5s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\sqrt{\frac{1}{\sqrt{k}}} \cdot \left(\sqrt{\frac{1}{\sqrt{k}}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\right)\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\sqrt{\frac{1}{\sqrt{k}}} \cdot \left(\sqrt{\frac{1}{\sqrt{k}}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\right)
double f(double k, double n) {
        double r141753 = 1.0;
        double r141754 = k;
        double r141755 = sqrt(r141754);
        double r141756 = r141753 / r141755;
        double r141757 = 2.0;
        double r141758 = atan2(1.0, 0.0);
        double r141759 = r141757 * r141758;
        double r141760 = n;
        double r141761 = r141759 * r141760;
        double r141762 = r141753 - r141754;
        double r141763 = r141762 / r141757;
        double r141764 = pow(r141761, r141763);
        double r141765 = r141756 * r141764;
        return r141765;
}
↓
double f(double k, double n) {
        double r141766 = 1.0;
        double r141767 = k;
        double r141768 = sqrt(r141767);
        double r141769 = r141766 / r141768;
        double r141770 = sqrt(r141769);
        double r141771 = 2.0;
        double r141772 = atan2(1.0, 0.0);
        double r141773 = r141771 * r141772;
        double r141774 = n;
        double r141775 = r141773 * r141774;
        double r141776 = r141766 - r141767;
        double r141777 = r141776 / r141771;
        double r141778 = pow(r141775, r141777);
        double r141779 = r141770 * r141778;
        double r141780 = r141770 * r141779;
        return r141780;
}

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 add-sqr-sqrt0.5

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

  4. Applied associate-*l*0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2019362 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))