Average Error: 0.4 → 0.4
Time: 2.5m
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
\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(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
double f(double k, double n) {
        double r17219721 = 1.0;
        double r17219722 = k;
        double r17219723 = sqrt(r17219722);
        double r17219724 = r17219721 / r17219723;
        double r17219725 = 2.0;
        double r17219726 = atan2(1.0, 0.0);
        double r17219727 = r17219725 * r17219726;
        double r17219728 = n;
        double r17219729 = r17219727 * r17219728;
        double r17219730 = r17219721 - r17219722;
        double r17219731 = r17219730 / r17219725;
        double r17219732 = pow(r17219729, r17219731);
        double r17219733 = r17219724 * r17219732;
        return r17219733;
}
↓
double f(double k, double n) {
        double r17219734 = 1.0;
        double r17219735 = k;
        double r17219736 = sqrt(r17219735);
        double r17219737 = r17219734 / r17219736;
        double r17219738 = atan2(1.0, 0.0);
        double r17219739 = 2.0;
        double r17219740 = r17219738 * r17219739;
        double r17219741 = n;
        double r17219742 = r17219740 * r17219741;
        double r17219743 = r17219734 - r17219735;
        double r17219744 = r17219743 / r17219739;
        double r17219745 = pow(r17219742, r17219744);
        double r17219746 = r17219737 * r17219745;
        return r17219746;
}

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. Simplified0.3

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

  4. Applied div-inv0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019104 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))