Average Error: 0.4 → 0.4
Time: 36.3s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\frac{\sqrt{k}}{{\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{1}{2} - \frac{k}{2}\right)}}}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{1}{\frac{\sqrt{k}}{{\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{1}{2} - \frac{k}{2}\right)}}}
double f(double k, double n) {
        double r3572745 = 1.0;
        double r3572746 = k;
        double r3572747 = sqrt(r3572746);
        double r3572748 = r3572745 / r3572747;
        double r3572749 = 2.0;
        double r3572750 = atan2(1.0, 0.0);
        double r3572751 = r3572749 * r3572750;
        double r3572752 = n;
        double r3572753 = r3572751 * r3572752;
        double r3572754 = r3572745 - r3572746;
        double r3572755 = r3572754 / r3572749;
        double r3572756 = pow(r3572753, r3572755);
        double r3572757 = r3572748 * r3572756;
        return r3572757;
}
↓
double f(double k, double n) {
        double r3572758 = 1.0;
        double r3572759 = k;
        double r3572760 = sqrt(r3572759);
        double r3572761 = n;
        double r3572762 = 2.0;
        double r3572763 = atan2(1.0, 0.0);
        double r3572764 = r3572762 * r3572763;
        double r3572765 = r3572761 * r3572764;
        double r3572766 = 0.5;
        double r3572767 = r3572759 / r3572762;
        double r3572768 = r3572766 - r3572767;
        double r3572769 = pow(r3572765, r3572768);
        double r3572770 = r3572760 / r3572769;
        double r3572771 = r3572758 / r3572770;
        return r3572771;
}

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. Simplified0.4

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

  4. Applied *-un-lft-identity0.4

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

  5. Applied associate-/l*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019142 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))