Average Error: 0.4 → 0.6
Time: 25.9s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\left(\frac{1}{\sqrt{k}} \cdot \left({2}^{\left(\frac{1 - k}{2}\right)} \cdot {\pi}^{\left(\frac{1 - k}{2}\right)}\right)\right) \cdot {n}^{\left(\frac{1 - k}{2}\right)}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\left(\frac{1}{\sqrt{k}} \cdot \left({2}^{\left(\frac{1 - k}{2}\right)} \cdot {\pi}^{\left(\frac{1 - k}{2}\right)}\right)\right) \cdot {n}^{\left(\frac{1 - k}{2}\right)}
double f(double k, double n) {
        double r79596 = 1.0;
        double r79597 = k;
        double r79598 = sqrt(r79597);
        double r79599 = r79596 / r79598;
        double r79600 = 2.0;
        double r79601 = atan2(1.0, 0.0);
        double r79602 = r79600 * r79601;
        double r79603 = n;
        double r79604 = r79602 * r79603;
        double r79605 = r79596 - r79597;
        double r79606 = r79605 / r79600;
        double r79607 = pow(r79604, r79606);
        double r79608 = r79599 * r79607;
        return r79608;
}
↓
double f(double k, double n) {
        double r79609 = 1.0;
        double r79610 = k;
        double r79611 = sqrt(r79610);
        double r79612 = r79609 / r79611;
        double r79613 = 2.0;
        double r79614 = r79609 - r79610;
        double r79615 = r79614 / r79613;
        double r79616 = pow(r79613, r79615);
        double r79617 = atan2(1.0, 0.0);
        double r79618 = pow(r79617, r79615);
        double r79619 = r79616 * r79618;
        double r79620 = r79612 * r79619;
        double r79621 = n;
        double r79622 = pow(r79621, r79615);
        double r79623 = r79620 * r79622;
        return r79623;
}

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 unpow-prod-down0.6

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

  4. Applied associate-*r*0.6

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

  6. Applied unpow-prod-down0.6

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

  7. Final simplification0.6

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

Reproduce

herbie shell --seed 2019326 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))