Average Error: 0.4 → 0.4
Time: 23.9s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)} \cdot 1}{\sqrt{k}}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)} \cdot 1}{\sqrt{k}}
double f(double k, double n) {
        double r90631 = 1.0;
        double r90632 = k;
        double r90633 = sqrt(r90632);
        double r90634 = r90631 / r90633;
        double r90635 = 2.0;
        double r90636 = atan2(1.0, 0.0);
        double r90637 = r90635 * r90636;
        double r90638 = n;
        double r90639 = r90637 * r90638;
        double r90640 = r90631 - r90632;
        double r90641 = r90640 / r90635;
        double r90642 = pow(r90639, r90641);
        double r90643 = r90634 * r90642;
        return r90643;
}
↓
double f(double k, double n) {
        double r90644 = 2.0;
        double r90645 = atan2(1.0, 0.0);
        double r90646 = r90644 * r90645;
        double r90647 = n;
        double r90648 = r90646 * r90647;
        double r90649 = 1.0;
        double r90650 = k;
        double r90651 = r90649 - r90650;
        double r90652 = r90651 / r90644;
        double r90653 = pow(r90648, r90652);
        double r90654 = r90653 * r90649;
        double r90655 = sqrt(r90650);
        double r90656 = r90654 / r90655;
        return r90656;
}

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-sqrt0.4

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

  4. Applied sqrt-prod0.5

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

  5. Applied associate-/r*0.5

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019303 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))