Average Error: 0.4 → 0.5
Time: 8.8s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\sqrt{k}} \cdot \left({\left(2 \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)} \cdot {n}^{\left(\frac{1 - k}{2}\right)}\right)\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{1}{\sqrt{k}} \cdot \left({\left(2 \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)} \cdot {n}^{\left(\frac{1 - k}{2}\right)}\right)
double f(double k, double n) {
        double r168489 = 1.0;
        double r168490 = k;
        double r168491 = sqrt(r168490);
        double r168492 = r168489 / r168491;
        double r168493 = 2.0;
        double r168494 = atan2(1.0, 0.0);
        double r168495 = r168493 * r168494;
        double r168496 = n;
        double r168497 = r168495 * r168496;
        double r168498 = r168489 - r168490;
        double r168499 = r168498 / r168493;
        double r168500 = pow(r168497, r168499);
        double r168501 = r168492 * r168500;
        return r168501;
}
↓
double f(double k, double n) {
        double r168502 = 1.0;
        double r168503 = k;
        double r168504 = sqrt(r168503);
        double r168505 = r168502 / r168504;
        double r168506 = 2.0;
        double r168507 = atan2(1.0, 0.0);
        double r168508 = r168506 * r168507;
        double r168509 = r168502 - r168503;
        double r168510 = r168509 / r168506;
        double r168511 = pow(r168508, r168510);
        double r168512 = n;
        double r168513 = pow(r168512, r168510);
        double r168514 = r168511 * r168513;
        double r168515 = r168505 * r168514;
        return r168515;
}

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-down0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2020083 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))