Average Error: 0.4 → 0.5
Time: 12.2s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\left(\frac{1}{\sqrt{k}} \cdot {\left(2 \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)}\right) \cdot {n}^{\left(\frac{1 - k}{2}\right)}\]
\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 \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)}\right) \cdot {n}^{\left(\frac{1 - k}{2}\right)}
double f(double k, double n) {
        double r150409 = 1.0;
        double r150410 = k;
        double r150411 = sqrt(r150410);
        double r150412 = r150409 / r150411;
        double r150413 = 2.0;
        double r150414 = atan2(1.0, 0.0);
        double r150415 = r150413 * r150414;
        double r150416 = n;
        double r150417 = r150415 * r150416;
        double r150418 = r150409 - r150410;
        double r150419 = r150418 / r150413;
        double r150420 = pow(r150417, r150419);
        double r150421 = r150412 * r150420;
        return r150421;
}
↓
double f(double k, double n) {
        double r150422 = 1.0;
        double r150423 = k;
        double r150424 = sqrt(r150423);
        double r150425 = r150422 / r150424;
        double r150426 = 2.0;
        double r150427 = atan2(1.0, 0.0);
        double r150428 = r150426 * r150427;
        double r150429 = r150422 - r150423;
        double r150430 = r150429 / r150426;
        double r150431 = pow(r150428, r150430);
        double r150432 = r150425 * r150431;
        double r150433 = n;
        double r150434 = pow(r150433, r150430);
        double r150435 = r150432 * r150434;
        return r150435;
}

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. Applied associate-*r*0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2019322 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))