Average Error: 0.4 → 0.5
Time: 6.9s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\sqrt{\frac{1 \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}} \cdot \sqrt{\frac{1 \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\sqrt{\frac{1 \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}} \cdot \sqrt{\frac{1 \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}}
double f(double k, double n) {
        double r133973 = 1.0;
        double r133974 = k;
        double r133975 = sqrt(r133974);
        double r133976 = r133973 / r133975;
        double r133977 = 2.0;
        double r133978 = atan2(1.0, 0.0);
        double r133979 = r133977 * r133978;
        double r133980 = n;
        double r133981 = r133979 * r133980;
        double r133982 = r133973 - r133974;
        double r133983 = r133982 / r133977;
        double r133984 = pow(r133981, r133983);
        double r133985 = r133976 * r133984;
        return r133985;
}
↓
double f(double k, double n) {
        double r133986 = 1.0;
        double r133987 = 2.0;
        double r133988 = atan2(1.0, 0.0);
        double r133989 = r133987 * r133988;
        double r133990 = n;
        double r133991 = r133989 * r133990;
        double r133992 = k;
        double r133993 = r133986 - r133992;
        double r133994 = r133993 / r133987;
        double r133995 = pow(r133991, r133994);
        double r133996 = r133986 * r133995;
        double r133997 = sqrt(r133992);
        double r133998 = r133996 / r133997;
        double r133999 = sqrt(r133998);
        double r134000 = r133999 * r133999;
        return r134000;
}

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 associate-*l/0.3

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

  5. Applied add-sqr-sqrt0.5

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2020021 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))