Average Error: 0.4 → 0.5
Time: 7.5s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\sqrt{\frac{1}{\sqrt{k}}} \cdot \left(\sqrt{\frac{1}{\sqrt{k}}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\right)\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\sqrt{\frac{1}{\sqrt{k}}} \cdot \left(\sqrt{\frac{1}{\sqrt{k}}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\right)
double f(double k, double n) {
        double r127886 = 1.0;
        double r127887 = k;
        double r127888 = sqrt(r127887);
        double r127889 = r127886 / r127888;
        double r127890 = 2.0;
        double r127891 = atan2(1.0, 0.0);
        double r127892 = r127890 * r127891;
        double r127893 = n;
        double r127894 = r127892 * r127893;
        double r127895 = r127886 - r127887;
        double r127896 = r127895 / r127890;
        double r127897 = pow(r127894, r127896);
        double r127898 = r127889 * r127897;
        return r127898;
}
↓
double f(double k, double n) {
        double r127899 = 1.0;
        double r127900 = k;
        double r127901 = sqrt(r127900);
        double r127902 = r127899 / r127901;
        double r127903 = sqrt(r127902);
        double r127904 = 2.0;
        double r127905 = atan2(1.0, 0.0);
        double r127906 = r127904 * r127905;
        double r127907 = n;
        double r127908 = r127906 * r127907;
        double r127909 = r127899 - r127900;
        double r127910 = r127909 / r127904;
        double r127911 = pow(r127908, r127910);
        double r127912 = r127903 * r127911;
        double r127913 = r127903 * r127912;
        return r127913;
}

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-sqrt0.5

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

  4. Applied associate-*l*0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2020060 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))