Average Error: 0.4 → 0.6
Time: 53.7s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\left({n}^{\left(\frac{1 - k}{2}\right)} \cdot {\left(2 \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)}\right) \cdot \frac{1}{\sqrt{k}}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\left({n}^{\left(\frac{1 - k}{2}\right)} \cdot {\left(2 \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)}\right) \cdot \frac{1}{\sqrt{k}}
double f(double k, double n) {
        double r5389033 = 1.0;
        double r5389034 = k;
        double r5389035 = sqrt(r5389034);
        double r5389036 = r5389033 / r5389035;
        double r5389037 = 2.0;
        double r5389038 = atan2(1.0, 0.0);
        double r5389039 = r5389037 * r5389038;
        double r5389040 = n;
        double r5389041 = r5389039 * r5389040;
        double r5389042 = r5389033 - r5389034;
        double r5389043 = r5389042 / r5389037;
        double r5389044 = pow(r5389041, r5389043);
        double r5389045 = r5389036 * r5389044;
        return r5389045;
}
↓
double f(double k, double n) {
        double r5389046 = n;
        double r5389047 = 1.0;
        double r5389048 = k;
        double r5389049 = r5389047 - r5389048;
        double r5389050 = 2.0;
        double r5389051 = r5389049 / r5389050;
        double r5389052 = pow(r5389046, r5389051);
        double r5389053 = atan2(1.0, 0.0);
        double r5389054 = r5389050 * r5389053;
        double r5389055 = pow(r5389054, r5389051);
        double r5389056 = r5389052 * r5389055;
        double r5389057 = sqrt(r5389048);
        double r5389058 = r5389047 / r5389057;
        double r5389059 = r5389056 * r5389058;
        return r5389059;
}

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-down0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2019168 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))