Average Error: 0.4 → 0.4
Time: 28.7s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\sqrt{k}} \cdot {\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{1 - k}{2}\right)}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{1}{\sqrt{k}} \cdot {\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{1 - k}{2}\right)}
double f(double k, double n) {
        double r4451025 = 1.0;
        double r4451026 = k;
        double r4451027 = sqrt(r4451026);
        double r4451028 = r4451025 / r4451027;
        double r4451029 = 2.0;
        double r4451030 = atan2(1.0, 0.0);
        double r4451031 = r4451029 * r4451030;
        double r4451032 = n;
        double r4451033 = r4451031 * r4451032;
        double r4451034 = r4451025 - r4451026;
        double r4451035 = r4451034 / r4451029;
        double r4451036 = pow(r4451033, r4451035);
        double r4451037 = r4451028 * r4451036;
        return r4451037;
}
↓
double f(double k, double n) {
        double r4451038 = 1.0;
        double r4451039 = k;
        double r4451040 = sqrt(r4451039);
        double r4451041 = r4451038 / r4451040;
        double r4451042 = n;
        double r4451043 = 2.0;
        double r4451044 = atan2(1.0, 0.0);
        double r4451045 = r4451043 * r4451044;
        double r4451046 = r4451042 * r4451045;
        double r4451047 = r4451038 - r4451039;
        double r4451048 = r4451047 / r4451043;
        double r4451049 = pow(r4451046, r4451048);
        double r4451050 = r4451041 * r4451049;
        return r4451050;
}

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 *-commutative0.4

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

  5. Applied *-commutative0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019172 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))