Average Error: 0.4 → 0.4
Time: 2.5m
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
\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(\left(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
double f(double k, double n) {
        double r30187941 = 1.0;
        double r30187942 = k;
        double r30187943 = sqrt(r30187942);
        double r30187944 = r30187941 / r30187943;
        double r30187945 = 2.0;
        double r30187946 = atan2(1.0, 0.0);
        double r30187947 = r30187945 * r30187946;
        double r30187948 = n;
        double r30187949 = r30187947 * r30187948;
        double r30187950 = r30187941 - r30187942;
        double r30187951 = r30187950 / r30187945;
        double r30187952 = pow(r30187949, r30187951);
        double r30187953 = r30187944 * r30187952;
        return r30187953;
}
↓
double f(double k, double n) {
        double r30187954 = 1.0;
        double r30187955 = k;
        double r30187956 = sqrt(r30187955);
        double r30187957 = r30187954 / r30187956;
        double r30187958 = atan2(1.0, 0.0);
        double r30187959 = 2.0;
        double r30187960 = r30187958 * r30187959;
        double r30187961 = n;
        double r30187962 = r30187960 * r30187961;
        double r30187963 = r30187954 - r30187955;
        double r30187964 = r30187963 / r30187959;
        double r30187965 = pow(r30187962, r30187964);
        double r30187966 = r30187957 * r30187965;
        return r30187966;
}

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. Simplified0.3

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

  4. Applied div-inv0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))