Average Error: 0.4 → 0.6
Time: 7.8s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\sqrt{k}} \cdot \left({\left(2 \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)} \cdot {n}^{\left(\frac{1 - k}{2}\right)}\right)\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{1}{\sqrt{k}} \cdot \left({\left(2 \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)} \cdot {n}^{\left(\frac{1 - k}{2}\right)}\right)
double f(double k, double n) {
        double r164941 = 1.0;
        double r164942 = k;
        double r164943 = sqrt(r164942);
        double r164944 = r164941 / r164943;
        double r164945 = 2.0;
        double r164946 = atan2(1.0, 0.0);
        double r164947 = r164945 * r164946;
        double r164948 = n;
        double r164949 = r164947 * r164948;
        double r164950 = r164941 - r164942;
        double r164951 = r164950 / r164945;
        double r164952 = pow(r164949, r164951);
        double r164953 = r164944 * r164952;
        return r164953;
}
↓
double f(double k, double n) {
        double r164954 = 1.0;
        double r164955 = k;
        double r164956 = sqrt(r164955);
        double r164957 = r164954 / r164956;
        double r164958 = 2.0;
        double r164959 = atan2(1.0, 0.0);
        double r164960 = r164958 * r164959;
        double r164961 = r164954 - r164955;
        double r164962 = r164961 / r164958;
        double r164963 = pow(r164960, r164962);
        double r164964 = n;
        double r164965 = pow(r164964, r164962);
        double r164966 = r164963 * r164965;
        double r164967 = r164957 * r164966;
        return r164967;
}

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

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

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))