Average Error: 0.4 → 0.4
Time: 31.6s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\left(\left(\frac{1}{\sqrt{k}} \cdot {2}^{\left(\frac{1 - k}{2}\right)}\right) \cdot {\pi}^{\left(\frac{1 - k}{2}\right)}\right) \cdot {n}^{\left(\frac{1 - k}{2}\right)}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\left(\left(\frac{1}{\sqrt{k}} \cdot {2}^{\left(\frac{1 - k}{2}\right)}\right) \cdot {\pi}^{\left(\frac{1 - k}{2}\right)}\right) \cdot {n}^{\left(\frac{1 - k}{2}\right)}
double f(double k, double n) {
        double r4351935 = 1.0;
        double r4351936 = k;
        double r4351937 = sqrt(r4351936);
        double r4351938 = r4351935 / r4351937;
        double r4351939 = 2.0;
        double r4351940 = atan2(1.0, 0.0);
        double r4351941 = r4351939 * r4351940;
        double r4351942 = n;
        double r4351943 = r4351941 * r4351942;
        double r4351944 = r4351935 - r4351936;
        double r4351945 = r4351944 / r4351939;
        double r4351946 = pow(r4351943, r4351945);
        double r4351947 = r4351938 * r4351946;
        return r4351947;
}
↓
double f(double k, double n) {
        double r4351948 = 1.0;
        double r4351949 = k;
        double r4351950 = sqrt(r4351949);
        double r4351951 = r4351948 / r4351950;
        double r4351952 = 2.0;
        double r4351953 = r4351948 - r4351949;
        double r4351954 = r4351953 / r4351952;
        double r4351955 = pow(r4351952, r4351954);
        double r4351956 = r4351951 * r4351955;
        double r4351957 = atan2(1.0, 0.0);
        double r4351958 = pow(r4351957, r4351954);
        double r4351959 = r4351956 * r4351958;
        double r4351960 = n;
        double r4351961 = pow(r4351960, r4351954);
        double r4351962 = r4351959 * r4351961;
        return r4351962;
}

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-down0.5

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

  4. Applied associate-*r*0.5

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

  6. Applied unpow-prod-down0.4

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

  7. Applied associate-*r*0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))