Average Error: 0.4 → 0.4
Time: 32.3s
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 r6244936 = 1.0;
        double r6244937 = k;
        double r6244938 = sqrt(r6244937);
        double r6244939 = r6244936 / r6244938;
        double r6244940 = 2.0;
        double r6244941 = atan2(1.0, 0.0);
        double r6244942 = r6244940 * r6244941;
        double r6244943 = n;
        double r6244944 = r6244942 * r6244943;
        double r6244945 = r6244936 - r6244937;
        double r6244946 = r6244945 / r6244940;
        double r6244947 = pow(r6244944, r6244946);
        double r6244948 = r6244939 * r6244947;
        return r6244948;
}
↓
double f(double k, double n) {
        double r6244949 = 1.0;
        double r6244950 = k;
        double r6244951 = sqrt(r6244950);
        double r6244952 = r6244949 / r6244951;
        double r6244953 = 2.0;
        double r6244954 = r6244949 - r6244950;
        double r6244955 = r6244954 / r6244953;
        double r6244956 = pow(r6244953, r6244955);
        double r6244957 = r6244952 * r6244956;
        double r6244958 = atan2(1.0, 0.0);
        double r6244959 = pow(r6244958, r6244955);
        double r6244960 = r6244957 * r6244959;
        double r6244961 = n;
        double r6244962 = pow(r6244961, r6244955);
        double r6244963 = r6244960 * r6244962;
        return r6244963;
}

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