Average Error: 0.4 → 0.5
Time: 27.5s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\sqrt{k}} \cdot \left({\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{\frac{1 - k}{2}}{2}\right)} \cdot {\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{\frac{1 - k}{2}}{2}\right)}\right)\]
\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(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{\frac{1 - k}{2}}{2}\right)} \cdot {\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{\frac{1 - k}{2}}{2}\right)}\right)
double f(double k, double n) {
        double r2609943 = 1.0;
        double r2609944 = k;
        double r2609945 = sqrt(r2609944);
        double r2609946 = r2609943 / r2609945;
        double r2609947 = 2.0;
        double r2609948 = atan2(1.0, 0.0);
        double r2609949 = r2609947 * r2609948;
        double r2609950 = n;
        double r2609951 = r2609949 * r2609950;
        double r2609952 = r2609943 - r2609944;
        double r2609953 = r2609952 / r2609947;
        double r2609954 = pow(r2609951, r2609953);
        double r2609955 = r2609946 * r2609954;
        return r2609955;
}
↓
double f(double k, double n) {
        double r2609956 = 1.0;
        double r2609957 = k;
        double r2609958 = sqrt(r2609957);
        double r2609959 = r2609956 / r2609958;
        double r2609960 = n;
        double r2609961 = 2.0;
        double r2609962 = atan2(1.0, 0.0);
        double r2609963 = r2609961 * r2609962;
        double r2609964 = r2609960 * r2609963;
        double r2609965 = r2609956 - r2609957;
        double r2609966 = r2609965 / r2609961;
        double r2609967 = r2609966 / r2609961;
        double r2609968 = pow(r2609964, r2609967);
        double r2609969 = r2609968 * r2609968;
        double r2609970 = r2609959 * r2609969;
        return r2609970;
}

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 sqr-pow0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2019132 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))