Average Error: 0.4 → 0.4
Time: 8.6s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\frac{\sqrt{k}}{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{1}{\frac{\sqrt{k}}{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}}
double f(double k, double n) {
        double r137959 = 1.0;
        double r137960 = k;
        double r137961 = sqrt(r137960);
        double r137962 = r137959 / r137961;
        double r137963 = 2.0;
        double r137964 = atan2(1.0, 0.0);
        double r137965 = r137963 * r137964;
        double r137966 = n;
        double r137967 = r137965 * r137966;
        double r137968 = r137959 - r137960;
        double r137969 = r137968 / r137963;
        double r137970 = pow(r137967, r137969);
        double r137971 = r137962 * r137970;
        return r137971;
}
↓
double f(double k, double n) {
        double r137972 = 1.0;
        double r137973 = k;
        double r137974 = sqrt(r137973);
        double r137975 = 2.0;
        double r137976 = atan2(1.0, 0.0);
        double r137977 = r137975 * r137976;
        double r137978 = n;
        double r137979 = r137977 * r137978;
        double r137980 = r137972 - r137973;
        double r137981 = r137980 / r137975;
        double r137982 = pow(r137979, r137981);
        double r137983 = r137974 / r137982;
        double r137984 = r137972 / r137983;
        return r137984;
}

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 associate-*l/0.3

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

  5. Applied associate-/l*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019346 +o rules:numerics
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))