Average Error: 0.4 → 0.4
Time: 47.1s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\frac{\sqrt{k}}{{\left(\left(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}}\]
\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(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}}
double f(double k, double n) {
        double r5401131 = 1.0;
        double r5401132 = k;
        double r5401133 = sqrt(r5401132);
        double r5401134 = r5401131 / r5401133;
        double r5401135 = 2.0;
        double r5401136 = atan2(1.0, 0.0);
        double r5401137 = r5401135 * r5401136;
        double r5401138 = n;
        double r5401139 = r5401137 * r5401138;
        double r5401140 = r5401131 - r5401132;
        double r5401141 = r5401140 / r5401135;
        double r5401142 = pow(r5401139, r5401141);
        double r5401143 = r5401134 * r5401142;
        return r5401143;
}
↓
double f(double k, double n) {
        double r5401144 = 1.0;
        double r5401145 = k;
        double r5401146 = sqrt(r5401145);
        double r5401147 = atan2(1.0, 0.0);
        double r5401148 = 2.0;
        double r5401149 = r5401147 * r5401148;
        double r5401150 = n;
        double r5401151 = r5401149 * r5401150;
        double r5401152 = r5401144 - r5401145;
        double r5401153 = r5401152 / r5401148;
        double r5401154 = pow(r5401151, r5401153);
        double r5401155 = r5401146 / r5401154;
        double r5401156 = r5401144 / r5401155;
        return r5401156;
}

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

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

Reproduce

herbie shell --seed 2019200 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))