Average Error: 0.4 → 0.4
Time: 22.1s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1 \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{1 \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}
double f(double k, double n) {
        double r64117 = 1.0;
        double r64118 = k;
        double r64119 = sqrt(r64118);
        double r64120 = r64117 / r64119;
        double r64121 = 2.0;
        double r64122 = atan2(1.0, 0.0);
        double r64123 = r64121 * r64122;
        double r64124 = n;
        double r64125 = r64123 * r64124;
        double r64126 = r64117 - r64118;
        double r64127 = r64126 / r64121;
        double r64128 = pow(r64125, r64127);
        double r64129 = r64120 * r64128;
        return r64129;
}
↓
double f(double k, double n) {
        double r64130 = 1.0;
        double r64131 = 2.0;
        double r64132 = atan2(1.0, 0.0);
        double r64133 = r64131 * r64132;
        double r64134 = n;
        double r64135 = r64133 * r64134;
        double r64136 = k;
        double r64137 = r64130 - r64136;
        double r64138 = r64137 / r64131;
        double r64139 = pow(r64135, r64138);
        double r64140 = r64130 * r64139;
        double r64141 = sqrt(r64136);
        double r64142 = r64140 / r64141;
        return r64142;
}

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/0.4

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2019212 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))