Average Error: 0.4 → 0.6
Time: 8.0s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\sqrt{k}} \cdot \left({\left(2 \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)} \cdot {n}^{\left(\frac{1 - k}{2}\right)}\right)\]
\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(2 \cdot \pi\right)}^{\left(\frac{1 - k}{2}\right)} \cdot {n}^{\left(\frac{1 - k}{2}\right)}\right)
double f(double k, double n) {
        double r145113 = 1.0;
        double r145114 = k;
        double r145115 = sqrt(r145114);
        double r145116 = r145113 / r145115;
        double r145117 = 2.0;
        double r145118 = atan2(1.0, 0.0);
        double r145119 = r145117 * r145118;
        double r145120 = n;
        double r145121 = r145119 * r145120;
        double r145122 = r145113 - r145114;
        double r145123 = r145122 / r145117;
        double r145124 = pow(r145121, r145123);
        double r145125 = r145116 * r145124;
        return r145125;
}
↓
double f(double k, double n) {
        double r145126 = 1.0;
        double r145127 = k;
        double r145128 = sqrt(r145127);
        double r145129 = r145126 / r145128;
        double r145130 = 2.0;
        double r145131 = atan2(1.0, 0.0);
        double r145132 = r145130 * r145131;
        double r145133 = r145126 - r145127;
        double r145134 = r145133 / r145130;
        double r145135 = pow(r145132, r145134);
        double r145136 = n;
        double r145137 = pow(r145136, r145134);
        double r145138 = r145135 * r145137;
        double r145139 = r145129 * r145138;
        return r145139;
}

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-down0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2020018 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))