Average Error: 0.3 → 0.4
Time: 7.6s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\sqrt{k}} \cdot \left(\sqrt{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}} \cdot \sqrt{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}\right)\]
\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(\sqrt{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}} \cdot \sqrt{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}\right)
double f(double k, double n) {
        double r130154 = 1.0;
        double r130155 = k;
        double r130156 = sqrt(r130155);
        double r130157 = r130154 / r130156;
        double r130158 = 2.0;
        double r130159 = atan2(1.0, 0.0);
        double r130160 = r130158 * r130159;
        double r130161 = n;
        double r130162 = r130160 * r130161;
        double r130163 = r130154 - r130155;
        double r130164 = r130163 / r130158;
        double r130165 = pow(r130162, r130164);
        double r130166 = r130157 * r130165;
        return r130166;
}
↓
double f(double k, double n) {
        double r130167 = 1.0;
        double r130168 = k;
        double r130169 = sqrt(r130168);
        double r130170 = r130167 / r130169;
        double r130171 = 2.0;
        double r130172 = atan2(1.0, 0.0);
        double r130173 = r130171 * r130172;
        double r130174 = n;
        double r130175 = r130173 * r130174;
        double r130176 = r130167 - r130168;
        double r130177 = r130176 / r130171;
        double r130178 = pow(r130175, r130177);
        double r130179 = sqrt(r130178);
        double r130180 = r130179 * r130179;
        double r130181 = r130170 * r130180;
        return r130181;
}

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 0.3

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

  3. Applied add-sqr-sqrt0.4

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2020001 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))