Average Error: 0.4 → 0.5
Time: 8.1s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\sqrt{\frac{1}{\sqrt{k}}} \cdot \left(\sqrt{\frac{1}{\sqrt{k}}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\right)\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\sqrt{\frac{1}{\sqrt{k}}} \cdot \left(\sqrt{\frac{1}{\sqrt{k}}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\right)
double f(double k, double n) {
        double r140174 = 1.0;
        double r140175 = k;
        double r140176 = sqrt(r140175);
        double r140177 = r140174 / r140176;
        double r140178 = 2.0;
        double r140179 = atan2(1.0, 0.0);
        double r140180 = r140178 * r140179;
        double r140181 = n;
        double r140182 = r140180 * r140181;
        double r140183 = r140174 - r140175;
        double r140184 = r140183 / r140178;
        double r140185 = pow(r140182, r140184);
        double r140186 = r140177 * r140185;
        return r140186;
}
↓
double f(double k, double n) {
        double r140187 = 1.0;
        double r140188 = k;
        double r140189 = sqrt(r140188);
        double r140190 = r140187 / r140189;
        double r140191 = sqrt(r140190);
        double r140192 = 2.0;
        double r140193 = atan2(1.0, 0.0);
        double r140194 = r140192 * r140193;
        double r140195 = n;
        double r140196 = r140194 * r140195;
        double r140197 = r140187 - r140188;
        double r140198 = r140197 / r140192;
        double r140199 = pow(r140196, r140198);
        double r140200 = r140191 * r140199;
        double r140201 = r140191 * r140200;
        return r140201;
}

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 add-sqr-sqrt0.5

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

  4. Applied associate-*l*0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2020024 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))