Average Error: 0.3 → 0.4
Time: 29.3s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\sqrt{\frac{{\left(\left(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)} \cdot 1}{\sqrt{k}}} \cdot \sqrt{\frac{{\left(\left(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)} \cdot 1}{\sqrt{k}}}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\sqrt{\frac{{\left(\left(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)} \cdot 1}{\sqrt{k}}} \cdot \sqrt{\frac{{\left(\left(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)} \cdot 1}{\sqrt{k}}}
double f(double k, double n) {
        double r4331248 = 1.0;
        double r4331249 = k;
        double r4331250 = sqrt(r4331249);
        double r4331251 = r4331248 / r4331250;
        double r4331252 = 2.0;
        double r4331253 = atan2(1.0, 0.0);
        double r4331254 = r4331252 * r4331253;
        double r4331255 = n;
        double r4331256 = r4331254 * r4331255;
        double r4331257 = r4331248 - r4331249;
        double r4331258 = r4331257 / r4331252;
        double r4331259 = pow(r4331256, r4331258);
        double r4331260 = r4331251 * r4331259;
        return r4331260;
}
↓
double f(double k, double n) {
        double r4331261 = atan2(1.0, 0.0);
        double r4331262 = 2.0;
        double r4331263 = r4331261 * r4331262;
        double r4331264 = n;
        double r4331265 = r4331263 * r4331264;
        double r4331266 = 1.0;
        double r4331267 = k;
        double r4331268 = r4331266 - r4331267;
        double r4331269 = r4331268 / r4331262;
        double r4331270 = pow(r4331265, r4331269);
        double r4331271 = r4331270 * r4331266;
        double r4331272 = sqrt(r4331267);
        double r4331273 = r4331271 / r4331272;
        double r4331274 = sqrt(r4331273);
        double r4331275 = r4331274 * r4331274;
        return r4331275;
}

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 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 add-sqr-sqrt0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019171 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))