Average Error: 0.4 → 0.4
Time: 24.6s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[1 \cdot \frac{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
1 \cdot \frac{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}
double f(double k, double n) {
        double r74277 = 1.0;
        double r74278 = k;
        double r74279 = sqrt(r74278);
        double r74280 = r74277 / r74279;
        double r74281 = 2.0;
        double r74282 = atan2(1.0, 0.0);
        double r74283 = r74281 * r74282;
        double r74284 = n;
        double r74285 = r74283 * r74284;
        double r74286 = r74277 - r74278;
        double r74287 = r74286 / r74281;
        double r74288 = pow(r74285, r74287);
        double r74289 = r74280 * r74288;
        return r74289;
}
↓
double f(double k, double n) {
        double r74290 = 1.0;
        double r74291 = 2.0;
        double r74292 = atan2(1.0, 0.0);
        double r74293 = r74291 * r74292;
        double r74294 = n;
        double r74295 = r74293 * r74294;
        double r74296 = k;
        double r74297 = r74290 - r74296;
        double r74298 = r74297 / r74291;
        double r74299 = pow(r74295, r74298);
        double r74300 = sqrt(r74296);
        double r74301 = r74299 / r74300;
        double r74302 = r74290 * r74301;
        return r74302;
}

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 div-inv0.4

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

  4. Applied associate-*l*0.4

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

  5. Simplified0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019291 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))