Average Error: 0.4 → 0.4
Time: 19.4s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\frac{\sqrt{k}}{1 \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{1}{\frac{\sqrt{k}}{1 \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}}
double f(double k, double n) {
        double r161340 = 1.0;
        double r161341 = k;
        double r161342 = sqrt(r161341);
        double r161343 = r161340 / r161342;
        double r161344 = 2.0;
        double r161345 = atan2(1.0, 0.0);
        double r161346 = r161344 * r161345;
        double r161347 = n;
        double r161348 = r161346 * r161347;
        double r161349 = r161340 - r161341;
        double r161350 = r161349 / r161344;
        double r161351 = pow(r161348, r161350);
        double r161352 = r161343 * r161351;
        return r161352;
}
↓
double f(double k, double n) {
        double r161353 = 1.0;
        double r161354 = k;
        double r161355 = sqrt(r161354);
        double r161356 = 1.0;
        double r161357 = 2.0;
        double r161358 = atan2(1.0, 0.0);
        double r161359 = r161357 * r161358;
        double r161360 = n;
        double r161361 = r161359 * r161360;
        double r161362 = r161356 - r161354;
        double r161363 = r161362 / r161357;
        double r161364 = pow(r161361, r161363);
        double r161365 = r161356 * r161364;
        double r161366 = r161355 / r161365;
        double r161367 = r161353 / r161366;
        return r161367;
}

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 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 clear-num0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020047 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))