Average Error: 0.4 → 0.4
Time: 18.7s
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 r164301 = 1.0;
        double r164302 = k;
        double r164303 = sqrt(r164302);
        double r164304 = r164301 / r164303;
        double r164305 = 2.0;
        double r164306 = atan2(1.0, 0.0);
        double r164307 = r164305 * r164306;
        double r164308 = n;
        double r164309 = r164307 * r164308;
        double r164310 = r164301 - r164302;
        double r164311 = r164310 / r164305;
        double r164312 = pow(r164309, r164311);
        double r164313 = r164304 * r164312;
        return r164313;
}
↓
double f(double k, double n) {
        double r164314 = 1.0;
        double r164315 = k;
        double r164316 = sqrt(r164315);
        double r164317 = 1.0;
        double r164318 = 2.0;
        double r164319 = atan2(1.0, 0.0);
        double r164320 = r164318 * r164319;
        double r164321 = n;
        double r164322 = r164320 * r164321;
        double r164323 = r164317 - r164315;
        double r164324 = r164323 / r164318;
        double r164325 = pow(r164322, r164324);
        double r164326 = r164317 * r164325;
        double r164327 = r164316 / r164326;
        double r164328 = r164314 / r164327;
        return r164328;
}

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))))