Average Error: 0.4 → 0.4
Time: 8.3s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\frac{\sqrt{k}}{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}}\]
\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}}{{\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}}
double f(double k, double n) {
        double r169236 = 1.0;
        double r169237 = k;
        double r169238 = sqrt(r169237);
        double r169239 = r169236 / r169238;
        double r169240 = 2.0;
        double r169241 = atan2(1.0, 0.0);
        double r169242 = r169240 * r169241;
        double r169243 = n;
        double r169244 = r169242 * r169243;
        double r169245 = r169236 - r169237;
        double r169246 = r169245 / r169240;
        double r169247 = pow(r169244, r169246);
        double r169248 = r169239 * r169247;
        return r169248;
}
↓
double f(double k, double n) {
        double r169249 = 1.0;
        double r169250 = k;
        double r169251 = sqrt(r169250);
        double r169252 = 2.0;
        double r169253 = atan2(1.0, 0.0);
        double r169254 = r169252 * r169253;
        double r169255 = n;
        double r169256 = r169254 * r169255;
        double r169257 = r169249 - r169250;
        double r169258 = r169257 / r169252;
        double r169259 = pow(r169256, r169258);
        double r169260 = r169251 / r169259;
        double r169261 = r169249 / r169260;
        return r169261;
}

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/0.4

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

  5. Applied associate-/l*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020020 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))