Average Error: 0.4 → 0.4
Time: 25.8s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\frac{\sqrt{k}}{{\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{1 - k}{2}\right)}}}\]
\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(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{1 - k}{2}\right)}}}
double f(double k, double n) {
        double r2303599 = 1.0;
        double r2303600 = k;
        double r2303601 = sqrt(r2303600);
        double r2303602 = r2303599 / r2303601;
        double r2303603 = 2.0;
        double r2303604 = atan2(1.0, 0.0);
        double r2303605 = r2303603 * r2303604;
        double r2303606 = n;
        double r2303607 = r2303605 * r2303606;
        double r2303608 = r2303599 - r2303600;
        double r2303609 = r2303608 / r2303603;
        double r2303610 = pow(r2303607, r2303609);
        double r2303611 = r2303602 * r2303610;
        return r2303611;
}
↓
double f(double k, double n) {
        double r2303612 = 1.0;
        double r2303613 = k;
        double r2303614 = sqrt(r2303613);
        double r2303615 = n;
        double r2303616 = 2.0;
        double r2303617 = atan2(1.0, 0.0);
        double r2303618 = r2303616 * r2303617;
        double r2303619 = r2303615 * r2303618;
        double r2303620 = r2303612 - r2303613;
        double r2303621 = r2303620 / r2303616;
        double r2303622 = pow(r2303619, r2303621);
        double r2303623 = r2303614 / r2303622;
        double r2303624 = r2303612 / r2303623;
        return r2303624;
}

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. Simplified0.3

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

  4. Applied clear-num0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))