Average Error: 0.4 → 0.4
Time: 1.3m
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\frac{\sqrt{k}}{{\left(n \cdot \left(2 \cdot \pi\right)\right)}^{\left(\frac{1}{2} - \frac{k}{2}\right)}}}\]
\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}{2} - \frac{k}{2}\right)}}}
double f(double k, double n) {
        double r6098141 = 1.0;
        double r6098142 = k;
        double r6098143 = sqrt(r6098142);
        double r6098144 = r6098141 / r6098143;
        double r6098145 = 2.0;
        double r6098146 = atan2(1.0, 0.0);
        double r6098147 = r6098145 * r6098146;
        double r6098148 = n;
        double r6098149 = r6098147 * r6098148;
        double r6098150 = r6098141 - r6098142;
        double r6098151 = r6098150 / r6098145;
        double r6098152 = pow(r6098149, r6098151);
        double r6098153 = r6098144 * r6098152;
        return r6098153;
}
↓
double f(double k, double n) {
        double r6098154 = 1.0;
        double r6098155 = k;
        double r6098156 = sqrt(r6098155);
        double r6098157 = n;
        double r6098158 = 2.0;
        double r6098159 = atan2(1.0, 0.0);
        double r6098160 = r6098158 * r6098159;
        double r6098161 = r6098157 * r6098160;
        double r6098162 = 0.5;
        double r6098163 = r6098155 / r6098158;
        double r6098164 = r6098162 - r6098163;
        double r6098165 = pow(r6098161, r6098164);
        double r6098166 = r6098156 / r6098165;
        double r6098167 = r6098154 / r6098166;
        return r6098167;
}

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

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

  4. Applied clear-num0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))