Average Error: 0.4 → 0.4
Time: 26.5s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{{\left(\left(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{{\left(\left(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}
double f(double k, double n) {
        double r2920556 = 1.0;
        double r2920557 = k;
        double r2920558 = sqrt(r2920557);
        double r2920559 = r2920556 / r2920558;
        double r2920560 = 2.0;
        double r2920561 = atan2(1.0, 0.0);
        double r2920562 = r2920560 * r2920561;
        double r2920563 = n;
        double r2920564 = r2920562 * r2920563;
        double r2920565 = r2920556 - r2920557;
        double r2920566 = r2920565 / r2920560;
        double r2920567 = pow(r2920564, r2920566);
        double r2920568 = r2920559 * r2920567;
        return r2920568;
}
↓
double f(double k, double n) {
        double r2920569 = atan2(1.0, 0.0);
        double r2920570 = 2.0;
        double r2920571 = r2920569 * r2920570;
        double r2920572 = n;
        double r2920573 = r2920571 * r2920572;
        double r2920574 = 1.0;
        double r2920575 = k;
        double r2920576 = r2920574 - r2920575;
        double r2920577 = r2920576 / r2920570;
        double r2920578 = pow(r2920573, r2920577);
        double r2920579 = sqrt(r2920575);
        double r2920580 = r2920578 / r2920579;
        return r2920580;
}

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. Simplified0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019143 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))