Average Error: 0.4 → 0.4
Time: 23.5s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\frac{\sqrt{k}}{{\left(2 \cdot \left(\pi \cdot n\right)\right)}^{\left(\frac{1 - k}{2}\right)}}}\]
\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(2 \cdot \left(\pi \cdot n\right)\right)}^{\left(\frac{1 - k}{2}\right)}}}
double f(double k, double n) {
        double r82572 = 1.0;
        double r82573 = k;
        double r82574 = sqrt(r82573);
        double r82575 = r82572 / r82574;
        double r82576 = 2.0;
        double r82577 = atan2(1.0, 0.0);
        double r82578 = r82576 * r82577;
        double r82579 = n;
        double r82580 = r82578 * r82579;
        double r82581 = r82572 - r82573;
        double r82582 = r82581 / r82576;
        double r82583 = pow(r82580, r82582);
        double r82584 = r82575 * r82583;
        return r82584;
}
↓
double f(double k, double n) {
        double r82585 = 1.0;
        double r82586 = k;
        double r82587 = sqrt(r82586);
        double r82588 = 2.0;
        double r82589 = atan2(1.0, 0.0);
        double r82590 = n;
        double r82591 = r82589 * r82590;
        double r82592 = r82588 * r82591;
        double r82593 = r82585 - r82586;
        double r82594 = r82593 / r82588;
        double r82595 = pow(r82592, r82594);
        double r82596 = r82587 / r82595;
        double r82597 = r82585 / r82596;
        return r82597;
}

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. Simplified0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019179 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))