Average Error: 0.4 → 0.5
Time: 39.1s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\left(\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{\frac{1 - k}{2}}{2}\right)}\right) \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{\frac{1 - k}{2}}{2}\right)}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\left(\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{\frac{1 - k}{2}}{2}\right)}\right) \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{\frac{1 - k}{2}}{2}\right)}
double f(double k, double n) {
        double r7510402 = 1.0;
        double r7510403 = k;
        double r7510404 = sqrt(r7510403);
        double r7510405 = r7510402 / r7510404;
        double r7510406 = 2.0;
        double r7510407 = atan2(1.0, 0.0);
        double r7510408 = r7510406 * r7510407;
        double r7510409 = n;
        double r7510410 = r7510408 * r7510409;
        double r7510411 = r7510402 - r7510403;
        double r7510412 = r7510411 / r7510406;
        double r7510413 = pow(r7510410, r7510412);
        double r7510414 = r7510405 * r7510413;
        return r7510414;
}
↓
double f(double k, double n) {
        double r7510415 = 1.0;
        double r7510416 = k;
        double r7510417 = sqrt(r7510416);
        double r7510418 = r7510415 / r7510417;
        double r7510419 = 2.0;
        double r7510420 = atan2(1.0, 0.0);
        double r7510421 = r7510419 * r7510420;
        double r7510422 = n;
        double r7510423 = r7510421 * r7510422;
        double r7510424 = r7510415 - r7510416;
        double r7510425 = r7510424 / r7510419;
        double r7510426 = 2.0;
        double r7510427 = r7510425 / r7510426;
        double r7510428 = pow(r7510423, r7510427);
        double r7510429 = r7510418 * r7510428;
        double r7510430 = r7510429 * r7510428;
        return r7510430;
}

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 sqr-pow0.5

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

  4. Applied associate-*r*0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2019173 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))