Average Error: 0.4 → 0.4
Time: 48.3s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1}{\frac{\sqrt{k}}{{\left(\left(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}}\]
\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(\left(\pi \cdot 2\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}}
double f(double k, double n) {
        double r3704202 = 1.0;
        double r3704203 = k;
        double r3704204 = sqrt(r3704203);
        double r3704205 = r3704202 / r3704204;
        double r3704206 = 2.0;
        double r3704207 = atan2(1.0, 0.0);
        double r3704208 = r3704206 * r3704207;
        double r3704209 = n;
        double r3704210 = r3704208 * r3704209;
        double r3704211 = r3704202 - r3704203;
        double r3704212 = r3704211 / r3704206;
        double r3704213 = pow(r3704210, r3704212);
        double r3704214 = r3704205 * r3704213;
        return r3704214;
}
↓
double f(double k, double n) {
        double r3704215 = 1.0;
        double r3704216 = k;
        double r3704217 = sqrt(r3704216);
        double r3704218 = atan2(1.0, 0.0);
        double r3704219 = 2.0;
        double r3704220 = r3704218 * r3704219;
        double r3704221 = n;
        double r3704222 = r3704220 * r3704221;
        double r3704223 = r3704215 - r3704216;
        double r3704224 = r3704223 / r3704219;
        double r3704225 = pow(r3704222, r3704224);
        double r3704226 = r3704217 / r3704225;
        double r3704227 = r3704215 / r3704226;
        return r3704227;
}

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/0.3

    \[\leadsto \color{blue}{\frac{1 \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}}\]
  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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))