Average Error: 0.4 → 0.4
Time: 24.8s
Precision: 64
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{1 \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}\]
\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}
↓
\frac{1 \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}
double f(double k, double n) {
        double r94094 = 1.0;
        double r94095 = k;
        double r94096 = sqrt(r94095);
        double r94097 = r94094 / r94096;
        double r94098 = 2.0;
        double r94099 = atan2(1.0, 0.0);
        double r94100 = r94098 * r94099;
        double r94101 = n;
        double r94102 = r94100 * r94101;
        double r94103 = r94094 - r94095;
        double r94104 = r94103 / r94098;
        double r94105 = pow(r94102, r94104);
        double r94106 = r94097 * r94105;
        return r94106;
}
↓
double f(double k, double n) {
        double r94107 = 1.0;
        double r94108 = 2.0;
        double r94109 = atan2(1.0, 0.0);
        double r94110 = r94108 * r94109;
        double r94111 = n;
        double r94112 = r94110 * r94111;
        double r94113 = k;
        double r94114 = r94107 - r94113;
        double r94115 = r94114 / r94108;
        double r94116 = pow(r94112, r94115);
        double r94117 = r94107 * r94116;
        double r94118 = sqrt(r94113);
        double r94119 = r94117 / r94118;
        return r94119;
}

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  :precision binary64
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))