Error

Derivation

1. Initial program 0.6

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

2. Applied simplify0.5

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

4. Applied *-un-lft-identity0.5

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

5. Applied unpow-prod-down0.6

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

6. Applied times-frac0.6

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

7. Applied simplify0.6

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

9. Applied div-sub0.6

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

10. Applied pow-sub0.5

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

Runtime

Time bar (total: 1.0m)Debug logProfile

herbie shell --seed '#(1071501266 3581234924 1086666455 2685055582 1243441566 1802958749)' +o rules:numerics
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))