Error

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. Applied simplify0.4

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

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

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

5. Applied unpow-prod-down0.6

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

6. Applied times-frac0.6

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

8. Applied pow-to-exp0.5

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

10. Applied div-sub0.5

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

11. Applied pow-sub0.4

    \[\leadsto \frac{\color{blue}{\frac{{\left(n + n\right)}^{\left(\frac{1}{2}\right)}}{{\left(n + n\right)}^{\left(\frac{k}{2}\right)}}}}{1} \cdot \frac{e^{\log \pi \cdot \frac{1 - k}{2}}}{\sqrt{k}}\]
12. Removed slow pow expressions.

Runtime

Time bar (total: 2.6m)Debug logProfile

herbie shell --seed '#(1063282112 2455465480 4141627379 3773598652 1647277307 776739644)' 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))