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 add-sqr-sqrt0.5

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

5. Applied associate-*l*0.5

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

7. Applied sum-double0.5

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

8. Applied sqrt-prod0.5

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

9. Applied associate-*l*0.4

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

Runtime

Time bar (total: 2.4m)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))