Error

Derivation

1. Initial program 0.5

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

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 div-sub0.5

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

5. Applied pow-sub0.4

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

7. Applied unpow-prod-down0.6

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

9. Applied add-sqr-sqrt1.0

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

10. Applied pow-unpow0.5

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

Runtime

Time bar (total: 1.9m)Debug logProfile

herbie shell --seed '#(1071852389 864846987 1238109217 3425890003 4124793586 650694553)' 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))