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

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

4. Applied div-sub0.5

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

5. Applied pow-sub0.4

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

7. Applied add-cube-cbrt0.4

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

8. Applied associate-*l*0.4

   \[\leadsto \frac{\frac{{\left(\left(n + n\right) \cdot \pi\right)}^{\left(\frac{1}{2}\right)}}{{\color{blue}{\left(\left(\sqrt[3]{n + n} \cdot \sqrt[3]{n + n}\right) \cdot \left(\sqrt[3]{n + n} \cdot \pi\right)\right)}}^{\left(\frac{k}{2}\right)}}}{\sqrt{k}}\]
9. Removed slow pow expressions.

Runtime

Time bar (total: 3.1m)Debug logProfile

herbie shell --seed '#(1063185673 2139736501 2393378123 1907444849 1070993796 1007244912)' 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))