Average Error: 0.5 → 0.5
Time: 1.7m
Precision: 64
Internal Precision: 1344
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{e^{\log \pi \cdot \frac{1 - k}{2}} \cdot {\left(n \cdot 2\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{k}}\]

Error

Bits error versus k

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Initial simplification0.4

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

  4. Applied unpow-prod-down0.6

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

  6. Applied pow-to-exp0.5

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

  7. Final simplification0.5

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

Runtime

Time bar (total: 1.7m)Debug logProfile

herbie shell --seed 2018220 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))