Average Error: 0.5 → 0.6
Time: 1.6m
Precision: 64
Internal Precision: 1408
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{\frac{{\left(n \cdot \left(\pi \cdot 2\right)\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{\sqrt{k}}}}{\sqrt{\sqrt{k}}}\]

Error

Bits error versus k

Bits error versus n

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 add-sqr-sqrt0.6

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

  5. Applied associate-/r*0.6

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

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed '#(1070706311 3771791028 4128836681 4194990999 2341756049 504035650)' 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))