Average Error: 0.6 → 0.7
Time: 1.4m
Precision: 64
Internal Precision: 1344
\[\frac{1}{\sqrt{k}} \cdot {\left(\left(2 \cdot \pi\right) \cdot n\right)}^{\left(\frac{1 - k}{2}\right)}\]
↓
\[\frac{{n}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{\sqrt{k}}} \cdot \frac{{\left(\pi \cdot 2\right)}^{\left(\frac{1 - k}{2}\right)}}{\sqrt{\sqrt{k}}}\]

Error

Bits error versus k

Bits error versus n

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.6

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

  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-sqrt0.7

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

  5. Applied unpow-prod-down0.7

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

  6. Applied times-frac0.7

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

Runtime

Time bar (total: 1.4m)Debug logProfile

herbie shell --seed 2018201 
(FPCore (k n)
  :name "Migdal et al, Equation (51)"
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))