Average Error: 16.2 → 12.1
Time: 1.0m
Precision: 64
Internal Precision: 2432
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\ell \cdot \pi - \frac{\tan \left(\ell \cdot \pi\right) \cdot \frac{1}{F}}{F}\]

Error

Bits error versus F

Bits error versus l

Derivation

  1. Initial program 16.2

    \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]

  2. Applied simplify16.0

    \[\leadsto \color{blue}{\ell \cdot \pi - \frac{\tan \left(\ell \cdot \pi\right)}{F \cdot F}}\]
  3. Using strategy rm

  4. Applied associate-/r*12.1

    \[\leadsto \ell \cdot \pi - \color{blue}{\frac{\frac{\tan \left(\ell \cdot \pi\right)}{F}}{F}}\]
  5. Using strategy rm

  6. Applied div-inv12.1

    \[\leadsto \ell \cdot \pi - \frac{\color{blue}{\tan \left(\ell \cdot \pi\right) \cdot \frac{1}{F}}}{F}\]

Runtime

Time bar (total: 1.0m)Debug logProfile

herbie shell --seed '#(1070833653 108281690 3330367898 3632331308 3494323072 43156186)' 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))