Average Error: 16.2 → 12.1
Time: 1.8m
Precision: 64
Internal Precision: 3392
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\ell \cdot \pi - \frac{1}{F} \cdot \frac{\tan \left(\ell \cdot \pi\right)}{F}\]

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 *-un-lft-identity16.0

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

  5. Applied times-frac12.1

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

Runtime

Time bar (total: 1.8m)Debug logProfile

herbie shell --seed '#(1071852389 864846987 1238109217 3425890003 4124793586 650694553)' 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))