Error

Derivation

1. Initial program 8.5

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

2. Simplified8.1

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

4. Applied *-commutative8.1

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

5. Applied associate-/r*0.7

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

7. Applied clear-num0.7

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

8. Final simplification0.7

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

Reproduce

herbie shell --seed 2019072 +o rules:numerics
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))