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Derivation

1. Initial program 15.9

   \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
2. Using strategy rm

3. Applied associate-*l/15.7

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

4. Simplified15.7

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

6. Applied *-un-lft-identity15.7

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

7. Applied times-frac12.0

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

9. Applied associate-*r/12.0

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

10. Final simplification12.0

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

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed 2018242 +o rules:numerics
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))