Average Error: 16.3 → 8.4

Time: 1.8m

Precision: 64

Internal Precision: 3904

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

↓

\[\pi \cdot \ell - \frac{\frac{1}{\frac{F}{\pi \cdot \ell} - \left(F \cdot \left(\pi \cdot \ell\right)\right) \cdot \frac{1}{3}}}{F}\]

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Initial program 16.3
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
Initial simplification16.1
\[\leadsto \pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}\]
Using strategy rm
Applied associate-/r*12.3
\[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}}\]
Using strategy rm
Applied clear-num12.3
\[\leadsto \pi \cdot \ell - \frac{\color{blue}{\frac{1}{\frac{F}{\tan \left(\pi \cdot \ell\right)}}}}{F}\]
Taylor expanded around 0 8.4
\[\leadsto \pi \cdot \ell - \frac{\frac{1}{\color{blue}{\frac{F}{\pi \cdot \ell} - \frac{1}{3} \cdot \left(F \cdot \left(\pi \cdot \ell\right)\right)}}}{F}\]
Final simplification8.4
\[\leadsto \pi \cdot \ell - \frac{\frac{1}{\frac{F}{\pi \cdot \ell} - \left(F \cdot \left(\pi \cdot \ell\right)\right) \cdot \frac{1}{3}}}{F}\]

	Baseline	Herbie	Oracle	Span	%
Regimes	8.4	8.4	8.0	0.4	0%

herbie shell --seed 2018295 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))