Error

Derivation

1. Initial program 0.1

   \[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]

2. Simplified0.1

   \[\leadsto \color{blue}{\frac{e}{(\left(\cos v\right) \cdot e + 1)_*} \cdot \sin v}\]

3. Taylor expanded around 0 1.0

   \[\leadsto \color{blue}{\left(\left(e + {e}^{3}\right) - {e}^{2}\right)} \cdot \sin v\]

4. Simplified1.0

   \[\leadsto \color{blue}{(\left(e \cdot e\right) \cdot e + \left(e - e \cdot e\right))_*} \cdot \sin v\]

5. Final simplification1.0

   \[\leadsto (\left(e \cdot e\right) \cdot e + \left(e - e \cdot e\right))_* \cdot \sin v\]

Reproduce

herbie shell --seed 2019094 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))