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. Using strategy rm

4. Applied associate-*l/0.1

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

6. Applied div-inv0.1

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

7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019090 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))