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Derivation

1. Initial program 0.1

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

2. Initial simplification0.1

   \[\leadsto \frac{e \cdot \sin v}{\cos v \cdot e + 1}\]
3. Using strategy rm

4. Applied div-inv0.1

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

6. Applied flip-+0.1

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

7. Applied associate-/r/0.1

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

8. Final simplification0.1

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

Runtime

Time bar (total: 13.6s)Debug logProfile

herbie shell --seed 2018285 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))