Error

Derivation

1. Initial program 0.1

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

2. Initial simplification0.1

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

3. Taylor expanded around -inf 0.1

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

5. Applied add-sqr-sqrt0.1

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

6. Applied associate-/r*0.2

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

7. Final simplification0.2

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

Runtime

Time bar (total: 29.6s)Debug logProfile

herbie shell --seed 2018227 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))