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. Using strategy rm

4. Applied *-un-lft-identity0.1

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

5. Applied times-frac0.1

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

6. Simplified0.1

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

8. Applied expm1-log1p-u0.2

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

9. Final simplification0.2

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

Runtime

Time bar (total: 15.9s)Debug logProfile

herbie shell --seed 2018339 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))