Error

Derivation

1. Initial program 0.1

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

2. Simplified0.1

   \[\leadsto \color{blue}{\frac{e \cdot \sin v}{(\left(\cos v\right) \cdot e + 1)_*}}\]
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 log1p-expm1-u0.2

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

9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019005 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))

Details

Time bar (total: 17.6s)Debug log