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 add-sqr-sqrt0.2

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

5. Applied times-frac0.2

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

7. Applied clear-num0.2

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

9. Applied pow10.2

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

10. Applied pow10.2

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

11. Applied pow-prod-down0.2

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

12. Simplified0.1

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

13. Final simplification0.1

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

Runtime

Time bar (total: 35.0s)Debug logProfile

herbie shell --seed 2018277 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))