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-sqrt0.1

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

5. Applied associate-/r*0.1

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

7. Applied add-sqr-sqrt0.2

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

8. Applied add-sqr-sqrt0.2

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

9. Applied sqrt-prod0.2

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

10. Applied times-frac0.2

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

11. Applied times-frac0.2

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

12. Simplified0.2

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

13. Simplified0.1

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

14. Final simplification0.1

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

Runtime

Time bar (total: 40.1s)Debug logProfile

herbie shell --seed 2018235 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))