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 times-frac0.1

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

7. Applied add-cube-cbrt0.2

   \[\leadsto \frac{e}{\sqrt{\color{blue}{\left(\sqrt[3]{(\left(\cos v\right) \cdot e + 1)_*} \cdot \sqrt[3]{(\left(\cos v\right) \cdot e + 1)_*}\right) \cdot \sqrt[3]{(\left(\cos v\right) \cdot e + 1)_*}}}} \cdot \frac{\sin v}{\sqrt{(\left(\cos v\right) \cdot e + 1)_*}}\]

8. Applied sqrt-prod0.2

   \[\leadsto \frac{e}{\color{blue}{\sqrt{\sqrt[3]{(\left(\cos v\right) \cdot e + 1)_*} \cdot \sqrt[3]{(\left(\cos v\right) \cdot e + 1)_*}} \cdot \sqrt{\sqrt[3]{(\left(\cos v\right) \cdot e + 1)_*}}}} \cdot \frac{\sin v}{\sqrt{(\left(\cos v\right) \cdot e + 1)_*}}\]

9. Applied associate-/r*0.2

   \[\leadsto \color{blue}{\frac{\frac{e}{\sqrt{\sqrt[3]{(\left(\cos v\right) \cdot e + 1)_*} \cdot \sqrt[3]{(\left(\cos v\right) \cdot e + 1)_*}}}}{\sqrt{\sqrt[3]{(\left(\cos v\right) \cdot e + 1)_*}}}} \cdot \frac{\sin v}{\sqrt{(\left(\cos v\right) \cdot e + 1)_*}}\]

10. Final simplification0.2

    \[\leadsto \frac{\frac{e}{\sqrt{\sqrt[3]{(\left(\cos v\right) \cdot e + 1)_*} \cdot \sqrt[3]{(\left(\cos v\right) \cdot e + 1)_*}}}}{\sqrt{\sqrt[3]{(\left(\cos v\right) \cdot e + 1)_*}}} \cdot \frac{\sin v}{\sqrt{(\left(\cos v\right) \cdot e + 1)_*}}\]

Runtime

Time bar (total: 46.1s)Debug logProfile

herbie shell --seed 2018348 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))