Error

Derivation

1. Initial program 15.2

   \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]

2. Initial simplification15.2

   \[\leadsto \frac{r \cdot \sin b}{\cos \left(b + a\right)}\]
3. Using strategy rm

4. Applied cos-sum0.3

   \[\leadsto \frac{r \cdot \sin b}{\color{blue}{\cos b \cdot \cos a - \sin b \cdot \sin a}}\]
5. Using strategy rm

6. Applied *-un-lft-identity0.3

   \[\leadsto \frac{r \cdot \sin b}{\color{blue}{1 \cdot \left(\cos b \cdot \cos a - \sin b \cdot \sin a\right)}}\]

7. Applied times-frac0.3

   \[\leadsto \color{blue}{\frac{r}{1} \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin b \cdot \sin a}}\]

8. Simplified0.3

   \[\leadsto \color{blue}{r} \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin b \cdot \sin a}\]
9. Using strategy rm

10. Applied fma-neg0.3

    \[\leadsto r \cdot \frac{\sin b}{\color{blue}{(\left(\cos b\right) \cdot \left(\cos a\right) + \left(-\sin b \cdot \sin a\right))_*}}\]
11. Using strategy rm

12. Applied div-inv0.4

    \[\leadsto r \cdot \color{blue}{\left(\sin b \cdot \frac{1}{(\left(\cos b\right) \cdot \left(\cos a\right) + \left(-\sin b \cdot \sin a\right))_*}\right)}\]

13. Applied associate-*r*0.4

    \[\leadsto \color{blue}{\left(r \cdot \sin b\right) \cdot \frac{1}{(\left(\cos b\right) \cdot \left(\cos a\right) + \left(-\sin b \cdot \sin a\right))_*}}\]

14. Final simplification0.4

    \[\leadsto \frac{1}{(\left(\cos b\right) \cdot \left(\cos a\right) + \left(-\sin b \cdot \sin a\right))_*} \cdot \left(r \cdot \sin b\right)\]

Runtime

Time bar (total: 34.4s)Debug logProfile

herbie shell --seed 2018285 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))