Error

Try it out

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 associate-/l*0.4

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

8. Applied *-un-lft-identity0.4

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

9. Applied associate-/r*0.4

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

10. Simplified0.4

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

12. Applied fma-udef0.4

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

13. Final simplification0.4

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

Runtime

Time bar (total: 23.2s)Debug logProfile

herbie shell --seed 2018274 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))