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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

    \[\leadsto \frac{\frac{r}{1}}{\color{blue}{\cos b \cdot \frac{\cos a}{\sin b} - \sin a}}\]
11. Using strategy rm

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

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

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

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

14. Applied times-frac0.4

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

15. Simplified0.4

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

16. Simplified0.4

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

17. Final simplification0.4

    \[\leadsto \frac{r}{\frac{\cos b}{\frac{\sin b}{\cos a}} - \sin a}\]

Runtime

Time bar (total: 22.7s)Debug logProfile

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