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Derivation

1. Initial program 14.9

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

2. Initial simplification14.9

   \[\leadsto \frac{r \cdot \sin b}{\cos \left(b + a\right)}\]
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 associate-*r/0.3

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

12. Applied associate-/l*0.4

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

13. Final simplification0.4

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

Runtime

Time bar (total: 19.4s)Debug logProfile

herbie shell --seed 2018286 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))