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Derivation

1. Initial program 15.3

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

2. Initial simplification15.3

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

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

9. Final simplification0.3

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

Runtime

Time bar (total: 24.4s)Debug logProfile

herbie shell --seed 2018297 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))