Error

Derivation

1. Initial program 15.5

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

3. Applied cos-sum0.3

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

4. Taylor expanded around inf 0.3

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

5. Simplified0.4

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

7. Applied div-inv0.4

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

8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019088 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))