Error

Derivation

1. Initial program 14.2

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

3. Applied cos-sum0.3

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

5. Applied div-inv0.4

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

6. Applied associate-*r*0.4

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

7. Taylor expanded around inf 0.3

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

8. Simplified0.4

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

9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019094 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))