Error

Derivation

1. Initial program 14.7

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

5. Applied add-log-exp0.4

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

6. Taylor expanded around -inf 0.3

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

7. Simplified0.4

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

8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019091 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))