Error

Derivation

1. Initial program 14.7

   \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
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. Taylor expanded around -inf 0.3

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

5. Simplified0.4

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

7. Applied fma-neg0.4

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

8. Final simplification0.4

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

Reproduce

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