Error

Derivation

1. Initial program 15.0

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
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 *-un-lft-identity0.3

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

6. Applied times-frac0.3

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

7. Simplified0.3

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

9. Applied add-log-exp0.4

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

11. Applied exp-prod0.4

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

12. Applied log-pow0.4

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

13. Final simplification0.4

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

Reproduce

herbie shell --seed 2019100 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))