Error

Derivation

1. Initial program 15.5

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

3. Applied +-commutative15.5

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

4. Applied cos-sum0.3

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

6. Applied add-log-exp0.4

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

8. Applied *-commutative0.4

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

9. Applied exp-prod0.4

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

10. Applied log-pow0.4

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

12. Applied associate-*r/0.4

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

13. Simplified0.3

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

14. Final simplification0.3

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

Reproduce

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