Error

Derivation

1. Initial program 15.1

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
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 pow10.3

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

10. Applied pow10.3

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

11. Applied pow-prod-down0.3

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

12. Simplified0.4

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

13. Final simplification0.4

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

Reproduce

herbie shell --seed 2019089 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))