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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 associate-/l*0.4

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

7. Applied div-sub0.4

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

9. Applied *-un-lft-identity0.4

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

10. Applied times-frac0.4

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

11. Simplified0.4

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

12. Final simplification0.4

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

Runtime

Time bar (total: 37.6s)Debug logProfile

herbie shell --seed 2018355 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))