Error

Derivation

1. Initial program 14.8

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
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 div-inv0.4

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

7. Applied flip--0.5

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

8. Applied associate-/r/0.5

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

9. Applied associate-*r*0.5

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

10. Applied simplify0.4

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

Runtime

Time bar (total: 32.5s)Debug logProfile

herbie shell --seed '#(1064397287 3527694221 3797617954 1138343853 2854031332 1153838279)' 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))