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 flip--0.4

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

6. Applied associate-/r/0.4

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

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

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

9. Applied associate-*r*0.4

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

10. Applied simplify0.4

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

Runtime

Time bar (total: 2.0m)Debug logProfile

herbie shell --seed '#(1071821486 549052472 3784827256 1559736200 3548510075 881134285)' 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))