Error

Derivation

1. Initial program 14.8

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

2. Initial simplification14.8

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

4. Applied cos-sum0.3

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

6. Applied div-inv0.4

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

8. Applied fma-neg0.4

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

10. Applied associate-*l*0.4

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

11. Final simplification0.4

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

Runtime

Time bar (total: 21.9s)Debug logProfile

herbie shell --seed 2018339 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))