Error

Derivation

1. Initial program 14.9

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
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 fma-neg0.3

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

7. Applied associate-/l*0.4

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

8. Final simplification0.4

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

Runtime

Time bar (total: 22.6s)Debug logProfile

herbie shell --seed 2018252 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))