Error

Derivation

1. Initial program 15.1

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

3. Applied cos-sum0.3

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

5. Applied fma-neg0.3

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

7. Applied associate-*r/0.3

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

9. Applied div-inv0.4

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

10. Final simplification0.4

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

Runtime

Time bar (total: 27.1s)Debug logProfile

herbie shell --seed 2018351 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))