Error

Derivation

1. Initial program 15.1

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
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 *-un-lft-identity0.3

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

8. Applied times-frac0.3

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

9. Simplified0.3

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

11. Applied div-inv0.4

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

12. Applied associate-*r*0.4

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

13. 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: 30.5s)Debug logProfile

herbie shell --seed 2018348 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))