Error

Derivation

1. Initial program 14.6

   \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
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 add-log-exp0.4

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

8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019068 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))