Error

Derivation

1. Initial program 15.3

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

3. Applied +-commutative15.3

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

4. Applied cos-sum0.3

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

6. Applied expm1-log1p-u0.4

   \[\leadsto r \cdot \frac{\sin b}{\cos b \cdot \cos a - \color{blue}{(e^{\log_* (1 + \sin b \cdot \sin a)} - 1)^*}}\]

7. Final simplification0.4

   \[\leadsto \frac{\sin b}{\cos b \cdot \cos a - (e^{\log_* (1 + \sin a \cdot \sin b)} - 1)^*} \cdot r\]

Reproduce

herbie shell --seed 2019072 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))