Error

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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. Taylor expanded around -inf 0.3

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

6. Applied expm1-log1p-u0.3

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

7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019002 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))

Details

Time bar (total: 22.0s)Debug log