Error

Derivation

1. Initial program 15.2

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

2. Initial simplification15.2

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

4. Applied cos-sum0.3

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

6. Applied log1p-expm1-u0.4

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

8. Applied associate-/l*0.4

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

10. Applied *-un-lft-identity0.4

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

11. Applied associate-/r*0.4

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

12. Simplified0.4

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

13. Final simplification0.4

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

Runtime

Time bar (total: 30.0s)Debug logProfile

herbie shell --seed 2018354 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))