Error

Derivation

1. Initial program 15.2

   \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
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 associate-/l*0.4

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

7. Applied fma-neg0.4

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

9. Applied log1p-expm1-u0.4

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

10. Final simplification0.4

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

Runtime

Time bar (total: 25.0s)Debug logProfile

herbie shell --seed 2018274 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))