\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
Test:
r*sin(b)/cos(a+b), A
Bits:
128 bits
Bits error versus r
Bits error versus a
Bits error versus b
Time: 9.3 s
Input Error: 14.6
Output Error: 0.4
Log: ⚲
Profile: 🕒
\(\frac{r}{\frac{\cos a}{\frac{\sin b}{\cos b}} - \sin a}\)
  1. Started with
    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
    14.6
  2. Using strategy rm
    14.6
  3. Applied cos-sum to get
    \[\frac{r \cdot \sin b}{\color{red}{\cos \left(a + b\right)}} \leadsto \frac{r \cdot \sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
    0.3
  4. Using strategy rm
    0.3
  5. Applied associate-/l* to get
    \[\color{red}{\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}} \leadsto \color{blue}{\frac{r}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}}\]
    0.4
  6. Applied simplify to get
    \[\frac{r}{\color{red}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}} \leadsto \frac{r}{\color{blue}{\frac{\cos a}{\frac{\sin b}{\cos b}} - \sin a}}\]
    0.4
  7. Removed slow pow expressions

Original test:


(lambda ((r default) (a default) (b default))
  #:name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))