\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
Test:
r*sin(b)/cos(a+b), A
Bits:
128 bits
Bits error versus r
Bits error versus a
Bits error versus b
Time: 10.3 s
Input Error: 14.8
Output Error: 0.4
Log: ⚲
Profile: 🕒
\(\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\)
  1. Started with
    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
    14.8
  2. Using strategy rm
    14.8
  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 div-inv to get
    \[\color{red}{\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}} \leadsto \color{blue}{\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
    0.4
  6. 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))))