\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
Test:
r*sin(b)/cos(a+b), A
Bits:
128 bits
Bits error versus r
Bits error versus a
Bits error versus b
Time: 6.1 s
Input Error: 7.4
Output Error: 0.3
Log: ⚲
Profile: 🕒
\(\frac{r \cdot \sin b}{(e^{\log_* (1 + \cos a \cdot \cos b)} - 1)^* - \sin a \cdot \sin b}\)
  1. Started with
    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
    7.4
  2. Using strategy rm
    7.4
  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 expm1-log1p-u to get
    \[\frac{r \cdot \sin b}{\color{red}{\cos a \cdot \cos b} - \sin a \cdot \sin b} \leadsto \frac{r \cdot \sin b}{\color{blue}{(e^{\log_* (1 + \cos a \cdot \cos b)} - 1)^*} - \sin a \cdot \sin b}\]
    0.3

Original test:


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