\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
Test:
r*sin(b)/cos(a+b), B
Bits:
128 bits
Bits error versus r
Bits error versus a
Bits error versus b
Time: 13.7 s
Input Error: 14.8
Output Error: 0.4
Log: ⚲
Profile: 🕒
\(r \cdot \frac{\sin b}{\log_* (1 + (e^{\cos a \cdot \cos b} - 1)^*) - \sin a \cdot \sin b}\)
  1. Started with
    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
    14.8
  2. Using strategy rm
    14.8
  3. Applied cos-sum to get
    \[r \cdot \frac{\sin b}{\color{red}{\cos \left(a + b\right)}} \leadsto r \cdot \frac{\sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
    0.3
  4. Using strategy rm
    0.3
  5. Applied log1p-expm1-u to get
    \[r \cdot \frac{\sin b}{\color{red}{\cos a \cdot \cos b} - \sin a \cdot \sin b} \leadsto r \cdot \frac{\sin b}{\color{blue}{\log_* (1 + (e^{\cos a \cdot \cos b} - 1)^*)} - \sin a \cdot \sin b}\]
    0.4

Original test:


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