\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
Test:
r*sin(b)/cos(a+b), B
Bits:
128 bits
Bits error versus r
Bits error versus a
Bits error versus b
Time: 11.1 s
Input Error: 7.5
Output Error: 0.3
Log: ⚲
Profile: 🕒
\(r \cdot \frac{\sin b}{\cos a \cdot \cos b - (e^{\log_* (1 + \sin a \cdot \sin b)} - 1)^*}\)
  1. Started with
    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
    7.5
  2. Using strategy rm
    7.5
  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 expm1-log1p-u to get
    \[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{red}{\sin a \cdot \sin b}} \leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{(e^{\log_* (1 + \sin a \cdot \sin b)} - 1)^*}}\]
    0.3
  6. Removed slow pow expressions

Original test:


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