\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
Test:
r*sin(b)/cos(a+b), B
Bits:
128 bits
Bits error versus r
Bits error versus a
Bits error versus b
Time: 7.9 s
Input Error: 7.7
Output Error: 0.5
Log: ⚲
Profile: 🕒
\(r \cdot \frac{\sin b}{\log_* (1 + (e^{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)} - 1)^*)}\)
  1. Started with
    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
    7.7
  2. Using strategy rm
    7.7
  3. Applied cos-sum to get
    \[r \cdot \frac{\sin b}{\color{red}{\cos \left(a + b\right)}} \leadsto r \cdot \frac{\sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
    0.2
  4. Using strategy rm
    0.2
  5. Applied log1p-expm1-u to get
    \[r \cdot \frac{\sin b}{\color{red}{\cos a \cdot \cos b - \sin a \cdot \sin b}} \leadsto r \cdot \frac{\sin b}{\color{blue}{\log_* (1 + (e^{\cos a \cdot \cos b - \sin a \cdot \sin b} - 1)^*)}}\]
    0.4
  6. Using strategy rm
    0.4
  7. Applied add-log-exp to get
    \[r \cdot \frac{\sin b}{\log_* (1 + (e^{\cos a \cdot \cos b - \color{red}{\sin a \cdot \sin b}} - 1)^*)} \leadsto r \cdot \frac{\sin b}{\log_* (1 + (e^{\cos a \cdot \cos b - \color{blue}{\log \left(e^{\sin a \cdot \sin b}\right)}} - 1)^*)}\]
    0.5

Original test:


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