\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
Test:
r*sin(b)/cos(a+b), B
Bits:
128 bits
Bits error versus r
Bits error versus a
Bits error versus b
Time: 9.9 s
Input Error: 7.4
Output Error: 0.3
Log: ⚲
Profile: 🕒
\(r \cdot \frac{\sin b}{{\left(\cos a \cdot \cos b\right)}^{1} - \sin a \cdot \sin b}\)
  1. Started with
    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
    7.4
  2. Using strategy rm
    7.4
  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 pow1 to get
    \[r \cdot \frac{\sin b}{\cos a \cdot \color{red}{\cos b} - \sin a \cdot \sin b} \leadsto r \cdot \frac{\sin b}{\cos a \cdot \color{blue}{{\left(\cos b\right)}^{1}} - \sin a \cdot \sin b}\]
    0.3
  6. Applied pow1 to get
    \[r \cdot \frac{\sin b}{\color{red}{\cos a} \cdot {\left(\cos b\right)}^{1} - \sin a \cdot \sin b} \leadsto r \cdot \frac{\sin b}{\color{blue}{{\left(\cos a\right)}^{1}} \cdot {\left(\cos b\right)}^{1} - \sin a \cdot \sin b}\]
    0.3
  7. Applied pow-prod-down to get
    \[r \cdot \frac{\sin b}{\color{red}{{\left(\cos a\right)}^{1} \cdot {\left(\cos b\right)}^{1}} - \sin a \cdot \sin b} \leadsto r \cdot \frac{\sin b}{\color{blue}{{\left(\cos a \cdot \cos b\right)}^{1}} - \sin a \cdot \sin b}\]
    0.3
  8. 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)))))