\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
Test:
r*sin(b)/cos(a+b), B
Bits:
128 bits
Bits error versus r
Bits error versus a
Bits error versus b
Time: 9.4 s
Input Error: 7.7
Output Error: 0.3
Log: ⚲
Profile: 🕒
\(r \cdot \frac{\sin b}{\frac{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}{(\left(\sin a\right) * \left(\sin b\right) + \left(\cos b \cdot \cos a\right))_*}}\)
  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 flip-- to get
    \[r \cdot \frac{\sin b}{\color{red}{\cos a \cdot \cos b - \sin a \cdot \sin b}} \leadsto r \cdot \frac{\sin b}{\color{blue}{\frac{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}{\cos a \cdot \cos b + \sin a \cdot \sin b}}}\]
    0.2
  6. Applied simplify to get
    \[r \cdot \frac{\sin b}{\frac{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}{\color{red}{\cos a \cdot \cos b + \sin a \cdot \sin b}}} \leadsto r \cdot \frac{\sin b}{\frac{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}{\color{blue}{(\left(\sin a\right) * \left(\sin b\right) + \left(\cos b \cdot \cos a\right))_*}}}\]
    0.3

Original test:


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