\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
Test:
r*sin(b)/cos(a+b), B
Bits:
128 bits
Bits error versus r
Bits error versus a
Bits error versus b
Time: 14.7 s
Input Error: 14.8
Output Error: 0.4
Log: ⚲
Profile: 🕒
\(\left(r \cdot \frac{\sin b}{{\left(\cos a\right)}^2 \cdot {\left(\cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}\right) \cdot \left(\cos a \cdot \cos b + \sin a \cdot \sin b\right)\)
  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 flip-- to get
    \[r \cdot \frac{\sin b}{\color{red}{\cos a \cdot \cos b - \sin a \cdot \sin b}} \leadsto r \cdot \frac{\sin b}{\color{blue}{\frac{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}{\cos a \cdot \cos b + \sin a \cdot \sin b}}}\]
    0.4
  6. Applied associate-/r/ to get
    \[r \cdot \color{red}{\frac{\sin b}{\frac{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}{\cos a \cdot \cos b + \sin a \cdot \sin b}}} \leadsto r \cdot \color{blue}{\left(\frac{\sin b}{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2} \cdot \left(\cos a \cdot \cos b + \sin a \cdot \sin b\right)\right)}\]
    0.4
  7. Applied associate-*r* to get
    \[\color{red}{r \cdot \left(\frac{\sin b}{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2} \cdot \left(\cos a \cdot \cos b + \sin a \cdot \sin b\right)\right)} \leadsto \color{blue}{\left(r \cdot \frac{\sin b}{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}\right) \cdot \left(\cos a \cdot \cos b + \sin a \cdot \sin b\right)}\]
    0.4
  8. Using strategy rm
    0.4
  9. Applied square-prod to get
    \[\left(r \cdot \frac{\sin b}{\color{red}{{\left(\cos a \cdot \cos b\right)}^2} - {\left(\sin a \cdot \sin b\right)}^2}\right) \cdot \left(\cos a \cdot \cos b + \sin a \cdot \sin b\right) \leadsto \left(r \cdot \frac{\sin b}{\color{blue}{{\left(\cos a\right)}^2 \cdot {\left(\cos b\right)}^2} - {\left(\sin a \cdot \sin b\right)}^2}\right) \cdot \left(\cos a \cdot \cos b + \sin a \cdot \sin b\right)\]
    0.4
  10. 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)))))