\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
Test:
r*sin(b)/cos(a+b), B
Bits:
128 bits
Bits error versus r
Bits error versus a
Bits error versus b
Time: 7.1 s
Input Error: 7.8
Output Error: 0.3
Log: ⚲
Profile: 🕒
\(\left(r \cdot {\left(\frac{\sin b}{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}\right)}^{1}\right) \cdot {\left(\cos a \cdot \cos b + \sin a \cdot \sin b\right)}^{1}\)
  1. Started with
    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
    7.8
  2. Using strategy rm
    7.8
  3. Applied cos-sum to get
    \[r \cdot \frac{\sin b}{\color{red}{\cos \left(a + b\right)}} \leadsto r \cdot \frac{\sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
    0.2
  4. Using strategy rm
    0.2
  5. Applied pow1 to get
    \[r \cdot \color{red}{\frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}} \leadsto r \cdot \color{blue}{{\left(\frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\right)}^{1}}\]
    0.3
  6. Using strategy rm
    0.3
  7. Applied flip-- to get
    \[r \cdot {\left(\frac{\sin b}{\color{red}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\right)}^{1} \leadsto r \cdot {\left(\frac{\sin b}{\color{blue}{\frac{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}{\cos a \cdot \cos b + \sin a \cdot \sin b}}}\right)}^{1}\]
    0.3
  8. Applied associate-/r/ to get
    \[r \cdot {\color{red}{\left(\frac{\sin b}{\frac{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}{\cos a \cdot \cos b + \sin a \cdot \sin b}}\right)}}^{1} \leadsto r \cdot {\color{blue}{\left(\frac{\sin b}{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2} \cdot \left(\cos a \cdot \cos b + \sin a \cdot \sin b\right)\right)}}^{1}\]
    0.3
  9. Applied unpow-prod-down to get
    \[r \cdot \color{red}{{\left(\frac{\sin b}{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2} \cdot \left(\cos a \cdot \cos b + \sin a \cdot \sin b\right)\right)}^{1}} \leadsto r \cdot \color{blue}{\left({\left(\frac{\sin b}{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}\right)}^{1} \cdot {\left(\cos a \cdot \cos b + \sin a \cdot \sin b\right)}^{1}\right)}\]
    0.3
  10. Applied associate-*r* to get
    \[\color{red}{r \cdot \left({\left(\frac{\sin b}{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}\right)}^{1} \cdot {\left(\cos a \cdot \cos b + \sin a \cdot \sin b\right)}^{1}\right)} \leadsto \color{blue}{\left(r \cdot {\left(\frac{\sin b}{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}\right)}^{1}\right) \cdot {\left(\cos a \cdot \cos b + \sin a \cdot \sin b\right)}^{1}}\]
    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)))))