\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
Test:
r*sin(b)/cos(a+b), B
Bits:
128 bits
Bits error versus r
Bits error versus a
Bits error versus b
Time: 5.8 s
Input Error: 7.8
Output Error: 0.3
Log: ⚲
Profile: 🕒
\(r \cdot \frac{\sin b}{\cos a \cdot \cos b - {\left(\sqrt[3]{\sin a} \cdot \sqrt[3]{\sin b}\right)}^3}\)
  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 add-cube-cbrt to get
    \[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \color{red}{\sin b}} \leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \color{blue}{{\left(\sqrt[3]{\sin b}\right)}^3}}\]
    0.3
  6. Applied add-cube-cbrt to get
    \[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{red}{\sin a} \cdot {\left(\sqrt[3]{\sin b}\right)}^3} \leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{{\left(\sqrt[3]{\sin a}\right)}^3} \cdot {\left(\sqrt[3]{\sin b}\right)}^3}\]
    0.3
  7. Applied cube-unprod to get
    \[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{red}{{\left(\sqrt[3]{\sin a}\right)}^3 \cdot {\left(\sqrt[3]{\sin b}\right)}^3}} \leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{{\left(\sqrt[3]{\sin a} \cdot \sqrt[3]{\sin b}\right)}^3}}\]
    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)))))