\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
Test:
r*sin(b)/cos(a+b), B
Bits:
128 bits
Bits error versus r
Bits error versus a
Bits error versus b
Time: 8.4 s
Input Error: 7.5
Output Error: 0.3
Log: ⚲
Profile: 🕒
\(r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin a\right)}^3 \cdot {\left(\sin b\right)}^3}}\)
  1. Started with
    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
    7.5
  2. Using strategy rm
    7.5
  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-cbrt-cube to get
    \[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \color{red}{\sin b}} \leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \color{blue}{\sqrt[3]{{\left(\sin b\right)}^3}}}\]
    0.2
  6. Applied add-cbrt-cube to get
    \[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{red}{\sin a} \cdot \sqrt[3]{{\left(\sin b\right)}^3}} \leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{{\left(\sin a\right)}^3}} \cdot \sqrt[3]{{\left(\sin b\right)}^3}}\]
    0.2
  7. Applied cbrt-unprod to get
    \[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{red}{\sqrt[3]{{\left(\sin a\right)}^3} \cdot \sqrt[3]{{\left(\sin b\right)}^3}}} \leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{{\left(\sin a\right)}^3 \cdot {\left(\sin b\right)}^3}}}\]
    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)))))