\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
Test:
r*sin(b)/cos(a+b), A
Bits:
128 bits
Bits error versus r
Bits error versus a
Bits error versus b
Time: 10.9 s
Input Error: 14.6
Output Error: 0.4
Log: ⚲
Profile: 🕒
\(\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin a\right)}^3 \cdot {\left(\sin b\right)}^3}}\)
  1. Started with
    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
    14.6
  2. Using strategy rm
    14.6
  3. Applied cos-sum to get
    \[\frac{r \cdot \sin b}{\color{red}{\cos \left(a + b\right)}} \leadsto \frac{r \cdot \sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
    0.3
  4. Using strategy rm
    0.3
  5. Applied add-cbrt-cube to get
    \[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \color{red}{\sin b}} \leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \color{blue}{\sqrt[3]{{\left(\sin b\right)}^3}}}\]
    0.4
  6. Applied add-cbrt-cube to get
    \[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \color{red}{\sin a} \cdot \sqrt[3]{{\left(\sin b\right)}^3}} \leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{{\left(\sin a\right)}^3}} \cdot \sqrt[3]{{\left(\sin b\right)}^3}}\]
    0.4
  7. Applied cbrt-unprod to get
    \[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \color{red}{\sqrt[3]{{\left(\sin a\right)}^3} \cdot \sqrt[3]{{\left(\sin b\right)}^3}}} \leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{{\left(\sin a\right)}^3 \cdot {\left(\sin b\right)}^3}}}\]
    0.4

Original test:


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