\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
Test:
r*sin(b)/cos(a+b), A
Bits:
128 bits
Bits error versus r
Bits error versus a
Bits error versus b
Time: 13.4 s
Input Error: 15.8
Output Error: 0.4
Log: ⚲
Profile: 🕒
\(\frac{r}{1} \cdot \frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin a\right)}^3 \cdot {\left(\sin b\right)}^3}}\)
  1. Started with
    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
    15.8
  2. Using strategy rm
    15.8
  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 *-un-lft-identity to get
    \[\frac{r \cdot \sin b}{\color{red}{\cos a \cdot \cos b - \sin a \cdot \sin b}} \leadsto \frac{r \cdot \sin b}{\color{blue}{1 \cdot \left(\cos a \cdot \cos b - \sin a \cdot \sin b\right)}}\]
    0.3
  6. Applied times-frac to get
    \[\color{red}{\frac{r \cdot \sin b}{1 \cdot \left(\cos a \cdot \cos b - \sin a \cdot \sin b\right)}} \leadsto \color{blue}{\frac{r}{1} \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
    0.3
  7. Using strategy rm
    0.3
  8. Applied add-cbrt-cube to get
    \[\frac{r}{1} \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \color{red}{\sin b}} \leadsto \frac{r}{1} \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \color{blue}{\sqrt[3]{{\left(\sin b\right)}^3}}}\]
    0.4
  9. Applied add-cbrt-cube to get
    \[\frac{r}{1} \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{red}{\sin a} \cdot \sqrt[3]{{\left(\sin b\right)}^3}} \leadsto \frac{r}{1} \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{{\left(\sin a\right)}^3}} \cdot \sqrt[3]{{\left(\sin b\right)}^3}}\]
    0.4
  10. Applied cbrt-unprod to get
    \[\frac{r}{1} \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{red}{\sqrt[3]{{\left(\sin a\right)}^3} \cdot \sqrt[3]{{\left(\sin b\right)}^3}}} \leadsto \frac{r}{1} \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{{\left(\sin a\right)}^3 \cdot {\left(\sin b\right)}^3}}}\]
    0.4
  11. Removed slow pow expressions

Original test:


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