\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
Test:
r*sin(b)/cos(a+b), A
Bits:
128 bits
Bits error versus r
Bits error versus a
Bits error versus b
Time: 13.1 s
Input Error: 15.0
Output Error: 0.4
Log: ⚲
Profile: 🕒
\(\frac{r \cdot \sin b}{\frac{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}{(\left(\sin a\right) * \left(\sin b\right) + \left(\cos b \cdot \cos a\right))_*}}\)
  1. Started with
    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
    15.0
  2. Using strategy rm
    15.0
  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 flip-- to get
    \[\frac{r \cdot \sin b}{\color{red}{\cos a \cdot \cos b - \sin a \cdot \sin b}} \leadsto \frac{r \cdot \sin b}{\color{blue}{\frac{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}{\cos a \cdot \cos b + \sin a \cdot \sin b}}}\]
    0.4
  6. Applied simplify to get
    \[\frac{r \cdot \sin b}{\frac{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}{\color{red}{\cos a \cdot \cos b + \sin a \cdot \sin b}}} \leadsto \frac{r \cdot \sin b}{\frac{{\left(\cos a \cdot \cos b\right)}^2 - {\left(\sin a \cdot \sin b\right)}^2}{\color{blue}{(\left(\sin a\right) * \left(\sin b\right) + \left(\cos b \cdot \cos a\right))_*}}}\]
    0.4
  7. 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))))