\[\frac{1 - \cos x}{\sin x}\]
Test:
NMSE example 3.4
Bits:
128 bits
Bits error versus x
Time: 4.6 s
Input Error: 13.9
Output Error: 0.4
Log: ⚲
Profile: 🕒
\(\frac{\frac{{\left(\sin x\right)}^2}{1 + \cos x}}{\sin x}\)
  1. Started with
    \[\frac{1 - \cos x}{\sin x}\]
    13.9
  2. Using strategy rm
    13.9
  3. Applied flip-- to get
    \[\frac{\color{red}{1 - \cos x}}{\sin x} \leadsto \frac{\color{blue}{\frac{{1}^2 - {\left(\cos x\right)}^2}{1 + \cos x}}}{\sin x}\]
    13.9
  4. Applied simplify to get
    \[\frac{\frac{\color{red}{{1}^2 - {\left(\cos x\right)}^2}}{1 + \cos x}}{\sin x} \leadsto \frac{\frac{\color{blue}{{\left(\sin x\right)}^2}}{1 + \cos x}}{\sin x}\]
    0.4
  5. Removed slow pow expressions

Original test:


(lambda ((x default))
  #:name "NMSE example 3.4"
  (/ (- 1 (cos x)) (sin x))
  #:target
  (tan (/ x 2)))