\[\frac{1 - \cos x}{\sin x}\]
Test:
NMSE example 3.4
Bits:
128 bits
Bits error versus x
Time: 43.1 s
Input Error: 30.5
Output Error: 1.6
Log: ⚲
Profile: 🕒
\({\left(\sqrt[3]{\frac{\sin x}{\cos x + 1}}\right)}^3\)
  1. Started with
    \[\frac{1 - \cos x}{\sin x}\]
    30.5
  2. Using strategy rm
    30.5
  3. Applied flip-- to get
    \[\frac{\color{red}{1 - \cos x}}{\sin x} \leadsto \frac{\color{blue}{\frac{{1}^2 - {\left(\cos x\right)}^2}{1 + \cos x}}}{\sin x}\]
    30.7
  4. Applied simplify to get
    \[\frac{\frac{\color{red}{{1}^2 - {\left(\cos x\right)}^2}}{1 + \cos x}}{\sin x} \leadsto \frac{\frac{\color{blue}{{\left(\sin x\right)}^2}}{1 + \cos x}}{\sin x}\]
    15.0
  5. Using strategy rm
    15.0
  6. Applied add-cube-cbrt to get
    \[\color{red}{\frac{\frac{{\left(\sin x\right)}^2}{1 + \cos x}}{\sin x}} \leadsto \color{blue}{{\left(\sqrt[3]{\frac{\frac{{\left(\sin x\right)}^2}{1 + \cos x}}{\sin x}}\right)}^3}\]
    15.7
  7. Applied simplify to get
    \[{\color{red}{\left(\sqrt[3]{\frac{\frac{{\left(\sin x\right)}^2}{1 + \cos x}}{\sin x}}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{\frac{\sin x}{\cos x + 1}}\right)}}^3\]
    1.6

Original test:


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