\[\frac{1 - \cos x}{{x}^2}\]
Test:
NMSE problem 3.4.1
Bits:
128 bits
Bits error versus x
Time: 5.6 s
Input Error: 14.9
Output Error: 7.1
Log: ⚲
Profile: 🕒
\({\left(\frac{\sqrt{\frac{{\left(\sin x\right)}^2}{1 + \cos x}}}{x}\right)}^2\)
  1. Started with
    \[\frac{1 - \cos x}{{x}^2}\]
    14.9
  2. Using strategy rm
    14.9
  3. Applied flip-- to get
    \[\frac{\color{red}{1 - \cos x}}{{x}^2} \leadsto \frac{\color{blue}{\frac{{1}^2 - {\left(\cos x\right)}^2}{1 + \cos x}}}{{x}^2}\]
    14.9
  4. Applied simplify to get
    \[\frac{\frac{\color{red}{{1}^2 - {\left(\cos x\right)}^2}}{1 + \cos x}}{{x}^2} \leadsto \frac{\frac{\color{blue}{{\left(\sin x\right)}^2}}{1 + \cos x}}{{x}^2}\]
    7.3
  5. Using strategy rm
    7.3
  6. Applied add-sqr-sqrt to get
    \[\frac{\color{red}{\frac{{\left(\sin x\right)}^2}{1 + \cos x}}}{{x}^2} \leadsto \frac{\color{blue}{{\left(\sqrt{\frac{{\left(\sin x\right)}^2}{1 + \cos x}}\right)}^2}}{{x}^2}\]
    7.3
  7. Applied square-undiv to get
    \[\color{red}{\frac{{\left(\sqrt{\frac{{\left(\sin x\right)}^2}{1 + \cos x}}\right)}^2}{{x}^2}} \leadsto \color{blue}{{\left(\frac{\sqrt{\frac{{\left(\sin x\right)}^2}{1 + \cos x}}}{x}\right)}^2}\]
    7.1

Original test:


(lambda ((x default))
  #:name "NMSE problem 3.4.1"
  (/ (- 1 (cos x)) (sqr x)))