\[\frac{1 - \cos x}{{x}^2}\]
Test:
NMSE problem 3.4.1
Bits:
128 bits
Bits error versus x
Time: 17.7 s
Input Error: 31.4
Output Error: 15.7
Log: ⚲
Profile: 🕒
\(\frac{\frac{{\left(\sin x\right)}^2}{1 + \cos x}}{{x}^2}\)
  1. Started with
    \[\frac{1 - \cos x}{{x}^2}\]
    31.4
  2. Using strategy rm
    31.4
  3. Applied flip-- to get
    \[\frac{\color{red}{1 - \cos x}}{{x}^2} \leadsto \frac{\color{blue}{\frac{{1}^2 - {\left(\cos x\right)}^2}{1 + \cos x}}}{{x}^2}\]
    31.6
  4. Applied simplify to get
    \[\frac{\frac{\color{red}{{1}^2 - {\left(\cos x\right)}^2}}{1 + \cos x}}{{x}^2} \leadsto \frac{\frac{\color{blue}{{\left(\sin x\right)}^2}}{1 + \cos x}}{{x}^2}\]
    15.7

Original test:


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