\[\frac{1 - \cos x}{{x}^2}\]
Test:
NMSE problem 3.4.1
Bits:
128 bits
Bits error versus x
Time: 12.1 s
Input Error: 31.4
Output Error: 15.5
Log: ⚲
Profile: 🕒
\(\frac{{\left(\sin x\right)}^2}{x} \cdot \frac{1}{(\left(\cos x\right) * x + x)_*}\)
  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
  5. Using strategy rm
    15.7
  6. Applied square-mult to get
    \[\frac{\frac{{\left(\sin x\right)}^2}{1 + \cos x}}{\color{red}{{x}^2}} \leadsto \frac{\frac{{\left(\sin x\right)}^2}{1 + \cos x}}{\color{blue}{x \cdot x}}\]
    15.7
  7. Applied div-inv to get
    \[\frac{\color{red}{\frac{{\left(\sin x\right)}^2}{1 + \cos x}}}{x \cdot x} \leadsto \frac{\color{blue}{{\left(\sin x\right)}^2 \cdot \frac{1}{1 + \cos x}}}{x \cdot x}\]
    15.7
  8. Applied times-frac to get
    \[\color{red}{\frac{{\left(\sin x\right)}^2 \cdot \frac{1}{1 + \cos x}}{x \cdot x}} \leadsto \color{blue}{\frac{{\left(\sin x\right)}^2}{x} \cdot \frac{\frac{1}{1 + \cos x}}{x}}\]
    15.5
  9. Applied simplify to get
    \[\frac{{\left(\sin x\right)}^2}{x} \cdot \color{red}{\frac{\frac{1}{1 + \cos x}}{x}} \leadsto \frac{{\left(\sin x\right)}^2}{x} \cdot \color{blue}{\frac{1}{(\left(\cos x\right) * x + x)_*}}\]
    15.5

Original test:


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