\[\frac{1 - \cos x}{{x}^2}\]
Test:
NMSE problem 3.4.1
Bits:
128 bits
Bits error versus x
Time: 10.7 s
Input Error: 14.4
Output Error: 7.1
Log: ⚲
Profile: 🕒
\(\frac{{\left(\frac{\sqrt[3]{{\left(\sin x\right)}^2}}{\sqrt[3]{1 + \cos x}}\right)}^3}{{x}^2}\)
  1. Started with
    \[\frac{1 - \cos x}{{x}^2}\]
    14.4
  2. Using strategy rm
    14.4
  3. Applied flip-- to get
    \[\frac{\color{red}{1 - \cos x}}{{x}^2} \leadsto \frac{\color{blue}{\frac{{1}^2 - {\left(\cos x\right)}^2}{1 + \cos x}}}{{x}^2}\]
    14.4
  4. Applied simplify to get
    \[\frac{\frac{\color{red}{{1}^2 - {\left(\cos x\right)}^2}}{1 + \cos x}}{{x}^2} \leadsto \frac{\frac{\color{blue}{{\left(\sin x\right)}^2}}{1 + \cos x}}{{x}^2}\]
    7.2
  5. Using strategy rm
    7.2
  6. Applied add-cube-cbrt to get
    \[\frac{\frac{{\left(\sin x\right)}^2}{\color{red}{1 + \cos x}}}{{x}^2} \leadsto \frac{\frac{{\left(\sin x\right)}^2}{\color{blue}{{\left(\sqrt[3]{1 + \cos x}\right)}^3}}}{{x}^2}\]
    7.5
  7. Applied add-cube-cbrt to get
    \[\frac{\frac{\color{red}{{\left(\sin x\right)}^2}}{{\left(\sqrt[3]{1 + \cos x}\right)}^3}}{{x}^2} \leadsto \frac{\frac{\color{blue}{{\left(\sqrt[3]{{\left(\sin x\right)}^2}\right)}^3}}{{\left(\sqrt[3]{1 + \cos x}\right)}^3}}{{x}^2}\]
    7.1
  8. Applied cube-undiv to get
    \[\frac{\color{red}{\frac{{\left(\sqrt[3]{{\left(\sin x\right)}^2}\right)}^3}{{\left(\sqrt[3]{1 + \cos x}\right)}^3}}}{{x}^2} \leadsto \frac{\color{blue}{{\left(\frac{\sqrt[3]{{\left(\sin x\right)}^2}}{\sqrt[3]{1 + \cos x}}\right)}^3}}{{x}^2}\]
    7.1

Original test:


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