\[\cos \left(x + \varepsilon\right) - \cos x\]
Test:
NMSE problem 3.3.5
Bits:
128 bits
Bits error versus x
Bits error versus eps
Time: 20.9 s
Input Error: 39.7
Output Error: 24.3
Log: ⚲
Profile: 🕒
\(\sqrt[3]{{\left(\cos \varepsilon \cdot \cos x - (\left(\sin \varepsilon\right) * \left(\sin x\right) + \left(\cos x\right))_*\right)}^3}\)
  1. Started with
    \[\cos \left(x + \varepsilon\right) - \cos x\]
    39.7
  2. Using strategy rm
    39.7
  3. Applied cos-sum to get
    \[\color{red}{\cos \left(x + \varepsilon\right)} - \cos x \leadsto \color{blue}{\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon\right)} - \cos x\]
    24.1
  4. Using strategy rm
    24.1
  5. Applied add-cbrt-cube to get
    \[\color{red}{\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon\right) - \cos x} \leadsto \color{blue}{\sqrt[3]{{\left(\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon\right) - \cos x\right)}^3}}\]
    24.3
  6. Applied simplify to get
    \[\sqrt[3]{\color{red}{{\left(\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon\right) - \cos x\right)}^3}} \leadsto \sqrt[3]{\color{blue}{{\left(\cos \varepsilon \cdot \cos x - (\left(\sin \varepsilon\right) * \left(\sin x\right) + \left(\cos x\right))_*\right)}^3}}\]
    24.3

Original test:


(lambda ((x default) (eps default))
  #:name "NMSE problem 3.3.5"
  (- (cos (+ x eps)) (cos x)))