\[\cos \left(x + \varepsilon\right) - \cos x\]
Test:
NMSE problem 3.3.5
Bits:
128 bits
Bits error versus x
Bits error versus eps
Time: 8.9 s
Input Error: 18.2
Output Error: 9.2
Log: ⚲
Profile: 🕒
\(\sqrt[3]{{\left(\cos x \cdot \cos \varepsilon - \left(\sin x \cdot \sin \varepsilon + \cos x\right)\right)}^3}\)
  1. Started with
    \[\cos \left(x + \varepsilon\right) - \cos x\]
    18.2
  2. Using strategy rm
    18.2
  3. Applied cos-sum to get
    \[\color{red}{\cos \left(x + \varepsilon\right)} - \cos x \leadsto \color{blue}{\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon\right)} - \cos x\]
    9.1
  4. Applied associate--l- to get
    \[\color{red}{\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon\right) - \cos x} \leadsto \color{blue}{\cos x \cdot \cos \varepsilon - \left(\sin x \cdot \sin \varepsilon + \cos x\right)}\]
    9.1
  5. Using strategy rm
    9.1
  6. Applied add-cbrt-cube to get
    \[\color{red}{\cos x \cdot \cos \varepsilon - \left(\sin x \cdot \sin \varepsilon + \cos x\right)} \leadsto \color{blue}{\sqrt[3]{{\left(\cos x \cdot \cos \varepsilon - \left(\sin x \cdot \sin \varepsilon + \cos x\right)\right)}^3}}\]
    9.2

Original test:


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