\[\cos \left(x + \varepsilon\right) - \cos x\]
Test:
NMSE problem 3.3.5
Bits:
128 bits
Bits error versus x
Bits error versus eps
Time: 19.2 s
Input Error: 39.4
Output Error: 24.6
Log: ⚲
Profile: 🕒
\((\left(\cos x\right) * \left(\cos \varepsilon\right) + \left(\left(-\sin x \cdot \sin \varepsilon\right) - \cos x\right))_*\)
  1. Started with
    \[\cos \left(x + \varepsilon\right) - \cos x\]
    39.4
  2. Using strategy rm
    39.4
  3. Applied cos-sum to get
    \[\color{red}{\cos \left(x + \varepsilon\right)} - \cos x \leadsto \color{blue}{\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon\right)} - \cos x\]
    24.6
  4. Using strategy rm
    24.6
  5. Applied sub-neg to get
    \[\color{red}{\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon\right)} - \cos x \leadsto \color{blue}{\left(\cos x \cdot \cos \varepsilon + \left(-\sin x \cdot \sin \varepsilon\right)\right)} - \cos x\]
    24.6
  6. Applied associate--l+ to get
    \[\color{red}{\left(\cos x \cdot \cos \varepsilon + \left(-\sin x \cdot \sin \varepsilon\right)\right) - \cos x} \leadsto \color{blue}{\cos x \cdot \cos \varepsilon + \left(\left(-\sin x \cdot \sin \varepsilon\right) - \cos x\right)}\]
    24.6
  7. Using strategy rm
    24.6
  8. Applied fma-def to get
    \[\color{red}{\cos x \cdot \cos \varepsilon + \left(\left(-\sin x \cdot \sin \varepsilon\right) - \cos x\right)} \leadsto \color{blue}{(\left(\cos x\right) * \left(\cos \varepsilon\right) + \left(\left(-\sin x \cdot \sin \varepsilon\right) - \cos x\right))_*}\]
    24.6

Original test:


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