\[\cos \left(x + \varepsilon\right) - \cos x\]
Test:
NMSE problem 3.3.5
Bits:
128 bits
Bits error versus x
Bits error versus eps
Time: 5.8 s
Input Error: 18.3
Output Error: 9.1
Log: ⚲
Profile: 🕒
\(\left(\cos x \cdot \cos \varepsilon - \log_* (1 + (e^{\sin x \cdot \sin \varepsilon} - 1)^*)\right) - \cos x\)
  1. Started with
    \[\cos \left(x + \varepsilon\right) - \cos x\]
    18.3
  2. Using strategy rm
    18.3
  3. Applied cos-sum to get
    \[\color{red}{\cos \left(x + \varepsilon\right)} - \cos x \leadsto \color{blue}{\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon\right)} - \cos x\]
    9.0
  4. Using strategy rm
    9.0
  5. Applied log1p-expm1-u to get
    \[\left(\cos x \cdot \cos \varepsilon - \color{red}{\sin x \cdot \sin \varepsilon}\right) - \cos x \leadsto \left(\cos x \cdot \cos \varepsilon - \color{blue}{\log_* (1 + (e^{\sin x \cdot \sin \varepsilon} - 1)^*)}\right) - \cos x\]
    9.1

Original test:


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