\[\cos \left(x + \varepsilon\right) - \cos x\]
Test:
NMSE problem 3.3.5
Bits:
128 bits
Bits error versus x
Bits error versus eps
Time: 27.9 s
Input Error: 39.7
Output Error: 24.2
Log: ⚲
Profile: 🕒
\(\left(\cos x \cdot \cos \varepsilon - (e^{\log_* (1 + \sin x \cdot \sin \varepsilon)} - 1)^*\right) - \cos x\)
  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 expm1-log1p-u to get
    \[\left(\cos x \cdot \cos \varepsilon - \color{red}{\sin x \cdot \sin \varepsilon}\right) - \cos x \leadsto \left(\cos x \cdot \cos \varepsilon - \color{blue}{(e^{\log_* (1 + \sin x \cdot \sin \varepsilon)} - 1)^*}\right) - \cos x\]
    24.2

Original test:


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