\[\tan \left(x + \varepsilon\right) - \tan x\]
Test:
NMSE problem 3.3.2
Bits:
128 bits
Bits error versus x
Bits error versus eps
Time: 30.5 s
Input Error: 36.4
Output Error: 35.4
Log: ⚲
Profile: 🕒
\(\frac{\sin \left(x + \varepsilon\right)}{\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon} - \tan x\)
  1. Started with
    \[\tan \left(x + \varepsilon\right) - \tan x\]
    36.4
  2. Using strategy rm
    36.4
  3. Applied tan-quot to get
    \[\color{red}{\tan \left(x + \varepsilon\right)} - \tan x \leadsto \color{blue}{\frac{\sin \left(x + \varepsilon\right)}{\cos \left(x + \varepsilon\right)}} - \tan x\]
    36.5
  4. Using strategy rm
    36.5
  5. Applied cos-sum to get
    \[\frac{\sin \left(x + \varepsilon\right)}{\color{red}{\cos \left(x + \varepsilon\right)}} - \tan x \leadsto \frac{\sin \left(x + \varepsilon\right)}{\color{blue}{\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon}} - \tan x\]
    35.4

Original test:


(lambda ((x default) (eps default))
  #:name "NMSE problem 3.3.2"
  (- (tan (+ x eps)) (tan x))
  #:target
  (/ (sin eps) (* (cos x) (cos (+ x eps)))))