\[\tan \left(x + \varepsilon\right) - \tan x\]
Test:
NMSE problem 3.3.2
Bits:
128 bits
Bits error versus x
Bits error versus eps
Time: 3.3 s
Input Error: 16.8
Output Error: 16.9
Log: ⚲
Profile: 🕒
\(\tan \left(x + \varepsilon\right) - \frac{\sin x}{\cos x}\)
  1. Started with
    \[\tan \left(x + \varepsilon\right) - \tan x\]
    16.8
  2. Using strategy rm
    16.8
  3. Applied tan-quot to get
    \[\tan \left(x + \varepsilon\right) - \color{red}{\tan x} \leadsto \tan \left(x + \varepsilon\right) - \color{blue}{\frac{\sin x}{\cos x}}\]
    16.9

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)))))