\[\tan \left(x + \varepsilon\right) - \tan x\]
Test:
NMSE problem 3.3.2
Bits:
128 bits
Bits error versus x
Bits error versus eps
Time: 3.2 s
Input Error: 17.0
Output Error: 17.1
Log: ⚲
Profile: 🕒
\(\tan \left(x + \varepsilon\right) - \sin x \cdot \frac{1}{\cos x}\)
  1. Started with
    \[\tan \left(x + \varepsilon\right) - \tan x\]
    17.0
  2. Using strategy rm
    17.0
  3. Applied tan-quot to get
    \[\tan \left(x + \varepsilon\right) - \color{red}{\tan x} \leadsto \tan \left(x + \varepsilon\right) - \color{blue}{\frac{\sin x}{\cos x}}\]
    17.1
  4. Using strategy rm
    17.1
  5. Applied div-inv to get
    \[\tan \left(x + \varepsilon\right) - \color{red}{\frac{\sin x}{\cos x}} \leadsto \tan \left(x + \varepsilon\right) - \color{blue}{\sin x \cdot \frac{1}{\cos x}}\]
    17.1

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)))))