\[\tan \left(x + \varepsilon\right) - \tan x\]
Test:
NMSE problem 3.3.2
Bits:
128 bits
Bits error versus x
Bits error versus eps
Time: 16.5 s
Input Error: 37.4
Output Error: 37.4
Log: ⚲
Profile: 🕒
\(\frac{1}{\cos \left(x + \varepsilon\right)} \cdot \sin \left(x + \varepsilon\right) - \tan x\)
  1. Started with
    \[\tan \left(x + \varepsilon\right) - \tan x\]
    37.4
  2. Using strategy rm
    37.4
  3. Applied tan-cotan to get
    \[\color{red}{\tan \left(x + \varepsilon\right)} - \tan x \leadsto \color{blue}{\frac{1}{\cot \left(x + \varepsilon\right)}} - \tan x\]
    37.4
  4. Using strategy rm
    37.4
  5. Applied cotan-quot to get
    \[\frac{1}{\color{red}{\cot \left(x + \varepsilon\right)}} - \tan x \leadsto \frac{1}{\color{blue}{\frac{\cos \left(x + \varepsilon\right)}{\sin \left(x + \varepsilon\right)}}} - \tan x\]
    37.5
  6. Applied associate-/r/ to get
    \[\color{red}{\frac{1}{\frac{\cos \left(x + \varepsilon\right)}{\sin \left(x + \varepsilon\right)}}} - \tan x \leadsto \color{blue}{\frac{1}{\cos \left(x + \varepsilon\right)} \cdot \sin \left(x + \varepsilon\right)} - \tan x\]
    37.4

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)))))