\[\tan \left(x + \varepsilon\right) - \tan x\]
Test:
NMSE problem 3.3.2
Bits:
128 bits
Bits error versus x
Bits error versus eps
Time: 3.7 s
Input Error: 16.6
Output Error: 16.6
Log: ⚲
Profile: 🕒
\(\frac{{\left(\frac{1}{\cot \left(x + \varepsilon\right)}\right)}^2 - {\left(\tan x\right)}^2}{\frac{1}{\cot \left(x + \varepsilon\right)} + \tan x}\)
  1. Started with
    \[\tan \left(x + \varepsilon\right) - \tan x\]
    16.6
  2. Using strategy rm
    16.6
  3. Applied tan-cotan to get
    \[\color{red}{\tan \left(x + \varepsilon\right)} - \tan x \leadsto \color{blue}{\frac{1}{\cot \left(x + \varepsilon\right)}} - \tan x\]
    16.6
  4. Using strategy rm
    16.6
  5. Applied flip-- to get
    \[\color{red}{\frac{1}{\cot \left(x + \varepsilon\right)} - \tan x} \leadsto \color{blue}{\frac{{\left(\frac{1}{\cot \left(x + \varepsilon\right)}\right)}^2 - {\left(\tan x\right)}^2}{\frac{1}{\cot \left(x + \varepsilon\right)} + \tan x}}\]
    16.6

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)))))