\[\tan \left(x + \varepsilon\right) - \tan x\]
Test:
NMSE problem 3.3.2
Bits:
128 bits
Bits error versus x
Bits error versus eps
Time: 26.7 s
Input Error: 37.2
Output Error: 37.9
Log: ⚲
Profile: 🕒
\({\left(\sqrt[3]{\tan \left(x + \varepsilon\right)}\right)}^3 - \tan x\)
  1. Started with
    \[\tan \left(x + \varepsilon\right) - \tan x\]
    37.2
  2. Using strategy rm
    37.2
  3. Applied add-cube-cbrt to get
    \[\color{red}{\tan \left(x + \varepsilon\right)} - \tan x \leadsto \color{blue}{{\left(\sqrt[3]{\tan \left(x + \varepsilon\right)}\right)}^3} - \tan x\]
    37.9

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)))))