\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
Test:
NMSE problem 3.3.3
Bits:
128 bits
Bits error versus x
Time: 24.0 s
Input Error: 4.3
Output Error: 4.7
Log: ⚲
Profile: 🕒
\({\left(\sqrt[3]{\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}}\right)}^3\)
  1. Started with
    \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
    4.3
  2. Using strategy rm
    4.3
  3. Applied add-cube-cbrt to get
    \[\color{red}{\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}} \leadsto \color{blue}{{\left(\sqrt[3]{\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}}\right)}^3}\]
    4.7

Original test:


(lambda ((x default))
  #:name "NMSE problem 3.3.3"
  (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
  #:target
  (/ 2 (* x (- (sqr x) 1))))