\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
Test:
NMSE problem 3.3.3
Bits:
128 bits
Bits error versus x
Time: 5.2 s
Input Error: 10.3
Output Error: 26.0
Log: ⚲
Profile: 🕒
\(\frac{x - (2 * x + 2)_*}{(x * x + x)_*} + \frac{1}{x - 1}\)
  1. Started with
    \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
    10.3
  2. Using strategy rm
    10.3
  3. Applied frac-sub to get
    \[\color{red}{\left(\frac{1}{x + 1} - \frac{2}{x}\right)} + \frac{1}{x - 1} \leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}\]
    26.0
  4. Applied simplify to get
    \[\frac{\color{red}{1 \cdot x - \left(x + 1\right) \cdot 2}}{\left(x + 1\right) \cdot x} + \frac{1}{x - 1} \leadsto \frac{\color{blue}{x - (2 * x + 2)_*}}{\left(x + 1\right) \cdot x} + \frac{1}{x - 1}\]
    26.0
  5. Applied simplify to get
    \[\frac{x - (2 * x + 2)_*}{\color{red}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1} \leadsto \frac{x - (2 * x + 2)_*}{\color{blue}{(x * x + x)_*}} + \frac{1}{x - 1}\]
    26.0

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))))