\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
Test:
NMSE problem 3.3.3
Bits:
128 bits
Bits error versus x
Time: 11.9 s
Input Error: 9.5
Output Error: 25.2
Log: ⚲
Profile: 🕒
\(\frac{\left(x + {x}^2\right) + \left(\left(x - 2\right) - x \cdot 2\right) \cdot \left(x - 1\right)}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\)
  1. Started with
    \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
    9.5
  2. Using strategy rm
    9.5
  3. Applied frac-sub to get
    \[\color{red}{\left(\frac{1}{x + 1} - \frac{2}{x}\right)} + \frac{1}{x - 1} \leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}\]
    26.2
  4. Applied frac-add to get
    \[\color{red}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x} + \frac{1}{x - 1}} \leadsto \color{blue}{\frac{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}}\]
    25.0
  5. Applied simplify to get
    \[\frac{\color{red}{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)} \leadsto \frac{\color{blue}{\left(x + x \cdot x\right) + \left(\left(x - 2\right) - x \cdot 2\right) \cdot \left(x - 1\right)}}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\]
    25.2
  6. Applied simplify to get
    \[\frac{\color{red}{\left(x + x \cdot x\right)} + \left(\left(x - 2\right) - x \cdot 2\right) \cdot \left(x - 1\right)}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)} \leadsto \frac{\color{blue}{\left(x + {x}^2\right)} + \left(\left(x - 2\right) - x \cdot 2\right) \cdot \left(x - 1\right)}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\]
    25.2

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))))