\[\frac{1}{x + 1} - \frac{1}{x}\]
Test:
NMSE problem 3.3.1
Bits:
128 bits
Bits error versus x
Time: 1.6 s
Input Error: 5.7
Output Error: 0.5
Log: ⚲
Profile: 🕒
\(\frac{\left(x - x\right) - 1}{(x * x + x)_*}\)
  1. Started with
    \[\frac{1}{x + 1} - \frac{1}{x}\]
    5.7
  2. Using strategy rm
    5.7
  3. Applied frac-sub to get
    \[\color{red}{\frac{1}{x + 1} - \frac{1}{x}} \leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 1}{\left(x + 1\right) \cdot x}}\]
    4.8
  4. Applied simplify to get
    \[\frac{\color{red}{1 \cdot x - \left(x + 1\right) \cdot 1}}{\left(x + 1\right) \cdot x} \leadsto \frac{\color{blue}{\left(x - x\right) - 1}}{\left(x + 1\right) \cdot x}\]
    0.5
  5. Applied simplify to get
    \[\frac{\left(x - x\right) - 1}{\color{red}{\left(x + 1\right) \cdot x}} \leadsto \frac{\left(x - x\right) - 1}{\color{blue}{(x * x + x)_*}}\]
    0.5

Original test:


(lambda ((x default))
  #:name "NMSE problem 3.3.1"
  (- (/ 1 (+ x 1)) (/ 1 x)))