\[\frac{1}{x + 1} - \frac{1}{x}\]
Test:
NMSE problem 3.3.1
Bits:
128 bits
Bits error versus x
Time: 3.1 s
Input Error: 6.0
Output Error: 1.0
Log: ⚲
Profile: 🕒
\({\left(\frac{\sqrt[3]{-1}}{\sqrt[3]{(x * x + x)_*}}\right)}^3\)
  1. Started with
    \[\frac{1}{x + 1} - \frac{1}{x}\]
    6.0
  2. Using strategy rm
    6.0
  3. Applied frac-sub to get
    \[\color{red}{\frac{1}{x + 1} - \frac{1}{x}} \leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 1}{\left(x + 1\right) \cdot x}}\]
    5.0
  4. Applied simplify to get
    \[\frac{\color{red}{1 \cdot x - \left(x + 1\right) \cdot 1}}{\left(x + 1\right) \cdot x} \leadsto \frac{\color{blue}{\left(x - x\right) - 1}}{\left(x + 1\right) \cdot x}\]
    0.6
  5. Applied simplify to get
    \[\frac{\left(x - x\right) - 1}{\color{red}{\left(x + 1\right) \cdot x}} \leadsto \frac{\left(x - x\right) - 1}{\color{blue}{(x * x + x)_*}}\]
    0.6
  6. Using strategy rm
    0.6
  7. Applied add-cube-cbrt to get
    \[\frac{\left(x - x\right) - 1}{\color{red}{(x * x + x)_*}} \leadsto \frac{\left(x - x\right) - 1}{\color{blue}{{\left(\sqrt[3]{(x * x + x)_*}\right)}^3}}\]
    1.0
  8. Applied add-cube-cbrt to get
    \[\frac{\color{red}{\left(x - x\right) - 1}}{{\left(\sqrt[3]{(x * x + x)_*}\right)}^3} \leadsto \frac{\color{blue}{{\left(\sqrt[3]{\left(x - x\right) - 1}\right)}^3}}{{\left(\sqrt[3]{(x * x + x)_*}\right)}^3}\]
    1.0
  9. Applied cube-undiv to get
    \[\color{red}{\frac{{\left(\sqrt[3]{\left(x - x\right) - 1}\right)}^3}{{\left(\sqrt[3]{(x * x + x)_*}\right)}^3}} \leadsto \color{blue}{{\left(\frac{\sqrt[3]{\left(x - x\right) - 1}}{\sqrt[3]{(x * x + x)_*}}\right)}^3}\]
    1.0
  10. Applied simplify to get
    \[{\color{red}{\left(\frac{\sqrt[3]{\left(x - x\right) - 1}}{\sqrt[3]{(x * x + x)_*}}\right)}}^3 \leadsto {\color{blue}{\left(\frac{\sqrt[3]{-1}}{\sqrt[3]{(x * x + x)_*}}\right)}}^3\]
    1.0

Original test:


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