\[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
Test:
NMSE problem 3.4.6
Bits:
128 bits
Bits error versus x
Bits error versus n
Time: 21.6 s
Input Error: 31.9
Output Error: 31.9
Log: ⚲
Profile: 🕒
\(\sqrt[3]{{\left(\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right)}^3}\right)}^3}\)
  1. Started with
    \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
    31.9
  2. Using strategy rm
    31.9
  3. Applied add-cbrt-cube to get
    \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}} \leadsto \color{blue}{\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right)}^3}}\]
    31.9
  4. Using strategy rm
    31.9
  5. Applied add-cbrt-cube to get
    \[\sqrt[3]{{\color{red}{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right)}}^3} \leadsto \sqrt[3]{{\color{blue}{\left(\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right)}^3}\right)}}^3}\]
    31.9

Original test:


(lambda ((x default) (n default))
  #:name "NMSE problem 3.4.6"
  (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))