\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
Test:
NMSE problem 3.3.4
Bits:
128 bits
Bits error versus x
Time: 9.1 s
Input Error: 13.0
Output Error: 13.0
Log: ⚲
Profile: 🕒
\(e^{{\left(\sqrt[3]{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}\right)}^3}\)
  1. Started with
    \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
    13.0
  2. Using strategy rm
    13.0
  3. Applied add-exp-log to get
    \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}} \leadsto \color{blue}{e^{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}}\]
    13.0
  4. Using strategy rm
    13.0
  5. Applied add-cube-cbrt to get
    \[e^{\color{red}{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}} \leadsto e^{\color{blue}{{\left(\sqrt[3]{\log \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\right)}\right)}^3}}\]
    13.0

Original test:


(lambda ((x default))
  #:name "NMSE problem 3.3.4"
  (- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3))))