\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
Test:
NMSE problem 3.3.4
Bits:
128 bits
Bits error versus x
Time: 12.9 s
Input Error: 29.8
Output Error: 29.8
Log: ⚲
Profile: 🕒
\(e^{\frac{\log \left(x + 1\right)}{3}} - {\left(\sqrt[3]{{x}^{\left(\frac{1}{3}\right)}}\right)}^3\)
  1. Started with
    \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
    29.8
  2. Using strategy rm
    29.8
  3. Applied add-exp-log to get
    \[{\color{red}{\left(x + 1\right)}}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)} \leadsto {\color{blue}{\left(e^{\log \left(x + 1\right)}\right)}}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
    30.1
  4. Applied pow-exp to get
    \[\color{red}{{\left(e^{\log \left(x + 1\right)}\right)}^{\left(\frac{1}{3}\right)}} - {x}^{\left(\frac{1}{3}\right)} \leadsto \color{blue}{e^{\log \left(x + 1\right) \cdot \frac{1}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
    30.1
  5. Applied simplify to get
    \[e^{\color{red}{\log \left(x + 1\right) \cdot \frac{1}{3}}} - {x}^{\left(\frac{1}{3}\right)} \leadsto e^{\color{blue}{\frac{\log \left(x + 1\right)}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
    29.8
  6. Using strategy rm
    29.8
  7. Applied add-cube-cbrt to get
    \[e^{\frac{\log \left(x + 1\right)}{3}} - \color{red}{{x}^{\left(\frac{1}{3}\right)}} \leadsto e^{\frac{\log \left(x + 1\right)}{3}} - \color{blue}{{\left(\sqrt[3]{{x}^{\left(\frac{1}{3}\right)}}\right)}^3}\]
    29.8

Original test:


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