\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
Test:
NMSE problem 3.3.4
Bits:
128 bits
Bits error versus x
Time: 7.3 s
Input Error: 13.0
Output Error: 13.0
Log: ⚲
Profile: 🕒
\({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {\left(\sqrt{e^{\frac{\log x}{3}}}\right)}^2\)
  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 pow-to-exp to get
    \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{red}{{x}^{\left(\frac{1}{3}\right)}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{blue}{e^{\log x \cdot \frac{1}{3}}}\]
    13.3
  4. Applied simplify to get
    \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - e^{\color{red}{\log x \cdot \frac{1}{3}}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - e^{\color{blue}{\frac{\log x}{3}}}\]
    13.0
  5. Using strategy rm
    13.0
  6. Applied add-sqr-sqrt to get
    \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{red}{e^{\frac{\log x}{3}}} \leadsto {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - \color{blue}{{\left(\sqrt{e^{\frac{\log x}{3}}}\right)}^2}\]
    13.0
  7. Removed slow pow expressions

Original test:


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