\[\sqrt{x + 1} - \sqrt{x}\]
Test:
NMSE example 3.1
Bits:
128 bits
Bits error versus x
Time: 6.0 s
Input Error: 29.4
Output Error: 29.5
Log: ⚲
Profile: 🕒
\({\left({\left(\sqrt{\sqrt[3]{\sqrt{x + 1}}}\right)}^2\right)}^3 - \sqrt{x}\)
  1. Started with
    \[\sqrt{x + 1} - \sqrt{x}\]
    29.4
  2. Using strategy rm
    29.4
  3. Applied add-cube-cbrt to get
    \[\color{red}{\sqrt{x + 1}} - \sqrt{x} \leadsto \color{blue}{{\left(\sqrt[3]{\sqrt{x + 1}}\right)}^3} - \sqrt{x}\]
    29.5
  4. Using strategy rm
    29.5
  5. Applied add-sqr-sqrt to get
    \[{\color{red}{\left(\sqrt[3]{\sqrt{x + 1}}\right)}}^3 - \sqrt{x} \leadsto {\color{blue}{\left({\left(\sqrt{\sqrt[3]{\sqrt{x + 1}}}\right)}^2\right)}}^3 - \sqrt{x}\]
    29.5

Original test:


(lambda ((x default))
  #:name "NMSE example 3.1"
  (- (sqrt (+ x 1)) (sqrt x))
  #:target
  (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))