\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
Test:
NMSE problem 3.4.4
Bits:
128 bits
Bits error versus x
Time: 4.4 s
Input Error: 16.8
Output Error: 0.2
Log: ⚲
Profile: 🕒
\(\sqrt{e^{\log \left(\frac{(e^{x \cdot 2} - 1)^*}{(e^{x} - 1)^*}\right)}}\)
  1. Started with
    \[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
    16.8
  2. Applied simplify to get
    \[\color{red}{\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}} \leadsto \color{blue}{\sqrt{\frac{(e^{x \cdot 2} - 1)^*}{(e^{x} - 1)^*}}}\]
    0.2
  3. Using strategy rm
    0.2
  4. Applied add-exp-log to get
    \[\sqrt{\color{red}{\frac{(e^{x \cdot 2} - 1)^*}{(e^{x} - 1)^*}}} \leadsto \sqrt{\color{blue}{e^{\log \left(\frac{(e^{x \cdot 2} - 1)^*}{(e^{x} - 1)^*}\right)}}}\]
    0.2

Original test:


(lambda ((x default))
  #:name "NMSE problem 3.4.4"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))