\[\frac{e^{x}}{e^{x} - 1}\]
Test:
NMSE section 3.11
Bits:
128 bits
Bits error versus x
Time: 5.5 s
Input Error: 40.1
Output Error: 0.4
Log: ⚲
Profile: 🕒
\(\frac{1}{\frac{(e^{x} - 1)^*}{e^{x}}}\)
  1. Started with
    \[\frac{e^{x}}{e^{x} - 1}\]
    40.1
  2. Applied simplify to get
    \[\color{red}{\frac{e^{x}}{e^{x} - 1}} \leadsto \color{blue}{\frac{e^{x}}{(e^{x} - 1)^*}}\]
    0.4
  3. Using strategy rm
    0.4
  4. Applied clear-num to get
    \[\color{red}{\frac{e^{x}}{(e^{x} - 1)^*}} \leadsto \color{blue}{\frac{1}{\frac{(e^{x} - 1)^*}{e^{x}}}}\]
    0.4

Original test:


(lambda ((x default))
  #:name "NMSE section 3.11"
  (/ (exp x) (- (exp x) 1))
  #:target
  (/ 1 (- 1 (exp (- x)))))