\[\frac{x}{{x}^2 + 1}\]
Test:
x / (x^2 + 1)
Bits:
128 bits
Bits error versus x
Time: 3.9 s
Input Error: 7.0
Output Error: 7.0
Log: ⚲
Profile: 🕒
\(\log_* (1 + (e^{\frac{x}{{x}^2 + 1}} - 1)^*)\)
  1. Started with
    \[\frac{x}{{x}^2 + 1}\]
    7.0
  2. Using strategy rm
    7.0
  3. Applied log1p-expm1-u to get
    \[\color{red}{\frac{x}{{x}^2 + 1}} \leadsto \color{blue}{\log_* (1 + (e^{\frac{x}{{x}^2 + 1}} - 1)^*)}\]
    7.0

Original test:


(lambda ((x default))
  #:name "x / (x^2 + 1)"
  (/ x (+ (sqr x) 1))
  #:target
  (/ 1 (+ x (/ 1 x))))