\[\frac{x}{{x}^2 + 1}\]
Test:
x / (x^2 + 1)
Bits:
128 bits
Bits error versus x
Time: 1.7 s
Input Error: 6.9
Output Error: 6.9
Log: ⚲
Profile: 🕒
\(\frac{x}{(x * x + 1)_*}\)
  1. Started with
    \[\frac{x}{{x}^2 + 1}\]
    6.9
  2. Using strategy rm
    6.9
  3. Applied square-mult to get
    \[\frac{x}{\color{red}{{x}^2} + 1} \leadsto \frac{x}{\color{blue}{x \cdot x} + 1}\]
    6.9
  4. Applied fma-def to get
    \[\frac{x}{\color{red}{x \cdot x + 1}} \leadsto \frac{x}{\color{blue}{(x * x + 1)_*}}\]
    6.9

Original test:


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