\[\frac{e^{x} - 1}{x}\]
Test:
Kahan's exp quotient
Bits:
128 bits
Bits error versus x
Time: 2.6 s
Input Error: 17.0
Output Error: 0.1
Log: ⚲
Profile: 🕒
\((e^{\log_* (1 + \frac{(e^{x} - 1)^*}{x})} - 1)^*\)
  1. Started with
    \[\frac{e^{x} - 1}{x}\]
    17.0
  2. Applied simplify to get
    \[\color{red}{\frac{e^{x} - 1}{x}} \leadsto \color{blue}{\frac{(e^{x} - 1)^*}{x}}\]
    0.0
  3. Using strategy rm
    0.0
  4. Applied expm1-log1p-u to get
    \[\color{red}{\frac{(e^{x} - 1)^*}{x}} \leadsto \color{blue}{(e^{\log_* (1 + \frac{(e^{x} - 1)^*}{x})} - 1)^*}\]
    0.1
  5. Removed slow pow expressions

Original test:


(lambda ((x default))
  #:name "Kahan's exp quotient"
  (/ (- (exp x) 1) x)
  #:target
  (if (and (< x 1) (> x -1)) (/ (- (exp x) 1) (log (exp x))) (/ (- (exp x) 1) x)))