\[\frac{e^{x} - 1}{x}\]
Test:
Kahan's exp quotient
Bits:
128 bits
Bits error versus x
Time: 5.2 s
Input Error: 40.2
Output Error: 0.0
Log: ⚲
Profile: 🕒
\(\frac{\frac{1}{x}}{\frac{1}{(e^{x} - 1)^*}}\)
  1. Started with
    \[\frac{e^{x} - 1}{x}\]
    40.2
  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 clear-num to get
    \[\color{red}{\frac{(e^{x} - 1)^*}{x}} \leadsto \color{blue}{\frac{1}{\frac{x}{(e^{x} - 1)^*}}}\]
    0.0
  5. Using strategy rm
    0.0
  6. Applied div-inv to get
    \[\frac{1}{\color{red}{\frac{x}{(e^{x} - 1)^*}}} \leadsto \frac{1}{\color{blue}{x \cdot \frac{1}{(e^{x} - 1)^*}}}\]
    0.1
  7. Applied associate-/r* to get
    \[\color{red}{\frac{1}{x \cdot \frac{1}{(e^{x} - 1)^*}}} \leadsto \color{blue}{\frac{\frac{1}{x}}{\frac{1}{(e^{x} - 1)^*}}}\]
    0.0

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)))