Average Error: 60.1 → 58.0
Time: 5.6s
Precision: binary64
\[\frac{e^{x} - 1}{\log \left(e^{x}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;e^{x} \le 1:\\ \;\;\;\;\frac{e^{x}}{x} - \frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{x} - 1}{\log \left(e^{x}\right)}\\ \end{array}\]
\frac{e^{x} - 1}{\log \left(e^{x}\right)}
↓
\begin{array}{l}
\mathbf{if}\;e^{x} \le 1:\\
\;\;\;\;\frac{e^{x}}{x} - \frac{1}{x}\\

\mathbf{else}:\\
\;\;\;\;\frac{e^{x} - 1}{\log \left(e^{x}\right)}\\

\end{array}
double code(double x) {
	return ((double) (((double) (((double) exp(x)) - 1.0)) / ((double) log(((double) exp(x))))));
}
↓
double code(double x) {
	double VAR;
	if ((((double) exp(x)) <= 1.0)) {
		VAR = ((double) (((double) (((double) exp(x)) / x)) - ((double) (1.0 / x))));
	} else {
		VAR = ((double) (((double) (((double) exp(x)) - 1.0)) / ((double) log(((double) exp(x))))));
	}
	return VAR;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if (exp x) < 1

    1. Initial program 62.0

      \[\frac{e^{x} - 1}{\log \left(e^{x}\right)}\]

    2. Simplified59.8

      \[\leadsto \color{blue}{\frac{e^{x}}{x} - \frac{1}{x}}\]

    if 1 < (exp x)

    1. Initial program 0.2

      \[\frac{e^{x} - 1}{\log \left(e^{x}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification58.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;e^{x} \le 1:\\ \;\;\;\;\frac{e^{x}}{x} - \frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{x} - 1}{\log \left(e^{x}\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ (- (exp x) 1) (log (exp x)))"
  :precision binary64
  (/ (- (exp x) 1.0) (log (exp x))))