?

Average Error: 0.9 → 0.3

Time: 5.2s

Precision: binary64

Cost: 6592

\[0.01 \leq x \land x \leq 708\]

\[\frac{e^{x} - 1}{x} \]

↓

\[\frac{\mathsf{expm1}\left(x\right)}{x} \]

(FPCore (x) :precision binary64 (/ (- (exp x) 1.0) x))

↓

(FPCore (x) :precision binary64 (/ (expm1 x) x))

double code(double x) {
	return (exp(x) - 1.0) / x;
}

↓

double code(double x) {
	return expm1(x) / x;
}

public static double code(double x) {
	return (Math.exp(x) - 1.0) / x;
}

↓

public static double code(double x) {
	return Math.expm1(x) / x;
}

def code(x):
	return (math.exp(x) - 1.0) / x

↓

def code(x):
	return math.expm1(x) / x

function code(x)
	return Float64(Float64(exp(x) - 1.0) / x)
end

↓

function code(x)
	return Float64(expm1(x) / x)
end

code[x_] := N[(N[(N[Exp[x], $MachinePrecision] - 1.0), $MachinePrecision] / x), $MachinePrecision]

↓

code[x_] := N[(N[(Exp[x] - 1), $MachinePrecision] / x), $MachinePrecision]

\frac{e^{x} - 1}{x}

↓

\frac{\mathsf{expm1}\left(x\right)}{x}

Try it out?

In
Out

Enter valid numbers for all inputs

[Start]0.9	\[ \frac{e^{x} - 1}{x} \]
expm1-def [=>]0.3	\[ \frac{\color{blue}{\mathsf{expm1}\left(x\right)}}{x} \]

Alternative 1
Error	50.9
Cost	832

\[\left(1 + \left(x \cdot 0.5 + \frac{1}{x}\right)\right) + \frac{-1}{x} \]

Alternative 2
Error	50.9
Cost	320

\[1 + x \cdot 0.5 \]

Alternative 3
Error	53.2
Cost	64

\[1 \]

herbie shell --seed 1 
(FPCore (x)
  :name "(exp(x)-1)/x"
  :precision binary64
  :pre (and (<= 0.01 x) (<= x 708.0))
  (/ (- (exp x) 1.0) x))