?

Average Error: 0.0 → 0
Time: 3.1s
Precision: binary64
Cost: 6464

?

\[-1000 \leq x \land x \leq 1000000\]
\[\frac{1}{e^{-x}} \]
\[e^{x} \]
(FPCore (x) :precision binary64 (/ 1.0 (exp (- x))))
(FPCore (x) :precision binary64 (exp x))
double code(double x) {
	return 1.0 / exp(-x);
}
double code(double x) {
	return exp(x);
}
real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 / exp(-x)
end function
real(8) function code(x)
    real(8), intent (in) :: x
    code = exp(x)
end function
public static double code(double x) {
	return 1.0 / Math.exp(-x);
}
public static double code(double x) {
	return Math.exp(x);
}
def code(x):
	return 1.0 / math.exp(-x)
def code(x):
	return math.exp(x)
function code(x)
	return Float64(1.0 / exp(Float64(-x)))
end
function code(x)
	return exp(x)
end
function tmp = code(x)
	tmp = 1.0 / exp(-x);
end
function tmp = code(x)
	tmp = exp(x);
end
code[x_] := N[(1.0 / N[Exp[(-x)], $MachinePrecision]), $MachinePrecision]
code[x_] := N[Exp[x], $MachinePrecision]
\frac{1}{e^{-x}}
e^{x}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.0

    \[\frac{1}{e^{-x}} \]
  2. Simplified0

    \[\leadsto \color{blue}{e^{x}} \]
    Proof

    [Start]0.0

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

    exp-neg [=>]0.0

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

    remove-double-div [=>]0

    \[ \color{blue}{e^{x}} \]
  3. Final simplification0

    \[\leadsto e^{x} \]

Reproduce?

herbie shell --seed 1 
(FPCore (x)
  :name "1/exp(-x)"
  :precision binary64
  :pre (and (<= -1000.0 x) (<= x 1000000.0))
  (/ 1.0 (exp (- x))))