Average Error: 0.0 → 0.0
Time: 3.3s
Precision: binary64
Cost: 26304
\[\frac{2}{e^{x} + e^{-x}} \]
↓
\[\begin{array}{l} t_0 := \sqrt{\frac{2}{2 \cdot \cosh x}}\\ t_0 \cdot t_0 \end{array} \]
(FPCore (x) :precision binary64 (/ 2.0 (+ (exp x) (exp (- x)))))
↓
(FPCore (x)
 :precision binary64
 (let* ((t_0 (sqrt (/ 2.0 (* 2.0 (cosh x)))))) (* t_0 t_0)))
double code(double x) {
	return 2.0 / (exp(x) + exp(-x));
}
↓
double code(double x) {
	double t_0 = sqrt((2.0 / (2.0 * cosh(x))));
	return t_0 * t_0;
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = 2.0d0 / (exp(x) + exp(-x))
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = sqrt((2.0d0 / (2.0d0 * cosh(x))))
    code = t_0 * t_0
end function

public static double code(double x) {
	return 2.0 / (Math.exp(x) + Math.exp(-x));
}
↓
public static double code(double x) {
	double t_0 = Math.sqrt((2.0 / (2.0 * Math.cosh(x))));
	return t_0 * t_0;
}

def code(x):
	return 2.0 / (math.exp(x) + math.exp(-x))
↓
def code(x):
	t_0 = math.sqrt((2.0 / (2.0 * math.cosh(x))))
	return t_0 * t_0

function code(x)
	return Float64(2.0 / Float64(exp(x) + exp(Float64(-x))))
end
↓
function code(x)
	t_0 = sqrt(Float64(2.0 / Float64(2.0 * cosh(x))))
	return Float64(t_0 * t_0)
end

function tmp = code(x)
	tmp = 2.0 / (exp(x) + exp(-x));
end
↓
function tmp = code(x)
	t_0 = sqrt((2.0 / (2.0 * cosh(x))));
	tmp = t_0 * t_0;
end

code[x_] := N[(2.0 / N[(N[Exp[x], $MachinePrecision] + N[Exp[(-x)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := Block[{t$95$0 = N[Sqrt[N[(2.0 / N[(2.0 * N[Cosh[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, N[(t$95$0 * t$95$0), $MachinePrecision]]

\frac{2}{e^{x} + e^{-x}}
↓
\begin{array}{l}
t_0 := \sqrt{\frac{2}{2 \cdot \cosh x}}\\
t_0 \cdot t_0
\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{2}{e^{x} + e^{-x}} \]

  2. Applied egg-rr0.0

    \[\leadsto \color{blue}{\sqrt{\frac{2}{2 \cdot \cosh x}} \cdot \sqrt{\frac{2}{2 \cdot \cosh x}}} \]

  3. Final simplification0.0

    \[\leadsto \sqrt{\frac{2}{2 \cdot \cosh x}} \cdot \sqrt{\frac{2}{2 \cdot \cosh x}} \]

Alternatives

Alternative 1
Error0.0
Cost19392
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{\cosh x}\right)\right) \]
Alternative 2
Error0.0
Cost19392
\[{\left({\cosh x}^{-0.5}\right)}^{2} \]
Alternative 3
Error0.0
Cost6592
\[\frac{1}{\cosh x} \]
Alternative 4
Error0.9
Cost1096
\[\begin{array}{l} t_0 := \left(1 + \frac{2}{x \cdot x}\right) + -1\\ \mathbf{if}\;x \leq -1.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.46:\\ \;\;\;\;1 + \left(x \cdot x\right) \cdot \left(-0.5 + x \cdot \left(x \cdot 0.20833333333333334\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 5
Error0.9
Cost840
\[\begin{array}{l} t_0 := \left(1 + \frac{2}{x \cdot x}\right) + -1\\ \mathbf{if}\;x \leq -5200000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 132000000:\\ \;\;\;\;\frac{2}{2 + x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 6
Error14.9
Cost712
\[\begin{array}{l} t_0 := \frac{2}{x \cdot x}\\ \mathbf{if}\;x \leq -1.25:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.25:\\ \;\;\;\;1 + -0.5 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 7
Error15.1
Cost584
\[\begin{array}{l} t_0 := \frac{2}{x \cdot x}\\ \mathbf{if}\;x \leq -1.42:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.4:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 8
Error14.9
Cost448
\[\frac{2}{2 + x \cdot x} \]
Alternative 9
Error30.5
Cost64
\[1 \]

Error

Reproduce

herbie shell --seed 2022330 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (- x)))))