Average Error: 0.0 → 0.0
Time: 1.6s
Precision: binary64
\[\frac{2}{e^{x} + e^{-x}} \]
↓
\[\sqrt{{\cosh x}^{-2}} \]
(FPCore (x) :precision binary64 (/ 2.0 (+ (exp x) (exp (- x)))))
↓
(FPCore (x) :precision binary64 (sqrt (pow (cosh x) -2.0)))
double code(double x) {
	return 2.0 / (exp(x) + exp(-x));
}
↓
double code(double x) {
	return sqrt(pow(cosh(x), -2.0));
}

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
    code = sqrt((cosh(x) ** (-2.0d0)))
end function

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

def code(x):
	return 2.0 / (math.exp(x) + math.exp(-x))
↓
def code(x):
	return math.sqrt(math.pow(math.cosh(x), -2.0))

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

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

code[x_] := N[(2.0 / N[(N[Exp[x], $MachinePrecision] + N[Exp[(-x)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[Sqrt[N[Power[N[Cosh[x], $MachinePrecision], -2.0], $MachinePrecision]], $MachinePrecision]

\frac{2}{e^{x} + e^{-x}}
↓
\sqrt{{\cosh x}^{-2}}

Error

Bits error versus x

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-rr0.5

    \[\leadsto \frac{2}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \cosh x\right)\right)}} \]

  3. Applied egg-rr0.1

    \[\leadsto \color{blue}{\sqrt[3]{{\left(\frac{1}{\cosh x}\right)}^{3}}} \]

  4. Applied egg-rr0.0

    \[\leadsto \color{blue}{\sqrt{{\cosh x}^{-2}}} \]

  5. Final simplification0.0

    \[\leadsto \sqrt{{\cosh x}^{-2}} \]

Reproduce

herbie shell --seed 2022155 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (- x)))))