Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
\[\frac{2}{e^{x} + e^{-x}} \]
↓
\[\sqrt{\frac{1}{\frac{1}{{\cosh x}^{-2}}}} \]
(FPCore (x) :precision binary64 (/ 2.0 (+ (exp x) (exp (- x)))))
↓
(FPCore (x) :precision binary64 (sqrt (/ 1.0 (/ 1.0 (pow (cosh x) -2.0)))))
double code(double x) {
	return 2.0 / (exp(x) + exp(-x));
}
↓
double code(double x) {
	return sqrt((1.0 / (1.0 / 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((1.0d0 / (1.0d0 / (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((1.0 / (1.0 / 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((1.0 / (1.0 / 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(Float64(1.0 / Float64(1.0 / (cosh(x) ^ -2.0))))
end

function tmp = code(x)
	tmp = 2.0 / (exp(x) + exp(-x));
end
↓
function tmp = code(x)
	tmp = sqrt((1.0 / (1.0 / (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[(1.0 / N[(1.0 / N[Power[N[Cosh[x], $MachinePrecision], -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

\frac{2}{e^{x} + e^{-x}}
↓
\sqrt{\frac{1}{\frac{1}{{\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-rr0.0

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

  3. Applied egg-rr0.0

    \[\leadsto \color{blue}{\sqrt{\frac{1}{{\cosh x}^{2}}}} \]

  4. Applied egg-rr0.0

    \[\leadsto \sqrt{\frac{1}{\color{blue}{\frac{1}{{\cosh x}^{-2}}}}} \]

  5. Final simplification0.0

    \[\leadsto \sqrt{\frac{1}{\frac{1}{{\cosh x}^{-2}}}} \]

Reproduce

herbie shell --seed 2022150 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (- x)))))