Average Error: 0.0 → 0.0
Time: 3.4s
Precision: binary64
\[\frac{2}{e^{x} + e^{-x}} \]
↓
\[\frac{\sqrt{\frac{2}{\cosh x}}}{\sqrt{2 \cdot \cosh x}} \]
(FPCore (x) :precision binary64 (/ 2.0 (+ (exp x) (exp (- x)))))
↓
(FPCore (x)
 :precision binary64
 (/ (sqrt (/ 2.0 (cosh x))) (sqrt (* 2.0 (cosh x)))))
double code(double x) {
	return 2.0 / (exp(x) + exp(-x));
}
↓
double code(double x) {
	return sqrt((2.0 / cosh(x))) / sqrt((2.0 * cosh(x)));
}

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((2.0d0 / cosh(x))) / sqrt((2.0d0 * cosh(x)))
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((2.0 / Math.cosh(x))) / Math.sqrt((2.0 * Math.cosh(x)));
}

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

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

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

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

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

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-rr0.1

    \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{2}{2 \cdot \cosh x} \cdot \frac{2}{2 \cdot \cosh x}\right) \cdot \frac{2}{2 \cdot \cosh x}}} \]

  3. Applied egg-rr0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2022210 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (- x)))))