Average Error: 0.0 → 0.0
Time: 1.3s
Precision: binary64
\[\frac{2}{e^{x} + e^{-x}} \]
↓
\[\frac{-2}{\frac{-1}{e^{x}} - e^{x}} \]
(FPCore (x) :precision binary64 (/ 2.0 (+ (exp x) (exp (- x)))))
↓
(FPCore (x) :precision binary64 (/ -2.0 (- (/ -1.0 (exp x)) (exp x))))
double code(double x) {
	return 2.0 / (exp(x) + exp(-x));
}
↓
double code(double x) {
	return -2.0 / ((-1.0 / exp(x)) - exp(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 = (-2.0d0) / (((-1.0d0) / exp(x)) - exp(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 -2.0 / ((-1.0 / Math.exp(x)) - Math.exp(x));
}

def code(x):
	return 2.0 / (math.exp(x) + math.exp(-x))
↓
def code(x):
	return -2.0 / ((-1.0 / math.exp(x)) - math.exp(x))

function code(x)
	return Float64(2.0 / Float64(exp(x) + exp(Float64(-x))))
end
↓
function code(x)
	return Float64(-2.0 / Float64(Float64(-1.0 / exp(x)) - exp(x)))
end

function tmp = code(x)
	tmp = 2.0 / (exp(x) + exp(-x));
end
↓
function tmp = code(x)
	tmp = -2.0 / ((-1.0 / exp(x)) - exp(x));
end

code[x_] := N[(2.0 / N[(N[Exp[x], $MachinePrecision] + N[Exp[(-x)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(-2.0 / N[(N[(-1.0 / N[Exp[x], $MachinePrecision]), $MachinePrecision] - N[Exp[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\frac{2}{e^{x} + e^{-x}}
↓
\frac{-2}{\frac{-1}{e^{x}} - e^{x}}

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 frac-2neg_binary640.0

    \[\leadsto \color{blue}{\frac{-2}{-\left(e^{x} + e^{-x}\right)}} \]

  3. Simplified0.0

    \[\leadsto \frac{\color{blue}{-2}}{-\left(e^{x} + e^{-x}\right)} \]

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2022131 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (- x)))))