Average Error: 0.0 → 0.1
Time: 1.5s
Precision: binary64
\[\frac{2}{e^{x} + e^{-x}} \]
↓
\[\sqrt[3]{{\left(\frac{2}{e^{-x} + e^{x}}\right)}^{3}} \]
(FPCore (x) :precision binary64 (/ 2.0 (+ (exp x) (exp (- x)))))
↓
(FPCore (x)
 :precision binary64
 (cbrt (pow (/ 2.0 (+ (exp (- x)) (exp x))) 3.0)))
double code(double x) {
	return 2.0 / (exp(x) + exp(-x));
}
↓
double code(double x) {
	return cbrt(pow((2.0 / (exp(-x) + exp(x))), 3.0));
}

public static double code(double x) {
	return 2.0 / (Math.exp(x) + Math.exp(-x));
}
↓
public static double code(double x) {
	return Math.cbrt(Math.pow((2.0 / (Math.exp(-x) + Math.exp(x))), 3.0));
}

function code(x)
	return Float64(2.0 / Float64(exp(x) + exp(Float64(-x))))
end
↓
function code(x)
	return cbrt((Float64(2.0 / Float64(exp(Float64(-x)) + exp(x))) ^ 3.0))
end

code[x_] := N[(2.0 / N[(N[Exp[x], $MachinePrecision] + N[Exp[(-x)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[Power[N[Power[N[(2.0 / N[(N[Exp[(-x)], $MachinePrecision] + N[Exp[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision]

\frac{2}{e^{x} + e^{-x}}
↓
\sqrt[3]{{\left(\frac{2}{e^{-x} + e^{x}}\right)}^{3}}

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 add-cbrt-cube_binary640.1

    \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{2}{e^{x} + e^{-x}} \cdot \frac{2}{e^{x} + e^{-x}}\right) \cdot \frac{2}{e^{x} + e^{-x}}}} \]

  3. Simplified0.1

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{2}{e^{-x} + e^{x}}\right)}^{3}}} \]

  4. Final simplification0.1

    \[\leadsto \sqrt[3]{{\left(\frac{2}{e^{-x} + e^{x}}\right)}^{3}} \]

Reproduce

herbie shell --seed 2022137 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (- x)))))