Hyperbolic secant

Average Error: 0.0 → 0.0

Time: 1.9s

Precision: binary64

Cost: 6720

Math

\[\frac{2}{e^{x} + e^{-x}} \]

↓

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

FPCore

(FPCore (x) :precision binary64 (/ 2.0 (+ (exp x) (exp (- x)))))

↓

(FPCore (x) :precision binary64 (/ 2.0 (* 2.0 (cosh x))))

C

double code(double x) {
	return 2.0 / (exp(x) + exp(-x));
}

↓

double code(double x) {
	return 2.0 / (2.0 * cosh(x));
}

Fortran

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 / (2.0d0 * cosh(x))
end function

Java

public static double code(double x) {
	return 2.0 / (Math.exp(x) + Math.exp(-x));
}

↓

public static double code(double x) {
	return 2.0 / (2.0 * Math.cosh(x));
}

Python

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

↓

def code(x):
	return 2.0 / (2.0 * math.cosh(x))

Julia

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

↓

function code(x)
	return Float64(2.0 / Float64(2.0 * cosh(x)))
end

MATLAB

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

↓

function tmp = code(x)
	tmp = 2.0 / (2.0 * cosh(x));
end

Wolfram

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

↓

code[x_] := N[(2.0 / N[(2.0 * N[Cosh[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[\frac{2}{e^{x} + e^{-x}} \]

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	32.0
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022284 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (- x)))))