Hyperbolic secant

Average Error: 0.0 → 0.0

Time: 1.0s

Precision: binary64

Cost: 13184

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

function tmp = code(x)
	tmp = 2.0 / (exp(x) + exp(-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[(N[Exp[x], $MachinePrecision] + N[Exp[(-x)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	15.1
Cost	7048

\[\begin{array}{l} t_0 := \frac{2}{{x}^{2}}\\ \mathbf{if}\;x \leq -1.25:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.25:\\ \;\;\;\;1 + -0.5 \cdot {x}^{2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	15.3
Cost	6920

\[\begin{array}{l} t_0 := \frac{2}{{x}^{2}}\\ \mathbf{if}\;x \leq -1.4:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.4:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	15.1
Cost	6784

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

Alternative 4
Error	31.2
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023053 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (- x)))))