NMSE Section 6.1 mentioned, A

Percentage Accurate: 73.7% → 99.7%

Time: 15.4s

Alternatives: 14

Speedup: 1.9×

• 38.5% of points produce a very large (infinite) output. You may want to add a precondition.

• could not determine a ground truth

  1. x = -1.99999999999999997e77
  2. eps = -2e-231

Specification

Math

\[\begin{array}{l} \\ \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (/
  (-
   (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
   (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))
  2.0))

C

double code(double x, double eps) {
	return (((1.0 + (1.0 / eps)) * exp(-((1.0 - eps) * x))) - (((1.0 / eps) - 1.0) * exp(-((1.0 + eps) * x)))) / 2.0;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    code = (((1.0d0 + (1.0d0 / eps)) * exp(-((1.0d0 - eps) * x))) - (((1.0d0 / eps) - 1.0d0) * exp(-((1.0d0 + eps) * x)))) / 2.0d0
end function

Java

public static double code(double x, double eps) {
	return (((1.0 + (1.0 / eps)) * Math.exp(-((1.0 - eps) * x))) - (((1.0 / eps) - 1.0) * Math.exp(-((1.0 + eps) * x)))) / 2.0;
}

Python

def code(x, eps):
	return (((1.0 + (1.0 / eps)) * math.exp(-((1.0 - eps) * x))) - (((1.0 / eps) - 1.0) * math.exp(-((1.0 + eps) * x)))) / 2.0

Julia

function code(x, eps)
	return Float64(Float64(Float64(Float64(1.0 + Float64(1.0 / eps)) * exp(Float64(-Float64(Float64(1.0 - eps) * x)))) - Float64(Float64(Float64(1.0 / eps) - 1.0) * exp(Float64(-Float64(Float64(1.0 + eps) * x))))) / 2.0)
end

MATLAB

function tmp = code(x, eps)
	tmp = (((1.0 + (1.0 / eps)) * exp(-((1.0 - eps) * x))) - (((1.0 / eps) - 1.0) * exp(-((1.0 + eps) * x)))) / 2.0;
end

Wolfram

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

Initial Program: 73.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (/
  (-
   (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
   (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))
  2.0))

C

double code(double x, double eps) {
	return (((1.0 + (1.0 / eps)) * exp(-((1.0 - eps) * x))) - (((1.0 / eps) - 1.0) * exp(-((1.0 + eps) * x)))) / 2.0;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    code = (((1.0d0 + (1.0d0 / eps)) * exp(-((1.0d0 - eps) * x))) - (((1.0d0 / eps) - 1.0d0) * exp(-((1.0d0 + eps) * x)))) / 2.0d0
end function

Java

public static double code(double x, double eps) {
	return (((1.0 + (1.0 / eps)) * Math.exp(-((1.0 - eps) * x))) - (((1.0 / eps) - 1.0) * Math.exp(-((1.0 + eps) * x)))) / 2.0;
}

Python

def code(x, eps):
	return (((1.0 + (1.0 / eps)) * math.exp(-((1.0 - eps) * x))) - (((1.0 / eps) - 1.0) * math.exp(-((1.0 + eps) * x)))) / 2.0

Julia

function code(x, eps)
	return Float64(Float64(Float64(Float64(1.0 + Float64(1.0 / eps)) * exp(Float64(-Float64(Float64(1.0 - eps) * x)))) - Float64(Float64(Float64(1.0 / eps) - 1.0) * exp(Float64(-Float64(Float64(1.0 + eps) * x))))) / 2.0)
end

MATLAB

function tmp = code(x, eps)
	tmp = (((1.0 + (1.0 / eps)) * exp(-((1.0 - eps) * x))) - (((1.0 / eps) - 1.0) * exp(-((1.0 + eps) * x)))) / 2.0;
end

Wolfram

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

Alternative 1: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + \frac{1}{\varepsilon}\right) \cdot e^{x \cdot \left(\varepsilon + -1\right)} + e^{x \cdot \left(-1 - \varepsilon\right)} \cdot \left(1 + \frac{-1}{\varepsilon}\right)\\ t_1 := e^{-x}\\ t_2 := t_1 + x \cdot t_1\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;\frac{t_2 + t_2}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (let* ((t_0
         (+
          (* (+ 1.0 (/ 1.0 eps)) (exp (* x (+ eps -1.0))))
          (* (exp (* x (- -1.0 eps))) (+ 1.0 (/ -1.0 eps)))))
        (t_1 (exp (- x)))
        (t_2 (+ t_1 (* x t_1))))
   (if (<= t_0 0.0) (/ (+ t_2 t_2) 2.0) (/ t_0 2.0))))

C

double code(double x, double eps) {
	double t_0 = ((1.0 + (1.0 / eps)) * exp((x * (eps + -1.0)))) + (exp((x * (-1.0 - eps))) * (1.0 + (-1.0 / eps)));
	double t_1 = exp(-x);
	double t_2 = t_1 + (x * t_1);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = (t_2 + t_2) / 2.0;
	} else {
		tmp = t_0 / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ((1.0d0 + (1.0d0 / eps)) * exp((x * (eps + (-1.0d0))))) + (exp((x * ((-1.0d0) - eps))) * (1.0d0 + ((-1.0d0) / eps)))
    t_1 = exp(-x)
    t_2 = t_1 + (x * t_1)
    if (t_0 <= 0.0d0) then
        tmp = (t_2 + t_2) / 2.0d0
    else
        tmp = t_0 / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double eps) {
	double t_0 = ((1.0 + (1.0 / eps)) * Math.exp((x * (eps + -1.0)))) + (Math.exp((x * (-1.0 - eps))) * (1.0 + (-1.0 / eps)));
	double t_1 = Math.exp(-x);
	double t_2 = t_1 + (x * t_1);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = (t_2 + t_2) / 2.0;
	} else {
		tmp = t_0 / 2.0;
	}
	return tmp;
}

Python

def code(x, eps):
	t_0 = ((1.0 + (1.0 / eps)) * math.exp((x * (eps + -1.0)))) + (math.exp((x * (-1.0 - eps))) * (1.0 + (-1.0 / eps)))
	t_1 = math.exp(-x)
	t_2 = t_1 + (x * t_1)
	tmp = 0
	if t_0 <= 0.0:
		tmp = (t_2 + t_2) / 2.0
	else:
		tmp = t_0 / 2.0
	return tmp

Julia

function code(x, eps)
	t_0 = Float64(Float64(Float64(1.0 + Float64(1.0 / eps)) * exp(Float64(x * Float64(eps + -1.0)))) + Float64(exp(Float64(x * Float64(-1.0 - eps))) * Float64(1.0 + Float64(-1.0 / eps))))
	t_1 = exp(Float64(-x))
	t_2 = Float64(t_1 + Float64(x * t_1))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(Float64(t_2 + t_2) / 2.0);
	else
		tmp = Float64(t_0 / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, eps)
	t_0 = ((1.0 + (1.0 / eps)) * exp((x * (eps + -1.0)))) + (exp((x * (-1.0 - eps))) * (1.0 + (-1.0 / eps)));
	t_1 = exp(-x);
	t_2 = t_1 + (x * t_1);
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = (t_2 + t_2) / 2.0;
	else
		tmp = t_0 / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, eps_] := Block[{t$95$0 = N[(N[(N[(1.0 + N[(1.0 / eps), $MachinePrecision]), $MachinePrecision] * N[Exp[N[(x * N[(eps + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Exp[N[(x * N[(-1.0 - eps), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(1.0 + N[(-1.0 / eps), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[(-x)], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], N[(N[(t$95$2 + t$95$2), $MachinePrecision] / 2.0), $MachinePrecision], N[(t$95$0 / 2.0), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + \frac{1}{\varepsilon}\right) \cdot e^{x \cdot \left(\varepsilon + -1\right)} + e^{x \cdot \left(-1 - \varepsilon\right)} \cdot \left(1 + \frac{-1}{\varepsilon}\right)\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;\frac{\frac{1 + x}{e^{x}} + e^{-x} \cdot \left(1 + x\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (let* ((t_0
         (+
          (* (+ 1.0 (/ 1.0 eps)) (exp (* x (+ eps -1.0))))
          (* (exp (* x (- -1.0 eps))) (+ 1.0 (/ -1.0 eps))))))
   (if (<= t_0 0.0)
     (/ (+ (/ (+ 1.0 x) (exp x)) (* (exp (- x)) (+ 1.0 x))) 2.0)
     (/ t_0 2.0))))

C

double code(double x, double eps) {
	double t_0 = ((1.0 + (1.0 / eps)) * exp((x * (eps + -1.0)))) + (exp((x * (-1.0 - eps))) * (1.0 + (-1.0 / eps)));
	double tmp;
	if (t_0 <= 0.0) {
		tmp = (((1.0 + x) / exp(x)) + (exp(-x) * (1.0 + x))) / 2.0;
	} else {
		tmp = t_0 / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((1.0d0 + (1.0d0 / eps)) * exp((x * (eps + (-1.0d0))))) + (exp((x * ((-1.0d0) - eps))) * (1.0d0 + ((-1.0d0) / eps)))
    if (t_0 <= 0.0d0) then
        tmp = (((1.0d0 + x) / exp(x)) + (exp(-x) * (1.0d0 + x))) / 2.0d0
    else
        tmp = t_0 / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double eps) {
	double t_0 = ((1.0 + (1.0 / eps)) * Math.exp((x * (eps + -1.0)))) + (Math.exp((x * (-1.0 - eps))) * (1.0 + (-1.0 / eps)));
	double tmp;
	if (t_0 <= 0.0) {
		tmp = (((1.0 + x) / Math.exp(x)) + (Math.exp(-x) * (1.0 + x))) / 2.0;
	} else {
		tmp = t_0 / 2.0;
	}
	return tmp;
}

Python

def code(x, eps):
	t_0 = ((1.0 + (1.0 / eps)) * math.exp((x * (eps + -1.0)))) + (math.exp((x * (-1.0 - eps))) * (1.0 + (-1.0 / eps)))
	tmp = 0
	if t_0 <= 0.0:
		tmp = (((1.0 + x) / math.exp(x)) + (math.exp(-x) * (1.0 + x))) / 2.0
	else:
		tmp = t_0 / 2.0
	return tmp

Julia

function code(x, eps)
	t_0 = Float64(Float64(Float64(1.0 + Float64(1.0 / eps)) * exp(Float64(x * Float64(eps + -1.0)))) + Float64(exp(Float64(x * Float64(-1.0 - eps))) * Float64(1.0 + Float64(-1.0 / eps))))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(1.0 + x) / exp(x)) + Float64(exp(Float64(-x)) * Float64(1.0 + x))) / 2.0);
	else
		tmp = Float64(t_0 / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, eps)
	t_0 = ((1.0 + (1.0 / eps)) * exp((x * (eps + -1.0)))) + (exp((x * (-1.0 - eps))) * (1.0 + (-1.0 / eps)));
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = (((1.0 + x) / exp(x)) + (exp(-x) * (1.0 + x))) / 2.0;
	else
		tmp = t_0 / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, eps_] := Block[{t$95$0 = N[(N[(N[(1.0 + N[(1.0 / eps), $MachinePrecision]), $MachinePrecision] * N[Exp[N[(x * N[(eps + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Exp[N[(x * N[(-1.0 - eps), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(1.0 + N[(-1.0 / eps), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], N[(N[(N[(N[(1.0 + x), $MachinePrecision] / N[Exp[x], $MachinePrecision]), $MachinePrecision] + N[(N[Exp[(-x)], $MachinePrecision] * N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(t$95$0 / 2.0), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 78.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\varepsilon \leq 5 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{1 + x}{e^{x}} + e^{-x} \cdot \left(1 + x\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{x \cdot \left(\varepsilon + -1\right)} + e^{\varepsilon \cdot \left(-x\right)}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (if (<= eps 5e-31)
   (/ (+ (/ (+ 1.0 x) (exp x)) (* (exp (- x)) (+ 1.0 x))) 2.0)
   (/ (+ (exp (* x (+ eps -1.0))) (exp (* eps (- x)))) 2.0)))

C

double code(double x, double eps) {
	double tmp;
	if (eps <= 5e-31) {
		tmp = (((1.0 + x) / exp(x)) + (exp(-x) * (1.0 + x))) / 2.0;
	} else {
		tmp = (exp((x * (eps + -1.0))) + exp((eps * -x))) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    real(8) :: tmp
    if (eps <= 5d-31) then
        tmp = (((1.0d0 + x) / exp(x)) + (exp(-x) * (1.0d0 + x))) / 2.0d0
    else
        tmp = (exp((x * (eps + (-1.0d0)))) + exp((eps * -x))) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double eps) {
	double tmp;
	if (eps <= 5e-31) {
		tmp = (((1.0 + x) / Math.exp(x)) + (Math.exp(-x) * (1.0 + x))) / 2.0;
	} else {
		tmp = (Math.exp((x * (eps + -1.0))) + Math.exp((eps * -x))) / 2.0;
	}
	return tmp;
}

Python

def code(x, eps):
	tmp = 0
	if eps <= 5e-31:
		tmp = (((1.0 + x) / math.exp(x)) + (math.exp(-x) * (1.0 + x))) / 2.0
	else:
		tmp = (math.exp((x * (eps + -1.0))) + math.exp((eps * -x))) / 2.0
	return tmp

Julia

function code(x, eps)
	tmp = 0.0
	if (eps <= 5e-31)
		tmp = Float64(Float64(Float64(Float64(1.0 + x) / exp(x)) + Float64(exp(Float64(-x)) * Float64(1.0 + x))) / 2.0);
	else
		tmp = Float64(Float64(exp(Float64(x * Float64(eps + -1.0))) + exp(Float64(eps * Float64(-x)))) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, eps)
	tmp = 0.0;
	if (eps <= 5e-31)
		tmp = (((1.0 + x) / exp(x)) + (exp(-x) * (1.0 + x))) / 2.0;
	else
		tmp = (exp((x * (eps + -1.0))) + exp((eps * -x))) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, eps_] := If[LessEqual[eps, 5e-31], N[(N[(N[(N[(1.0 + x), $MachinePrecision] / N[Exp[x], $MachinePrecision]), $MachinePrecision] + N[(N[Exp[(-x)], $MachinePrecision] * N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(N[Exp[N[(x * N[(eps + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[Exp[N[(eps * (-x)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\varepsilon \leq 3 \cdot 10^{-37}:\\ \;\;\;\;\frac{\frac{2}{e^{x}}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{x \cdot \left(\varepsilon + -1\right)} + e^{\varepsilon \cdot \left(-x\right)}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (if (<= eps 3e-37)
   (/ (/ 2.0 (exp x)) 2.0)
   (/ (+ (exp (* x (+ eps -1.0))) (exp (* eps (- x)))) 2.0)))

C

double code(double x, double eps) {
	double tmp;
	if (eps <= 3e-37) {
		tmp = (2.0 / exp(x)) / 2.0;
	} else {
		tmp = (exp((x * (eps + -1.0))) + exp((eps * -x))) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    real(8) :: tmp
    if (eps <= 3d-37) then
        tmp = (2.0d0 / exp(x)) / 2.0d0
    else
        tmp = (exp((x * (eps + (-1.0d0)))) + exp((eps * -x))) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double eps) {
	double tmp;
	if (eps <= 3e-37) {
		tmp = (2.0 / Math.exp(x)) / 2.0;
	} else {
		tmp = (Math.exp((x * (eps + -1.0))) + Math.exp((eps * -x))) / 2.0;
	}
	return tmp;
}

Python

def code(x, eps):
	tmp = 0
	if eps <= 3e-37:
		tmp = (2.0 / math.exp(x)) / 2.0
	else:
		tmp = (math.exp((x * (eps + -1.0))) + math.exp((eps * -x))) / 2.0
	return tmp

Julia

function code(x, eps)
	tmp = 0.0
	if (eps <= 3e-37)
		tmp = Float64(Float64(2.0 / exp(x)) / 2.0);
	else
		tmp = Float64(Float64(exp(Float64(x * Float64(eps + -1.0))) + exp(Float64(eps * Float64(-x)))) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, eps)
	tmp = 0.0;
	if (eps <= 3e-37)
		tmp = (2.0 / exp(x)) / 2.0;
	else
		tmp = (exp((x * (eps + -1.0))) + exp((eps * -x))) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, eps_] := If[LessEqual[eps, 3e-37], N[(N[(2.0 / N[Exp[x], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(N[Exp[N[(x * N[(eps + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[Exp[N[(eps * (-x)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 99.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \frac{e^{x \cdot \left(-1 - \varepsilon\right)} + e^{x \cdot \left(\varepsilon + -1\right)}}{2} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (/ (+ (exp (* x (- -1.0 eps))) (exp (* x (+ eps -1.0)))) 2.0))

C

double code(double x, double eps) {
	return (exp((x * (-1.0 - eps))) + exp((x * (eps + -1.0)))) / 2.0;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    code = (exp((x * ((-1.0d0) - eps))) + exp((x * (eps + (-1.0d0))))) / 2.0d0
end function

Java

public static double code(double x, double eps) {
	return (Math.exp((x * (-1.0 - eps))) + Math.exp((x * (eps + -1.0)))) / 2.0;
}

Python

def code(x, eps):
	return (math.exp((x * (-1.0 - eps))) + math.exp((x * (eps + -1.0)))) / 2.0

Julia

function code(x, eps)
	return Float64(Float64(exp(Float64(x * Float64(-1.0 - eps))) + exp(Float64(x * Float64(eps + -1.0)))) / 2.0)
end

MATLAB

function tmp = code(x, eps)
	tmp = (exp((x * (-1.0 - eps))) + exp((x * (eps + -1.0)))) / 2.0;
end

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 70.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-286}:\\ \;\;\;\;\frac{1 + e^{\varepsilon \cdot \left(-x\right)}}{2}\\ \mathbf{elif}\;x \leq 155000000000:\\ \;\;\;\;\frac{e^{x \cdot \left(\varepsilon + -1\right)} + \left(1 - \varepsilon \cdot x\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{e^{x}}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (if (<= x -1.1e-286)
   (/ (+ 1.0 (exp (* eps (- x)))) 2.0)
   (if (<= x 155000000000.0)
     (/ (+ (exp (* x (+ eps -1.0))) (- 1.0 (* eps x))) 2.0)
     (/ (/ 2.0 (exp x)) 2.0))))

C

double code(double x, double eps) {
	double tmp;
	if (x <= -1.1e-286) {
		tmp = (1.0 + exp((eps * -x))) / 2.0;
	} else if (x <= 155000000000.0) {
		tmp = (exp((x * (eps + -1.0))) + (1.0 - (eps * x))) / 2.0;
	} else {
		tmp = (2.0 / exp(x)) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    real(8) :: tmp
    if (x <= (-1.1d-286)) then
        tmp = (1.0d0 + exp((eps * -x))) / 2.0d0
    else if (x <= 155000000000.0d0) then
        tmp = (exp((x * (eps + (-1.0d0)))) + (1.0d0 - (eps * x))) / 2.0d0
    else
        tmp = (2.0d0 / exp(x)) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double eps) {
	double tmp;
	if (x <= -1.1e-286) {
		tmp = (1.0 + Math.exp((eps * -x))) / 2.0;
	} else if (x <= 155000000000.0) {
		tmp = (Math.exp((x * (eps + -1.0))) + (1.0 - (eps * x))) / 2.0;
	} else {
		tmp = (2.0 / Math.exp(x)) / 2.0;
	}
	return tmp;
}

Python

def code(x, eps):
	tmp = 0
	if x <= -1.1e-286:
		tmp = (1.0 + math.exp((eps * -x))) / 2.0
	elif x <= 155000000000.0:
		tmp = (math.exp((x * (eps + -1.0))) + (1.0 - (eps * x))) / 2.0
	else:
		tmp = (2.0 / math.exp(x)) / 2.0
	return tmp

Julia

function code(x, eps)
	tmp = 0.0
	if (x <= -1.1e-286)
		tmp = Float64(Float64(1.0 + exp(Float64(eps * Float64(-x)))) / 2.0);
	elseif (x <= 155000000000.0)
		tmp = Float64(Float64(exp(Float64(x * Float64(eps + -1.0))) + Float64(1.0 - Float64(eps * x))) / 2.0);
	else
		tmp = Float64(Float64(2.0 / exp(x)) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, eps)
	tmp = 0.0;
	if (x <= -1.1e-286)
		tmp = (1.0 + exp((eps * -x))) / 2.0;
	elseif (x <= 155000000000.0)
		tmp = (exp((x * (eps + -1.0))) + (1.0 - (eps * x))) / 2.0;
	else
		tmp = (2.0 / exp(x)) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, eps_] := If[LessEqual[x, -1.1e-286], N[(N[(1.0 + N[Exp[N[(eps * (-x)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[x, 155000000000.0], N[(N[(N[Exp[N[(x * N[(eps + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[(1.0 - N[(eps * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(2.0 / N[Exp[x], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 74.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-296} \lor \neg \left(x \leq 132000000000\right):\\ \;\;\;\;\frac{\frac{2}{e^{x}}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + e^{x \cdot \left(\varepsilon + -1\right)}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (if (or (<= x -1e-296) (not (<= x 132000000000.0)))
   (/ (/ 2.0 (exp x)) 2.0)
   (/ (+ 1.0 (exp (* x (+ eps -1.0)))) 2.0)))

C

double code(double x, double eps) {
	double tmp;
	if ((x <= -1e-296) || !(x <= 132000000000.0)) {
		tmp = (2.0 / exp(x)) / 2.0;
	} else {
		tmp = (1.0 + exp((x * (eps + -1.0)))) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    real(8) :: tmp
    if ((x <= (-1d-296)) .or. (.not. (x <= 132000000000.0d0))) then
        tmp = (2.0d0 / exp(x)) / 2.0d0
    else
        tmp = (1.0d0 + exp((x * (eps + (-1.0d0))))) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double eps) {
	double tmp;
	if ((x <= -1e-296) || !(x <= 132000000000.0)) {
		tmp = (2.0 / Math.exp(x)) / 2.0;
	} else {
		tmp = (1.0 + Math.exp((x * (eps + -1.0)))) / 2.0;
	}
	return tmp;
}

Python

def code(x, eps):
	tmp = 0
	if (x <= -1e-296) or not (x <= 132000000000.0):
		tmp = (2.0 / math.exp(x)) / 2.0
	else:
		tmp = (1.0 + math.exp((x * (eps + -1.0)))) / 2.0
	return tmp

Julia

function code(x, eps)
	tmp = 0.0
	if ((x <= -1e-296) || !(x <= 132000000000.0))
		tmp = Float64(Float64(2.0 / exp(x)) / 2.0);
	else
		tmp = Float64(Float64(1.0 + exp(Float64(x * Float64(eps + -1.0)))) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, eps)
	tmp = 0.0;
	if ((x <= -1e-296) || ~((x <= 132000000000.0)))
		tmp = (2.0 / exp(x)) / 2.0;
	else
		tmp = (1.0 + exp((x * (eps + -1.0)))) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, eps_] := If[Or[LessEqual[x, -1e-296], N[Not[LessEqual[x, 132000000000.0]], $MachinePrecision]], N[(N[(2.0 / N[Exp[x], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(1.0 + N[Exp[N[(x * N[(eps + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 70.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-296}:\\ \;\;\;\;\frac{1 + e^{\varepsilon \cdot \left(-x\right)}}{2}\\ \mathbf{elif}\;x \leq 235000000000:\\ \;\;\;\;\frac{1 + e^{x \cdot \left(\varepsilon + -1\right)}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{e^{x}}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (if (<= x -1e-296)
   (/ (+ 1.0 (exp (* eps (- x)))) 2.0)
   (if (<= x 235000000000.0)
     (/ (+ 1.0 (exp (* x (+ eps -1.0)))) 2.0)
     (/ (/ 2.0 (exp x)) 2.0))))

C

double code(double x, double eps) {
	double tmp;
	if (x <= -1e-296) {
		tmp = (1.0 + exp((eps * -x))) / 2.0;
	} else if (x <= 235000000000.0) {
		tmp = (1.0 + exp((x * (eps + -1.0)))) / 2.0;
	} else {
		tmp = (2.0 / exp(x)) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    real(8) :: tmp
    if (x <= (-1d-296)) then
        tmp = (1.0d0 + exp((eps * -x))) / 2.0d0
    else if (x <= 235000000000.0d0) then
        tmp = (1.0d0 + exp((x * (eps + (-1.0d0))))) / 2.0d0
    else
        tmp = (2.0d0 / exp(x)) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double eps) {
	double tmp;
	if (x <= -1e-296) {
		tmp = (1.0 + Math.exp((eps * -x))) / 2.0;
	} else if (x <= 235000000000.0) {
		tmp = (1.0 + Math.exp((x * (eps + -1.0)))) / 2.0;
	} else {
		tmp = (2.0 / Math.exp(x)) / 2.0;
	}
	return tmp;
}

Python

def code(x, eps):
	tmp = 0
	if x <= -1e-296:
		tmp = (1.0 + math.exp((eps * -x))) / 2.0
	elif x <= 235000000000.0:
		tmp = (1.0 + math.exp((x * (eps + -1.0)))) / 2.0
	else:
		tmp = (2.0 / math.exp(x)) / 2.0
	return tmp

Julia

function code(x, eps)
	tmp = 0.0
	if (x <= -1e-296)
		tmp = Float64(Float64(1.0 + exp(Float64(eps * Float64(-x)))) / 2.0);
	elseif (x <= 235000000000.0)
		tmp = Float64(Float64(1.0 + exp(Float64(x * Float64(eps + -1.0)))) / 2.0);
	else
		tmp = Float64(Float64(2.0 / exp(x)) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, eps)
	tmp = 0.0;
	if (x <= -1e-296)
		tmp = (1.0 + exp((eps * -x))) / 2.0;
	elseif (x <= 235000000000.0)
		tmp = (1.0 + exp((x * (eps + -1.0)))) / 2.0;
	else
		tmp = (2.0 / exp(x)) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, eps_] := If[LessEqual[x, -1e-296], N[(N[(1.0 + N[Exp[N[(eps * (-x)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[x, 235000000000.0], N[(N[(1.0 + N[Exp[N[(x * N[(eps + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(2.0 / N[Exp[x], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 70.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{2}{e^{x}}}{2} \end{array} \]

FPCore

(FPCore (x eps) :precision binary64 (/ (/ 2.0 (exp x)) 2.0))

C

double code(double x, double eps) {
	return (2.0 / exp(x)) / 2.0;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    code = (2.0d0 / exp(x)) / 2.0d0
end function

Java

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

Python

def code(x, eps):
	return (2.0 / math.exp(x)) / 2.0

Julia

function code(x, eps)
	return Float64(Float64(2.0 / exp(x)) / 2.0)
end

MATLAB

function tmp = code(x, eps)
	tmp = (2.0 / exp(x)) / 2.0;
end

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 59.1% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2:\\ \;\;\;\;\frac{x \cdot \left(-1 - \varepsilon\right) + 2}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(1 + \frac{1}{\varepsilon}\right) + \left(1 + \frac{-1}{\varepsilon}\right)}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (if (<= x 2.0)
   (/ (+ (* x (- -1.0 eps)) 2.0) 2.0)
   (/ (+ (+ 1.0 (/ 1.0 eps)) (+ 1.0 (/ -1.0 eps))) 2.0)))

C

double code(double x, double eps) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((x * (-1.0 - eps)) + 2.0) / 2.0;
	} else {
		tmp = ((1.0 + (1.0 / eps)) + (1.0 + (-1.0 / eps))) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    real(8) :: tmp
    if (x <= 2.0d0) then
        tmp = ((x * ((-1.0d0) - eps)) + 2.0d0) / 2.0d0
    else
        tmp = ((1.0d0 + (1.0d0 / eps)) + (1.0d0 + ((-1.0d0) / eps))) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double eps) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((x * (-1.0 - eps)) + 2.0) / 2.0;
	} else {
		tmp = ((1.0 + (1.0 / eps)) + (1.0 + (-1.0 / eps))) / 2.0;
	}
	return tmp;
}

Python

def code(x, eps):
	tmp = 0
	if x <= 2.0:
		tmp = ((x * (-1.0 - eps)) + 2.0) / 2.0
	else:
		tmp = ((1.0 + (1.0 / eps)) + (1.0 + (-1.0 / eps))) / 2.0
	return tmp

Julia

function code(x, eps)
	tmp = 0.0
	if (x <= 2.0)
		tmp = Float64(Float64(Float64(x * Float64(-1.0 - eps)) + 2.0) / 2.0);
	else
		tmp = Float64(Float64(Float64(1.0 + Float64(1.0 / eps)) + Float64(1.0 + Float64(-1.0 / eps))) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, eps)
	tmp = 0.0;
	if (x <= 2.0)
		tmp = ((x * (-1.0 - eps)) + 2.0) / 2.0;
	else
		tmp = ((1.0 + (1.0 / eps)) + (1.0 + (-1.0 / eps))) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, eps_] := If[LessEqual[x, 2.0], N[(N[(N[(x * N[(-1.0 - eps), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(N[(1.0 + N[(1.0 / eps), $MachinePrecision]), $MachinePrecision] + N[(1.0 + N[(-1.0 / eps), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 49.7% accurate, 16.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.064:\\ \;\;\;\;\frac{x \cdot \left(-1 - \varepsilon\right) + 2}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \varepsilon \cdot x}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x eps)
 :precision binary64
 (if (<= x -0.064)
   (/ (+ (* x (- -1.0 eps)) 2.0) 2.0)
   (/ (+ 2.0 (* eps x)) 2.0)))

C

double code(double x, double eps) {
	double tmp;
	if (x <= -0.064) {
		tmp = ((x * (-1.0 - eps)) + 2.0) / 2.0;
	} else {
		tmp = (2.0 + (eps * x)) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    real(8) :: tmp
    if (x <= (-0.064d0)) then
        tmp = ((x * ((-1.0d0) - eps)) + 2.0d0) / 2.0d0
    else
        tmp = (2.0d0 + (eps * x)) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double eps) {
	double tmp;
	if (x <= -0.064) {
		tmp = ((x * (-1.0 - eps)) + 2.0) / 2.0;
	} else {
		tmp = (2.0 + (eps * x)) / 2.0;
	}
	return tmp;
}

Python

def code(x, eps):
	tmp = 0
	if x <= -0.064:
		tmp = ((x * (-1.0 - eps)) + 2.0) / 2.0
	else:
		tmp = (2.0 + (eps * x)) / 2.0
	return tmp

Julia

function code(x, eps)
	tmp = 0.0
	if (x <= -0.064)
		tmp = Float64(Float64(Float64(x * Float64(-1.0 - eps)) + 2.0) / 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(eps * x)) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, eps)
	tmp = 0.0;
	if (x <= -0.064)
		tmp = ((x * (-1.0 - eps)) + 2.0) / 2.0;
	else
		tmp = (2.0 + (eps * x)) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, eps_] := If[LessEqual[x, -0.064], N[(N[(N[(x * N[(-1.0 - eps), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(2.0 + N[(eps * x), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 46.8% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 35:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\varepsilon \cdot x}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x eps) :precision binary64 (if (<= x 35.0) 1.0 (/ (* eps x) 2.0)))

C

double code(double x, double eps) {
	double tmp;
	if (x <= 35.0) {
		tmp = 1.0;
	} else {
		tmp = (eps * x) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    real(8) :: tmp
    if (x <= 35.0d0) then
        tmp = 1.0d0
    else
        tmp = (eps * x) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double eps) {
	double tmp;
	if (x <= 35.0) {
		tmp = 1.0;
	} else {
		tmp = (eps * x) / 2.0;
	}
	return tmp;
}

Python

def code(x, eps):
	tmp = 0
	if x <= 35.0:
		tmp = 1.0
	else:
		tmp = (eps * x) / 2.0
	return tmp

Julia

function code(x, eps)
	tmp = 0.0
	if (x <= 35.0)
		tmp = 1.0;
	else
		tmp = Float64(Float64(eps * x) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, eps)
	tmp = 0.0;
	if (x <= 35.0)
		tmp = 1.0;
	else
		tmp = (eps * x) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, eps_] := If[LessEqual[x, 35.0], 1.0, N[(N[(eps * x), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 49.9% accurate, 32.4× speedup

Math

\[\begin{array}{l} \\ \frac{2 + \varepsilon \cdot x}{2} \end{array} \]

FPCore

(FPCore (x eps) :precision binary64 (/ (+ 2.0 (* eps x)) 2.0))

C

double code(double x, double eps) {
	return (2.0 + (eps * x)) / 2.0;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    code = (2.0d0 + (eps * x)) / 2.0d0
end function

Java

public static double code(double x, double eps) {
	return (2.0 + (eps * x)) / 2.0;
}

Python

def code(x, eps):
	return (2.0 + (eps * x)) / 2.0

Julia

function code(x, eps)
	return Float64(Float64(2.0 + Float64(eps * x)) / 2.0)
end

MATLAB

function tmp = code(x, eps)
	tmp = (2.0 + (eps * x)) / 2.0;
end

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 14: 43.5% accurate, 227.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x eps) :precision binary64 1.0)

C

double code(double x, double eps) {
	return 1.0;
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    code = 1.0d0
end function

Java

public static double code(double x, double eps) {
	return 1.0;
}

Python

def code(x, eps):
	return 1.0

Julia

function code(x, eps)
	return 1.0
end

MATLAB

function tmp = code(x, eps)
	tmp = 1.0;
end

Wolfram

code[x_, eps_] := 1.0

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2024006 
(FPCore (x eps)
  :name "NMSE Section 6.1 mentioned, A"
  :precision binary64
  (/ (- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))) 2.0))