NMSE Section 6.1 mentioned, A

Percentage Accurate: 73.3% → 98.5%

Time: 12.8s

Alternatives: 13

Speedup: 2.0×

• 39.1% 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: 73.3% 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: 98.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} eps_m = \left|\varepsilon\right| \\ \begin{array}{l} \mathbf{if}\;eps_m \leq 5.1 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{x + 1}{e^{x}} + \left(x + 1\right) \cdot e^{-x}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{eps_m \cdot x} + e^{eps_m \cdot \left(-x\right)}}{2}\\ \end{array} \end{array} \]

FPCore

eps_m = (fabs.f64 eps)
(FPCore (x eps_m)
 :precision binary64
 (if (<= eps_m 5.1e-31)
   (/ (+ (/ (+ x 1.0) (exp x)) (* (+ x 1.0) (exp (- x)))) 2.0)
   (/ (+ (exp (* eps_m x)) (exp (* eps_m (- x)))) 2.0)))

C

eps_m = fabs(eps);
double code(double x, double eps_m) {
	double tmp;
	if (eps_m <= 5.1e-31) {
		tmp = (((x + 1.0) / exp(x)) + ((x + 1.0) * exp(-x))) / 2.0;
	} else {
		tmp = (exp((eps_m * x)) + exp((eps_m * -x))) / 2.0;
	}
	return tmp;
}

Fortran

eps_m = abs(eps)
real(8) function code(x, eps_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps_m
    real(8) :: tmp
    if (eps_m <= 5.1d-31) then
        tmp = (((x + 1.0d0) / exp(x)) + ((x + 1.0d0) * exp(-x))) / 2.0d0
    else
        tmp = (exp((eps_m * x)) + exp((eps_m * -x))) / 2.0d0
    end if
    code = tmp
end function

Java

eps_m = Math.abs(eps);
public static double code(double x, double eps_m) {
	double tmp;
	if (eps_m <= 5.1e-31) {
		tmp = (((x + 1.0) / Math.exp(x)) + ((x + 1.0) * Math.exp(-x))) / 2.0;
	} else {
		tmp = (Math.exp((eps_m * x)) + Math.exp((eps_m * -x))) / 2.0;
	}
	return tmp;
}

Python

eps_m = math.fabs(eps)
def code(x, eps_m):
	tmp = 0
	if eps_m <= 5.1e-31:
		tmp = (((x + 1.0) / math.exp(x)) + ((x + 1.0) * math.exp(-x))) / 2.0
	else:
		tmp = (math.exp((eps_m * x)) + math.exp((eps_m * -x))) / 2.0
	return tmp

Julia

eps_m = abs(eps)
function code(x, eps_m)
	tmp = 0.0
	if (eps_m <= 5.1e-31)
		tmp = Float64(Float64(Float64(Float64(x + 1.0) / exp(x)) + Float64(Float64(x + 1.0) * exp(Float64(-x)))) / 2.0);
	else
		tmp = Float64(Float64(exp(Float64(eps_m * x)) + exp(Float64(eps_m * Float64(-x)))) / 2.0);
	end
	return tmp
end

MATLAB

eps_m = abs(eps);
function tmp_2 = code(x, eps_m)
	tmp = 0.0;
	if (eps_m <= 5.1e-31)
		tmp = (((x + 1.0) / exp(x)) + ((x + 1.0) * exp(-x))) / 2.0;
	else
		tmp = (exp((eps_m * x)) + exp((eps_m * -x))) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

eps_m = N[Abs[eps], $MachinePrecision]
code[x_, eps$95$m_] := If[LessEqual[eps$95$m, 5.1e-31], N[(N[(N[(N[(x + 1.0), $MachinePrecision] / N[Exp[x], $MachinePrecision]), $MachinePrecision] + N[(N[(x + 1.0), $MachinePrecision] * N[Exp[(-x)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(N[Exp[N[(eps$95$m * x), $MachinePrecision]], $MachinePrecision] + N[Exp[N[(eps$95$m * (-x)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]

Derivation

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

Alternative 2: 98.9% accurate, 1.1× speedup

Math

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

FPCore

eps_m = (fabs.f64 eps)
(FPCore (x eps_m)
 :precision binary64
 (/ (+ (exp (* x (+ eps_m -1.0))) (exp (* x (- -1.0 eps_m)))) 2.0))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

eps_m = N[Abs[eps], $MachinePrecision]
code[x_, eps$95$m_] := N[(N[(N[Exp[N[(x * N[(eps$95$m + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[Exp[N[(x * N[(-1.0 - eps$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]

Derivation

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

Alternative 3: 85.6% accurate, 1.1× speedup

Math

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

FPCore

eps_m = (fabs.f64 eps)
(FPCore (x eps_m)
 :precision binary64
 (/ (+ (exp (* eps_m x)) (exp (* eps_m (- x)))) 2.0))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

eps_m = N[Abs[eps], $MachinePrecision]
code[x_, eps$95$m_] := N[(N[(N[Exp[N[(eps$95$m * x), $MachinePrecision]], $MachinePrecision] + N[Exp[N[(eps$95$m * (-x)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]

Derivation

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

Alternative 4: 77.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} eps_m = \left|\varepsilon\right| \\ \begin{array}{l} \mathbf{if}\;x \leq -145000:\\ \;\;\;\;\frac{\frac{\mathsf{expm1}\left(-x\right)}{eps_m}}{2}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+229}:\\ \;\;\;\;\frac{e^{eps_m \cdot x} - -1}{2}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+271}:\\ \;\;\;\;\frac{\left(1 - \frac{-1}{eps_m}\right) + \left(\frac{-1}{eps_m} - -1\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{eps_m \cdot x}{2}\\ \end{array} \end{array} \]

FPCore

eps_m = (fabs.f64 eps)
(FPCore (x eps_m)
 :precision binary64
 (if (<= x -145000.0)
   (/ (/ (expm1 (- x)) eps_m) 2.0)
   (if (<= x 1.25e+229)
     (/ (- (exp (* eps_m x)) -1.0) 2.0)
     (if (<= x 4.2e+271)
       (/ (+ (- 1.0 (/ -1.0 eps_m)) (- (/ -1.0 eps_m) -1.0)) 2.0)
       (/ (* eps_m x) 2.0)))))

C

eps_m = fabs(eps);
double code(double x, double eps_m) {
	double tmp;
	if (x <= -145000.0) {
		tmp = (expm1(-x) / eps_m) / 2.0;
	} else if (x <= 1.25e+229) {
		tmp = (exp((eps_m * x)) - -1.0) / 2.0;
	} else if (x <= 4.2e+271) {
		tmp = ((1.0 - (-1.0 / eps_m)) + ((-1.0 / eps_m) - -1.0)) / 2.0;
	} else {
		tmp = (eps_m * x) / 2.0;
	}
	return tmp;
}

Java

eps_m = Math.abs(eps);
public static double code(double x, double eps_m) {
	double tmp;
	if (x <= -145000.0) {
		tmp = (Math.expm1(-x) / eps_m) / 2.0;
	} else if (x <= 1.25e+229) {
		tmp = (Math.exp((eps_m * x)) - -1.0) / 2.0;
	} else if (x <= 4.2e+271) {
		tmp = ((1.0 - (-1.0 / eps_m)) + ((-1.0 / eps_m) - -1.0)) / 2.0;
	} else {
		tmp = (eps_m * x) / 2.0;
	}
	return tmp;
}

Python

eps_m = math.fabs(eps)
def code(x, eps_m):
	tmp = 0
	if x <= -145000.0:
		tmp = (math.expm1(-x) / eps_m) / 2.0
	elif x <= 1.25e+229:
		tmp = (math.exp((eps_m * x)) - -1.0) / 2.0
	elif x <= 4.2e+271:
		tmp = ((1.0 - (-1.0 / eps_m)) + ((-1.0 / eps_m) - -1.0)) / 2.0
	else:
		tmp = (eps_m * x) / 2.0
	return tmp

Julia

eps_m = abs(eps)
function code(x, eps_m)
	tmp = 0.0
	if (x <= -145000.0)
		tmp = Float64(Float64(expm1(Float64(-x)) / eps_m) / 2.0);
	elseif (x <= 1.25e+229)
		tmp = Float64(Float64(exp(Float64(eps_m * x)) - -1.0) / 2.0);
	elseif (x <= 4.2e+271)
		tmp = Float64(Float64(Float64(1.0 - Float64(-1.0 / eps_m)) + Float64(Float64(-1.0 / eps_m) - -1.0)) / 2.0);
	else
		tmp = Float64(Float64(eps_m * x) / 2.0);
	end
	return tmp
end

Wolfram

eps_m = N[Abs[eps], $MachinePrecision]
code[x_, eps$95$m_] := If[LessEqual[x, -145000.0], N[(N[(N[(Exp[(-x)] - 1), $MachinePrecision] / eps$95$m), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[x, 1.25e+229], N[(N[(N[Exp[N[(eps$95$m * x), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[x, 4.2e+271], N[(N[(N[(1.0 - N[(-1.0 / eps$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 / eps$95$m), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(eps$95$m * x), $MachinePrecision] / 2.0), $MachinePrecision]]]]

Derivation

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

Alternative 5: 84.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} eps_m = \left|\varepsilon\right| \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-298}:\\ \;\;\;\;\frac{1 + e^{eps_m \cdot \left(-x\right)}}{2}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+229}:\\ \;\;\;\;\frac{e^{eps_m \cdot x} - -1}{2}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+272}:\\ \;\;\;\;\frac{\left(1 - \frac{-1}{eps_m}\right) + \left(\frac{-1}{eps_m} - -1\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{eps_m \cdot x}{2}\\ \end{array} \end{array} \]

FPCore

eps_m = (fabs.f64 eps)
(FPCore (x eps_m)
 :precision binary64
 (if (<= x -2e-298)
   (/ (+ 1.0 (exp (* eps_m (- x)))) 2.0)
   (if (<= x 1.25e+229)
     (/ (- (exp (* eps_m x)) -1.0) 2.0)
     (if (<= x 1.9e+272)
       (/ (+ (- 1.0 (/ -1.0 eps_m)) (- (/ -1.0 eps_m) -1.0)) 2.0)
       (/ (* eps_m x) 2.0)))))

C

eps_m = fabs(eps);
double code(double x, double eps_m) {
	double tmp;
	if (x <= -2e-298) {
		tmp = (1.0 + exp((eps_m * -x))) / 2.0;
	} else if (x <= 1.25e+229) {
		tmp = (exp((eps_m * x)) - -1.0) / 2.0;
	} else if (x <= 1.9e+272) {
		tmp = ((1.0 - (-1.0 / eps_m)) + ((-1.0 / eps_m) - -1.0)) / 2.0;
	} else {
		tmp = (eps_m * x) / 2.0;
	}
	return tmp;
}

Fortran

eps_m = abs(eps)
real(8) function code(x, eps_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps_m
    real(8) :: tmp
    if (x <= (-2d-298)) then
        tmp = (1.0d0 + exp((eps_m * -x))) / 2.0d0
    else if (x <= 1.25d+229) then
        tmp = (exp((eps_m * x)) - (-1.0d0)) / 2.0d0
    else if (x <= 1.9d+272) then
        tmp = ((1.0d0 - ((-1.0d0) / eps_m)) + (((-1.0d0) / eps_m) - (-1.0d0))) / 2.0d0
    else
        tmp = (eps_m * x) / 2.0d0
    end if
    code = tmp
end function

Java

eps_m = Math.abs(eps);
public static double code(double x, double eps_m) {
	double tmp;
	if (x <= -2e-298) {
		tmp = (1.0 + Math.exp((eps_m * -x))) / 2.0;
	} else if (x <= 1.25e+229) {
		tmp = (Math.exp((eps_m * x)) - -1.0) / 2.0;
	} else if (x <= 1.9e+272) {
		tmp = ((1.0 - (-1.0 / eps_m)) + ((-1.0 / eps_m) - -1.0)) / 2.0;
	} else {
		tmp = (eps_m * x) / 2.0;
	}
	return tmp;
}

Python

eps_m = math.fabs(eps)
def code(x, eps_m):
	tmp = 0
	if x <= -2e-298:
		tmp = (1.0 + math.exp((eps_m * -x))) / 2.0
	elif x <= 1.25e+229:
		tmp = (math.exp((eps_m * x)) - -1.0) / 2.0
	elif x <= 1.9e+272:
		tmp = ((1.0 - (-1.0 / eps_m)) + ((-1.0 / eps_m) - -1.0)) / 2.0
	else:
		tmp = (eps_m * x) / 2.0
	return tmp

Julia

eps_m = abs(eps)
function code(x, eps_m)
	tmp = 0.0
	if (x <= -2e-298)
		tmp = Float64(Float64(1.0 + exp(Float64(eps_m * Float64(-x)))) / 2.0);
	elseif (x <= 1.25e+229)
		tmp = Float64(Float64(exp(Float64(eps_m * x)) - -1.0) / 2.0);
	elseif (x <= 1.9e+272)
		tmp = Float64(Float64(Float64(1.0 - Float64(-1.0 / eps_m)) + Float64(Float64(-1.0 / eps_m) - -1.0)) / 2.0);
	else
		tmp = Float64(Float64(eps_m * x) / 2.0);
	end
	return tmp
end

MATLAB

eps_m = abs(eps);
function tmp_2 = code(x, eps_m)
	tmp = 0.0;
	if (x <= -2e-298)
		tmp = (1.0 + exp((eps_m * -x))) / 2.0;
	elseif (x <= 1.25e+229)
		tmp = (exp((eps_m * x)) - -1.0) / 2.0;
	elseif (x <= 1.9e+272)
		tmp = ((1.0 - (-1.0 / eps_m)) + ((-1.0 / eps_m) - -1.0)) / 2.0;
	else
		tmp = (eps_m * x) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

eps_m = N[Abs[eps], $MachinePrecision]
code[x_, eps$95$m_] := If[LessEqual[x, -2e-298], N[(N[(1.0 + N[Exp[N[(eps$95$m * (-x)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[x, 1.25e+229], N[(N[(N[Exp[N[(eps$95$m * x), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[x, 1.9e+272], N[(N[(N[(1.0 - N[(-1.0 / eps$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 / eps$95$m), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(eps$95$m * x), $MachinePrecision] / 2.0), $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 6: 64.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} eps_m = \left|\varepsilon\right| \\ \begin{array}{l} t_0 := \frac{-1}{eps_m} - -1\\ \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x \cdot \left(t_0 \cdot \left(-1 - eps_m\right)\right)}{2}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+228}:\\ \;\;\;\;\frac{1 + e^{x}}{2}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+271}:\\ \;\;\;\;\frac{\left(1 - \frac{-1}{eps_m}\right) + t_0}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{eps_m \cdot x}{2}\\ \end{array} \end{array} \]

FPCore

eps_m = (fabs.f64 eps)
(FPCore (x eps_m)
 :precision binary64
 (let* ((t_0 (- (/ -1.0 eps_m) -1.0)))
   (if (<= x -1.0)
     (/ (* x (* t_0 (- -1.0 eps_m))) 2.0)
     (if (<= x 1.8e+228)
       (/ (+ 1.0 (exp x)) 2.0)
       (if (<= x 7.5e+271)
         (/ (+ (- 1.0 (/ -1.0 eps_m)) t_0) 2.0)
         (/ (* eps_m x) 2.0))))))

C

eps_m = fabs(eps);
double code(double x, double eps_m) {
	double t_0 = (-1.0 / eps_m) - -1.0;
	double tmp;
	if (x <= -1.0) {
		tmp = (x * (t_0 * (-1.0 - eps_m))) / 2.0;
	} else if (x <= 1.8e+228) {
		tmp = (1.0 + exp(x)) / 2.0;
	} else if (x <= 7.5e+271) {
		tmp = ((1.0 - (-1.0 / eps_m)) + t_0) / 2.0;
	} else {
		tmp = (eps_m * x) / 2.0;
	}
	return tmp;
}

Fortran

eps_m = abs(eps)
real(8) function code(x, eps_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps_m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((-1.0d0) / eps_m) - (-1.0d0)
    if (x <= (-1.0d0)) then
        tmp = (x * (t_0 * ((-1.0d0) - eps_m))) / 2.0d0
    else if (x <= 1.8d+228) then
        tmp = (1.0d0 + exp(x)) / 2.0d0
    else if (x <= 7.5d+271) then
        tmp = ((1.0d0 - ((-1.0d0) / eps_m)) + t_0) / 2.0d0
    else
        tmp = (eps_m * x) / 2.0d0
    end if
    code = tmp
end function

Java

eps_m = Math.abs(eps);
public static double code(double x, double eps_m) {
	double t_0 = (-1.0 / eps_m) - -1.0;
	double tmp;
	if (x <= -1.0) {
		tmp = (x * (t_0 * (-1.0 - eps_m))) / 2.0;
	} else if (x <= 1.8e+228) {
		tmp = (1.0 + Math.exp(x)) / 2.0;
	} else if (x <= 7.5e+271) {
		tmp = ((1.0 - (-1.0 / eps_m)) + t_0) / 2.0;
	} else {
		tmp = (eps_m * x) / 2.0;
	}
	return tmp;
}

Python

eps_m = math.fabs(eps)
def code(x, eps_m):
	t_0 = (-1.0 / eps_m) - -1.0
	tmp = 0
	if x <= -1.0:
		tmp = (x * (t_0 * (-1.0 - eps_m))) / 2.0
	elif x <= 1.8e+228:
		tmp = (1.0 + math.exp(x)) / 2.0
	elif x <= 7.5e+271:
		tmp = ((1.0 - (-1.0 / eps_m)) + t_0) / 2.0
	else:
		tmp = (eps_m * x) / 2.0
	return tmp

Julia

eps_m = abs(eps)
function code(x, eps_m)
	t_0 = Float64(Float64(-1.0 / eps_m) - -1.0)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(Float64(x * Float64(t_0 * Float64(-1.0 - eps_m))) / 2.0);
	elseif (x <= 1.8e+228)
		tmp = Float64(Float64(1.0 + exp(x)) / 2.0);
	elseif (x <= 7.5e+271)
		tmp = Float64(Float64(Float64(1.0 - Float64(-1.0 / eps_m)) + t_0) / 2.0);
	else
		tmp = Float64(Float64(eps_m * x) / 2.0);
	end
	return tmp
end

MATLAB

eps_m = abs(eps);
function tmp_2 = code(x, eps_m)
	t_0 = (-1.0 / eps_m) - -1.0;
	tmp = 0.0;
	if (x <= -1.0)
		tmp = (x * (t_0 * (-1.0 - eps_m))) / 2.0;
	elseif (x <= 1.8e+228)
		tmp = (1.0 + exp(x)) / 2.0;
	elseif (x <= 7.5e+271)
		tmp = ((1.0 - (-1.0 / eps_m)) + t_0) / 2.0;
	else
		tmp = (eps_m * x) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

eps_m = N[Abs[eps], $MachinePrecision]
code[x_, eps$95$m_] := Block[{t$95$0 = N[(N[(-1.0 / eps$95$m), $MachinePrecision] - -1.0), $MachinePrecision]}, If[LessEqual[x, -1.0], N[(N[(x * N[(t$95$0 * N[(-1.0 - eps$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[x, 1.8e+228], N[(N[(1.0 + N[Exp[x], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[x, 7.5e+271], N[(N[(N[(1.0 - N[(-1.0 / eps$95$m), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(eps$95$m * x), $MachinePrecision] / 2.0), $MachinePrecision]]]]]

Derivation

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1. Add Preprocessing

Alternative 7: 70.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} eps_m = \left|\varepsilon\right| \\ \begin{array}{l} \mathbf{if}\;x \leq -145000:\\ \;\;\;\;\frac{\frac{\mathsf{expm1}\left(-x\right)}{eps_m}}{2}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+227}:\\ \;\;\;\;\frac{1 + e^{x}}{2}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+273}:\\ \;\;\;\;\frac{\left(1 - \frac{-1}{eps_m}\right) + \left(\frac{-1}{eps_m} - -1\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{eps_m \cdot x}{2}\\ \end{array} \end{array} \]

FPCore

eps_m = (fabs.f64 eps)
(FPCore (x eps_m)
 :precision binary64
 (if (<= x -145000.0)
   (/ (/ (expm1 (- x)) eps_m) 2.0)
   (if (<= x 7.6e+227)
     (/ (+ 1.0 (exp x)) 2.0)
     (if (<= x 2.3e+273)
       (/ (+ (- 1.0 (/ -1.0 eps_m)) (- (/ -1.0 eps_m) -1.0)) 2.0)
       (/ (* eps_m x) 2.0)))))

C

eps_m = fabs(eps);
double code(double x, double eps_m) {
	double tmp;
	if (x <= -145000.0) {
		tmp = (expm1(-x) / eps_m) / 2.0;
	} else if (x <= 7.6e+227) {
		tmp = (1.0 + exp(x)) / 2.0;
	} else if (x <= 2.3e+273) {
		tmp = ((1.0 - (-1.0 / eps_m)) + ((-1.0 / eps_m) - -1.0)) / 2.0;
	} else {
		tmp = (eps_m * x) / 2.0;
	}
	return tmp;
}

Java

eps_m = Math.abs(eps);
public static double code(double x, double eps_m) {
	double tmp;
	if (x <= -145000.0) {
		tmp = (Math.expm1(-x) / eps_m) / 2.0;
	} else if (x <= 7.6e+227) {
		tmp = (1.0 + Math.exp(x)) / 2.0;
	} else if (x <= 2.3e+273) {
		tmp = ((1.0 - (-1.0 / eps_m)) + ((-1.0 / eps_m) - -1.0)) / 2.0;
	} else {
		tmp = (eps_m * x) / 2.0;
	}
	return tmp;
}

Python

eps_m = math.fabs(eps)
def code(x, eps_m):
	tmp = 0
	if x <= -145000.0:
		tmp = (math.expm1(-x) / eps_m) / 2.0
	elif x <= 7.6e+227:
		tmp = (1.0 + math.exp(x)) / 2.0
	elif x <= 2.3e+273:
		tmp = ((1.0 - (-1.0 / eps_m)) + ((-1.0 / eps_m) - -1.0)) / 2.0
	else:
		tmp = (eps_m * x) / 2.0
	return tmp

Julia

eps_m = abs(eps)
function code(x, eps_m)
	tmp = 0.0
	if (x <= -145000.0)
		tmp = Float64(Float64(expm1(Float64(-x)) / eps_m) / 2.0);
	elseif (x <= 7.6e+227)
		tmp = Float64(Float64(1.0 + exp(x)) / 2.0);
	elseif (x <= 2.3e+273)
		tmp = Float64(Float64(Float64(1.0 - Float64(-1.0 / eps_m)) + Float64(Float64(-1.0 / eps_m) - -1.0)) / 2.0);
	else
		tmp = Float64(Float64(eps_m * x) / 2.0);
	end
	return tmp
end

Wolfram

eps_m = N[Abs[eps], $MachinePrecision]
code[x_, eps$95$m_] := If[LessEqual[x, -145000.0], N[(N[(N[(Exp[(-x)] - 1), $MachinePrecision] / eps$95$m), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[x, 7.6e+227], N[(N[(1.0 + N[Exp[x], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[x, 2.3e+273], N[(N[(N[(1.0 - N[(-1.0 / eps$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 / eps$95$m), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(eps$95$m * x), $MachinePrecision] / 2.0), $MachinePrecision]]]]

Derivation

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

Alternative 8: 62.6% accurate, 9.7× speedup

Math

\[\begin{array}{l} eps_m = \left|\varepsilon\right| \\ \begin{array}{l} t_0 := \frac{-1}{eps_m} - -1\\ \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x \cdot \left(t_0 \cdot \left(-1 - eps_m\right)\right)}{2}\\ \mathbf{elif}\;x \leq 0.00095:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+149} \lor \neg \left(x \leq 2.75 \cdot 10^{+228}\right) \land x \leq 3.6 \cdot 10^{+271}:\\ \;\;\;\;\frac{\left(1 - \frac{-1}{eps_m}\right) + t_0}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{eps_m \cdot x}{2}\\ \end{array} \end{array} \]

FPCore

eps_m = (fabs.f64 eps)
(FPCore (x eps_m)
 :precision binary64
 (let* ((t_0 (- (/ -1.0 eps_m) -1.0)))
   (if (<= x -1.0)
     (/ (* x (* t_0 (- -1.0 eps_m))) 2.0)
     (if (<= x 0.00095)
       1.0
       (if (or (<= x 3.1e+149) (and (not (<= x 2.75e+228)) (<= x 3.6e+271)))
         (/ (+ (- 1.0 (/ -1.0 eps_m)) t_0) 2.0)
         (/ (* eps_m x) 2.0))))))

C

eps_m = fabs(eps);
double code(double x, double eps_m) {
	double t_0 = (-1.0 / eps_m) - -1.0;
	double tmp;
	if (x <= -1.0) {
		tmp = (x * (t_0 * (-1.0 - eps_m))) / 2.0;
	} else if (x <= 0.00095) {
		tmp = 1.0;
	} else if ((x <= 3.1e+149) || (!(x <= 2.75e+228) && (x <= 3.6e+271))) {
		tmp = ((1.0 - (-1.0 / eps_m)) + t_0) / 2.0;
	} else {
		tmp = (eps_m * x) / 2.0;
	}
	return tmp;
}

Fortran

eps_m = abs(eps)
real(8) function code(x, eps_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps_m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((-1.0d0) / eps_m) - (-1.0d0)
    if (x <= (-1.0d0)) then
        tmp = (x * (t_0 * ((-1.0d0) - eps_m))) / 2.0d0
    else if (x <= 0.00095d0) then
        tmp = 1.0d0
    else if ((x <= 3.1d+149) .or. (.not. (x <= 2.75d+228)) .and. (x <= 3.6d+271)) then
        tmp = ((1.0d0 - ((-1.0d0) / eps_m)) + t_0) / 2.0d0
    else
        tmp = (eps_m * x) / 2.0d0
    end if
    code = tmp
end function

Java

eps_m = Math.abs(eps);
public static double code(double x, double eps_m) {
	double t_0 = (-1.0 / eps_m) - -1.0;
	double tmp;
	if (x <= -1.0) {
		tmp = (x * (t_0 * (-1.0 - eps_m))) / 2.0;
	} else if (x <= 0.00095) {
		tmp = 1.0;
	} else if ((x <= 3.1e+149) || (!(x <= 2.75e+228) && (x <= 3.6e+271))) {
		tmp = ((1.0 - (-1.0 / eps_m)) + t_0) / 2.0;
	} else {
		tmp = (eps_m * x) / 2.0;
	}
	return tmp;
}

Python

eps_m = math.fabs(eps)
def code(x, eps_m):
	t_0 = (-1.0 / eps_m) - -1.0
	tmp = 0
	if x <= -1.0:
		tmp = (x * (t_0 * (-1.0 - eps_m))) / 2.0
	elif x <= 0.00095:
		tmp = 1.0
	elif (x <= 3.1e+149) or (not (x <= 2.75e+228) and (x <= 3.6e+271)):
		tmp = ((1.0 - (-1.0 / eps_m)) + t_0) / 2.0
	else:
		tmp = (eps_m * x) / 2.0
	return tmp

Julia

eps_m = abs(eps)
function code(x, eps_m)
	t_0 = Float64(Float64(-1.0 / eps_m) - -1.0)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(Float64(x * Float64(t_0 * Float64(-1.0 - eps_m))) / 2.0);
	elseif (x <= 0.00095)
		tmp = 1.0;
	elseif ((x <= 3.1e+149) || (!(x <= 2.75e+228) && (x <= 3.6e+271)))
		tmp = Float64(Float64(Float64(1.0 - Float64(-1.0 / eps_m)) + t_0) / 2.0);
	else
		tmp = Float64(Float64(eps_m * x) / 2.0);
	end
	return tmp
end

MATLAB

eps_m = abs(eps);
function tmp_2 = code(x, eps_m)
	t_0 = (-1.0 / eps_m) - -1.0;
	tmp = 0.0;
	if (x <= -1.0)
		tmp = (x * (t_0 * (-1.0 - eps_m))) / 2.0;
	elseif (x <= 0.00095)
		tmp = 1.0;
	elseif ((x <= 3.1e+149) || (~((x <= 2.75e+228)) && (x <= 3.6e+271)))
		tmp = ((1.0 - (-1.0 / eps_m)) + t_0) / 2.0;
	else
		tmp = (eps_m * x) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

eps_m = N[Abs[eps], $MachinePrecision]
code[x_, eps$95$m_] := Block[{t$95$0 = N[(N[(-1.0 / eps$95$m), $MachinePrecision] - -1.0), $MachinePrecision]}, If[LessEqual[x, -1.0], N[(N[(x * N[(t$95$0 * N[(-1.0 - eps$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[x, 0.00095], 1.0, If[Or[LessEqual[x, 3.1e+149], And[N[Not[LessEqual[x, 2.75e+228]], $MachinePrecision], LessEqual[x, 3.6e+271]]], N[(N[(N[(1.0 - N[(-1.0 / eps$95$m), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(eps$95$m * x), $MachinePrecision] / 2.0), $MachinePrecision]]]]]

Derivation

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

Alternative 9: 62.6% accurate, 14.8× speedup

Math

\[\begin{array}{l} eps_m = \left|\varepsilon\right| \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{eps_m \cdot \left(-x\right)}{2}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+21}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+152}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+228} \lor \neg \left(x \leq 2.4 \cdot 10^{+276}\right):\\ \;\;\;\;\frac{eps_m \cdot x}{2}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

eps_m = (fabs.f64 eps)
(FPCore (x eps_m)
 :precision binary64
 (if (<= x -1.0)
   (/ (* eps_m (- x)) 2.0)
   (if (<= x 5.2e+21)
     1.0
     (if (<= x 9.6e+152)
       0.0
       (if (or (<= x 8e+228) (not (<= x 2.4e+276)))
         (/ (* eps_m x) 2.0)
         0.0)))))

C

eps_m = fabs(eps);
double code(double x, double eps_m) {
	double tmp;
	if (x <= -1.0) {
		tmp = (eps_m * -x) / 2.0;
	} else if (x <= 5.2e+21) {
		tmp = 1.0;
	} else if (x <= 9.6e+152) {
		tmp = 0.0;
	} else if ((x <= 8e+228) || !(x <= 2.4e+276)) {
		tmp = (eps_m * x) / 2.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

eps_m = abs(eps)
real(8) function code(x, eps_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps_m
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = (eps_m * -x) / 2.0d0
    else if (x <= 5.2d+21) then
        tmp = 1.0d0
    else if (x <= 9.6d+152) then
        tmp = 0.0d0
    else if ((x <= 8d+228) .or. (.not. (x <= 2.4d+276))) then
        tmp = (eps_m * x) / 2.0d0
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

eps_m = Math.abs(eps);
public static double code(double x, double eps_m) {
	double tmp;
	if (x <= -1.0) {
		tmp = (eps_m * -x) / 2.0;
	} else if (x <= 5.2e+21) {
		tmp = 1.0;
	} else if (x <= 9.6e+152) {
		tmp = 0.0;
	} else if ((x <= 8e+228) || !(x <= 2.4e+276)) {
		tmp = (eps_m * x) / 2.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

eps_m = math.fabs(eps)
def code(x, eps_m):
	tmp = 0
	if x <= -1.0:
		tmp = (eps_m * -x) / 2.0
	elif x <= 5.2e+21:
		tmp = 1.0
	elif x <= 9.6e+152:
		tmp = 0.0
	elif (x <= 8e+228) or not (x <= 2.4e+276):
		tmp = (eps_m * x) / 2.0
	else:
		tmp = 0.0
	return tmp

Julia

eps_m = abs(eps)
function code(x, eps_m)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(Float64(eps_m * Float64(-x)) / 2.0);
	elseif (x <= 5.2e+21)
		tmp = 1.0;
	elseif (x <= 9.6e+152)
		tmp = 0.0;
	elseif ((x <= 8e+228) || !(x <= 2.4e+276))
		tmp = Float64(Float64(eps_m * x) / 2.0);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

eps_m = abs(eps);
function tmp_2 = code(x, eps_m)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = (eps_m * -x) / 2.0;
	elseif (x <= 5.2e+21)
		tmp = 1.0;
	elseif (x <= 9.6e+152)
		tmp = 0.0;
	elseif ((x <= 8e+228) || ~((x <= 2.4e+276)))
		tmp = (eps_m * x) / 2.0;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

eps_m = N[Abs[eps], $MachinePrecision]
code[x_, eps$95$m_] := If[LessEqual[x, -1.0], N[(N[(eps$95$m * (-x)), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[x, 5.2e+21], 1.0, If[LessEqual[x, 9.6e+152], 0.0, If[Or[LessEqual[x, 8e+228], N[Not[LessEqual[x, 2.4e+276]], $MachinePrecision]], N[(N[(eps$95$m * x), $MachinePrecision] / 2.0), $MachinePrecision], 0.0]]]]

Derivation

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

Alternative 10: 62.5% accurate, 14.8× speedup

Math

\[\begin{array}{l} eps_m = \left|\varepsilon\right| \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x \cdot \left(\left(\frac{-1}{eps_m} - -1\right) \cdot \left(-1 - eps_m\right)\right)}{2}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+21}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+153}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+228} \lor \neg \left(x \leq 3.35 \cdot 10^{+271}\right):\\ \;\;\;\;\frac{eps_m \cdot x}{2}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

eps_m = (fabs.f64 eps)
(FPCore (x eps_m)
 :precision binary64
 (if (<= x -1.0)
   (/ (* x (* (- (/ -1.0 eps_m) -1.0) (- -1.0 eps_m))) 2.0)
   (if (<= x 5.2e+21)
     1.0
     (if (<= x 1.65e+153)
       0.0
       (if (or (<= x 1.02e+228) (not (<= x 3.35e+271)))
         (/ (* eps_m x) 2.0)
         0.0)))))

C

eps_m = fabs(eps);
double code(double x, double eps_m) {
	double tmp;
	if (x <= -1.0) {
		tmp = (x * (((-1.0 / eps_m) - -1.0) * (-1.0 - eps_m))) / 2.0;
	} else if (x <= 5.2e+21) {
		tmp = 1.0;
	} else if (x <= 1.65e+153) {
		tmp = 0.0;
	} else if ((x <= 1.02e+228) || !(x <= 3.35e+271)) {
		tmp = (eps_m * x) / 2.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

eps_m = abs(eps)
real(8) function code(x, eps_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps_m
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = (x * ((((-1.0d0) / eps_m) - (-1.0d0)) * ((-1.0d0) - eps_m))) / 2.0d0
    else if (x <= 5.2d+21) then
        tmp = 1.0d0
    else if (x <= 1.65d+153) then
        tmp = 0.0d0
    else if ((x <= 1.02d+228) .or. (.not. (x <= 3.35d+271))) then
        tmp = (eps_m * x) / 2.0d0
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

eps_m = Math.abs(eps);
public static double code(double x, double eps_m) {
	double tmp;
	if (x <= -1.0) {
		tmp = (x * (((-1.0 / eps_m) - -1.0) * (-1.0 - eps_m))) / 2.0;
	} else if (x <= 5.2e+21) {
		tmp = 1.0;
	} else if (x <= 1.65e+153) {
		tmp = 0.0;
	} else if ((x <= 1.02e+228) || !(x <= 3.35e+271)) {
		tmp = (eps_m * x) / 2.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

eps_m = math.fabs(eps)
def code(x, eps_m):
	tmp = 0
	if x <= -1.0:
		tmp = (x * (((-1.0 / eps_m) - -1.0) * (-1.0 - eps_m))) / 2.0
	elif x <= 5.2e+21:
		tmp = 1.0
	elif x <= 1.65e+153:
		tmp = 0.0
	elif (x <= 1.02e+228) or not (x <= 3.35e+271):
		tmp = (eps_m * x) / 2.0
	else:
		tmp = 0.0
	return tmp

Julia

eps_m = abs(eps)
function code(x, eps_m)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(Float64(x * Float64(Float64(Float64(-1.0 / eps_m) - -1.0) * Float64(-1.0 - eps_m))) / 2.0);
	elseif (x <= 5.2e+21)
		tmp = 1.0;
	elseif (x <= 1.65e+153)
		tmp = 0.0;
	elseif ((x <= 1.02e+228) || !(x <= 3.35e+271))
		tmp = Float64(Float64(eps_m * x) / 2.0);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

eps_m = abs(eps);
function tmp_2 = code(x, eps_m)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = (x * (((-1.0 / eps_m) - -1.0) * (-1.0 - eps_m))) / 2.0;
	elseif (x <= 5.2e+21)
		tmp = 1.0;
	elseif (x <= 1.65e+153)
		tmp = 0.0;
	elseif ((x <= 1.02e+228) || ~((x <= 3.35e+271)))
		tmp = (eps_m * x) / 2.0;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

eps_m = N[Abs[eps], $MachinePrecision]
code[x_, eps$95$m_] := If[LessEqual[x, -1.0], N[(N[(x * N[(N[(N[(-1.0 / eps$95$m), $MachinePrecision] - -1.0), $MachinePrecision] * N[(-1.0 - eps$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], If[LessEqual[x, 5.2e+21], 1.0, If[LessEqual[x, 1.65e+153], 0.0, If[Or[LessEqual[x, 1.02e+228], N[Not[LessEqual[x, 3.35e+271]], $MachinePrecision]], N[(N[(eps$95$m * x), $MachinePrecision] / 2.0), $MachinePrecision], 0.0]]]]

Derivation

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

Alternative 11: 54.9% accurate, 17.1× speedup

Math

\[\begin{array}{l} eps_m = \left|\varepsilon\right| \\ \begin{array}{l} \mathbf{if}\;x \leq 5.2 \cdot 10^{+21}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+145}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+229} \lor \neg \left(x \leq 5.5 \cdot 10^{+272}\right):\\ \;\;\;\;\frac{eps_m \cdot x}{2}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

eps_m = (fabs.f64 eps)
(FPCore (x eps_m)
 :precision binary64
 (if (<= x 5.2e+21)
   1.0
   (if (<= x 5e+145)
     0.0
     (if (or (<= x 1.08e+229) (not (<= x 5.5e+272)))
       (/ (* eps_m x) 2.0)
       0.0))))

C

eps_m = fabs(eps);
double code(double x, double eps_m) {
	double tmp;
	if (x <= 5.2e+21) {
		tmp = 1.0;
	} else if (x <= 5e+145) {
		tmp = 0.0;
	} else if ((x <= 1.08e+229) || !(x <= 5.5e+272)) {
		tmp = (eps_m * x) / 2.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

eps_m = abs(eps)
real(8) function code(x, eps_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps_m
    real(8) :: tmp
    if (x <= 5.2d+21) then
        tmp = 1.0d0
    else if (x <= 5d+145) then
        tmp = 0.0d0
    else if ((x <= 1.08d+229) .or. (.not. (x <= 5.5d+272))) then
        tmp = (eps_m * x) / 2.0d0
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

eps_m = Math.abs(eps);
public static double code(double x, double eps_m) {
	double tmp;
	if (x <= 5.2e+21) {
		tmp = 1.0;
	} else if (x <= 5e+145) {
		tmp = 0.0;
	} else if ((x <= 1.08e+229) || !(x <= 5.5e+272)) {
		tmp = (eps_m * x) / 2.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

eps_m = math.fabs(eps)
def code(x, eps_m):
	tmp = 0
	if x <= 5.2e+21:
		tmp = 1.0
	elif x <= 5e+145:
		tmp = 0.0
	elif (x <= 1.08e+229) or not (x <= 5.5e+272):
		tmp = (eps_m * x) / 2.0
	else:
		tmp = 0.0
	return tmp

Julia

eps_m = abs(eps)
function code(x, eps_m)
	tmp = 0.0
	if (x <= 5.2e+21)
		tmp = 1.0;
	elseif (x <= 5e+145)
		tmp = 0.0;
	elseif ((x <= 1.08e+229) || !(x <= 5.5e+272))
		tmp = Float64(Float64(eps_m * x) / 2.0);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

eps_m = abs(eps);
function tmp_2 = code(x, eps_m)
	tmp = 0.0;
	if (x <= 5.2e+21)
		tmp = 1.0;
	elseif (x <= 5e+145)
		tmp = 0.0;
	elseif ((x <= 1.08e+229) || ~((x <= 5.5e+272)))
		tmp = (eps_m * x) / 2.0;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

eps_m = N[Abs[eps], $MachinePrecision]
code[x_, eps$95$m_] := If[LessEqual[x, 5.2e+21], 1.0, If[LessEqual[x, 5e+145], 0.0, If[Or[LessEqual[x, 1.08e+229], N[Not[LessEqual[x, 5.5e+272]], $MachinePrecision]], N[(N[(eps$95$m * x), $MachinePrecision] / 2.0), $MachinePrecision], 0.0]]]

Derivation

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

Alternative 12: 56.3% accurate, 74.1× speedup

Math

\[\begin{array}{l} eps_m = \left|\varepsilon\right| \\ \begin{array}{l} \mathbf{if}\;x \leq 5.2 \cdot 10^{+21}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

eps_m = (fabs.f64 eps)
(FPCore (x eps_m) :precision binary64 (if (<= x 5.2e+21) 1.0 0.0))

C

eps_m = fabs(eps);
double code(double x, double eps_m) {
	double tmp;
	if (x <= 5.2e+21) {
		tmp = 1.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

eps_m = abs(eps)
real(8) function code(x, eps_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps_m
    real(8) :: tmp
    if (x <= 5.2d+21) then
        tmp = 1.0d0
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

eps_m = Math.abs(eps);
public static double code(double x, double eps_m) {
	double tmp;
	if (x <= 5.2e+21) {
		tmp = 1.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

eps_m = math.fabs(eps)
def code(x, eps_m):
	tmp = 0
	if x <= 5.2e+21:
		tmp = 1.0
	else:
		tmp = 0.0
	return tmp

Julia

eps_m = abs(eps)
function code(x, eps_m)
	tmp = 0.0
	if (x <= 5.2e+21)
		tmp = 1.0;
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

eps_m = abs(eps);
function tmp_2 = code(x, eps_m)
	tmp = 0.0;
	if (x <= 5.2e+21)
		tmp = 1.0;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

eps_m = N[Abs[eps], $MachinePrecision]
code[x_, eps$95$m_] := If[LessEqual[x, 5.2e+21], 1.0, 0.0]

Derivation

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

Alternative 13: 15.9% accurate, 227.0× speedup

Math

\[\begin{array}{l} eps_m = \left|\varepsilon\right| \\ 0 \end{array} \]

FPCore

eps_m = (fabs.f64 eps)
(FPCore (x eps_m) :precision binary64 0.0)

C

eps_m = fabs(eps);
double code(double x, double eps_m) {
	return 0.0;
}

Fortran

eps_m = abs(eps)
real(8) function code(x, eps_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps_m
    code = 0.0d0
end function

Java

eps_m = Math.abs(eps);
public static double code(double x, double eps_m) {
	return 0.0;
}

Python

eps_m = math.fabs(eps)
def code(x, eps_m):
	return 0.0

Julia

eps_m = abs(eps)
function code(x, eps_m)
	return 0.0
end

MATLAB

eps_m = abs(eps);
function tmp = code(x, eps_m)
	tmp = 0.0;
end

Wolfram

eps_m = N[Abs[eps], $MachinePrecision]
code[x_, eps$95$m_] := 0.0

Derivation

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

Reproduce

herbie shell --seed 2023342 
(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))