Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A

Percentage Accurate: 95.9% → 99.9%

Time: 9.3s

Alternatives: 14

Speedup: 8.5×

Specification

Math

\[\begin{array}{l} \\ x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))

C

double code(double x, double y, double z) {
	return x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (y / ((1.1283791670955126d0 * exp(z)) - (x * y)))
end function

Java

public static double code(double x, double y, double z) {
	return x + (y / ((1.1283791670955126 * Math.exp(z)) - (x * y)));
}

Python

def code(x, y, z):
	return x + (y / ((1.1283791670955126 * math.exp(z)) - (x * y)))

Julia

function code(x, y, z)
	return Float64(x + Float64(y / Float64(Float64(1.1283791670955126 * exp(z)) - Float64(x * y))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y / N[(N[(1.1283791670955126 * N[Exp[z], $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))

C

double code(double x, double y, double z) {
	return x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (y / ((1.1283791670955126d0 * exp(z)) - (x * y)))
end function

Java

public static double code(double x, double y, double z) {
	return x + (y / ((1.1283791670955126 * Math.exp(z)) - (x * y)));
}

Python

def code(x, y, z):
	return x + (y / ((1.1283791670955126 * math.exp(z)) - (x * y)))

Julia

function code(x, y, z)
	return Float64(x + Float64(y / Float64(Float64(1.1283791670955126 * exp(z)) - Float64(x * y))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y / N[(N[(1.1283791670955126 * N[Exp[z], $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ x + \frac{-1}{\mathsf{fma}\left(e^{z}, \frac{-1.1283791670955126}{y}, x\right)} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ -1.0 (fma (exp z) (/ -1.1283791670955126 y) x))))

C

double code(double x, double y, double z) {
	return x + (-1.0 / fma(exp(z), (-1.1283791670955126 / y), x));
}

Julia

function code(x, y, z)
	return Float64(x + Float64(-1.0 / fma(exp(z), Float64(-1.1283791670955126 / y), x)))
end

Wolfram

code[x_, y_, z_] := N[(x + N[(-1.0 / N[(N[Exp[z], $MachinePrecision] * N[(-1.1283791670955126 / y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 2: 99.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{z} \leq 0:\\ \;\;\;\;x - \frac{1}{x}\\ \mathbf{elif}\;e^{z} \leq 1.001:\\ \;\;\;\;x + \frac{1}{1.1283791670955126 \cdot \left(\frac{1}{y} + \frac{z}{y}\right) - x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (exp z) 0.0)
   (- x (/ 1.0 x))
   (if (<= (exp z) 1.001)
     (+ x (/ 1.0 (- (* 1.1283791670955126 (+ (/ 1.0 y) (/ z y))) x)))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (exp(z) <= 0.0) {
		tmp = x - (1.0 / x);
	} else if (exp(z) <= 1.001) {
		tmp = x + (1.0 / ((1.1283791670955126 * ((1.0 / y) + (z / y))) - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (exp(z) <= 0.0d0) then
        tmp = x - (1.0d0 / x)
    else if (exp(z) <= 1.001d0) then
        tmp = x + (1.0d0 / ((1.1283791670955126d0 * ((1.0d0 / y) + (z / y))) - x))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (Math.exp(z) <= 0.0) {
		tmp = x - (1.0 / x);
	} else if (Math.exp(z) <= 1.001) {
		tmp = x + (1.0 / ((1.1283791670955126 * ((1.0 / y) + (z / y))) - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if math.exp(z) <= 0.0:
		tmp = x - (1.0 / x)
	elif math.exp(z) <= 1.001:
		tmp = x + (1.0 / ((1.1283791670955126 * ((1.0 / y) + (z / y))) - x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (exp(z) <= 0.0)
		tmp = Float64(x - Float64(1.0 / x));
	elseif (exp(z) <= 1.001)
		tmp = Float64(x + Float64(1.0 / Float64(Float64(1.1283791670955126 * Float64(Float64(1.0 / y) + Float64(z / y))) - x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (exp(z) <= 0.0)
		tmp = x - (1.0 / x);
	elseif (exp(z) <= 1.001)
		tmp = x + (1.0 / ((1.1283791670955126 * ((1.0 / y) + (z / y))) - x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[Exp[z], $MachinePrecision], 0.0], N[(x - N[(1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Exp[z], $MachinePrecision], 1.001], N[(x + N[(1.0 / N[(N[(1.1283791670955126 * N[(N[(1.0 / y), $MachinePrecision] + N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

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

Alternative 3: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ 1.0 (- (* 1.1283791670955126 (/ (exp z) y)) x))))

C

double code(double x, double y, double z) {
	return x + (1.0 / ((1.1283791670955126 * (exp(z) / y)) - x));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (1.0d0 / ((1.1283791670955126d0 * (exp(z) / y)) - x))
end function

Java

public static double code(double x, double y, double z) {
	return x + (1.0 / ((1.1283791670955126 * (Math.exp(z) / y)) - x));
}

Python

def code(x, y, z):
	return x + (1.0 / ((1.1283791670955126 * (math.exp(z) / y)) - x))

Julia

function code(x, y, z)
	return Float64(x + Float64(1.0 / Float64(Float64(1.1283791670955126 * Float64(exp(z) / y)) - x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (1.0 / ((1.1283791670955126 * (exp(z) / y)) - x));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(1.0 / N[(N[(1.1283791670955126 * N[(N[Exp[z], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 4: 84.5% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{1}{x}\\ t_1 := x + 0.8862269254527579 \cdot \frac{y}{z + 1}\\ \mathbf{if}\;z \leq -0.4:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-256}:\\ \;\;\;\;x + \frac{-1}{\frac{-1.1283791670955126}{y}}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-70}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ 1.0 x)))
        (t_1 (+ x (* 0.8862269254527579 (/ y (+ z 1.0))))))
   (if (<= z -0.4)
     t_0
     (if (<= z -1.75e-86)
       t_1
       (if (<= z -1.52e-176)
         t_0
         (if (<= z 2.8e-256)
           (+ x (/ -1.0 (/ -1.1283791670955126 y)))
           (if (<= z 3.7e-70) t_0 (if (<= z 1.75e-6) t_1 x))))))))

C

double code(double x, double y, double z) {
	double t_0 = x - (1.0 / x);
	double t_1 = x + (0.8862269254527579 * (y / (z + 1.0)));
	double tmp;
	if (z <= -0.4) {
		tmp = t_0;
	} else if (z <= -1.75e-86) {
		tmp = t_1;
	} else if (z <= -1.52e-176) {
		tmp = t_0;
	} else if (z <= 2.8e-256) {
		tmp = x + (-1.0 / (-1.1283791670955126 / y));
	} else if (z <= 3.7e-70) {
		tmp = t_0;
	} else if (z <= 1.75e-6) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x - (1.0d0 / x)
    t_1 = x + (0.8862269254527579d0 * (y / (z + 1.0d0)))
    if (z <= (-0.4d0)) then
        tmp = t_0
    else if (z <= (-1.75d-86)) then
        tmp = t_1
    else if (z <= (-1.52d-176)) then
        tmp = t_0
    else if (z <= 2.8d-256) then
        tmp = x + ((-1.0d0) / ((-1.1283791670955126d0) / y))
    else if (z <= 3.7d-70) then
        tmp = t_0
    else if (z <= 1.75d-6) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x - (1.0 / x);
	double t_1 = x + (0.8862269254527579 * (y / (z + 1.0)));
	double tmp;
	if (z <= -0.4) {
		tmp = t_0;
	} else if (z <= -1.75e-86) {
		tmp = t_1;
	} else if (z <= -1.52e-176) {
		tmp = t_0;
	} else if (z <= 2.8e-256) {
		tmp = x + (-1.0 / (-1.1283791670955126 / y));
	} else if (z <= 3.7e-70) {
		tmp = t_0;
	} else if (z <= 1.75e-6) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (1.0 / x)
	t_1 = x + (0.8862269254527579 * (y / (z + 1.0)))
	tmp = 0
	if z <= -0.4:
		tmp = t_0
	elif z <= -1.75e-86:
		tmp = t_1
	elif z <= -1.52e-176:
		tmp = t_0
	elif z <= 2.8e-256:
		tmp = x + (-1.0 / (-1.1283791670955126 / y))
	elif z <= 3.7e-70:
		tmp = t_0
	elif z <= 1.75e-6:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(1.0 / x))
	t_1 = Float64(x + Float64(0.8862269254527579 * Float64(y / Float64(z + 1.0))))
	tmp = 0.0
	if (z <= -0.4)
		tmp = t_0;
	elseif (z <= -1.75e-86)
		tmp = t_1;
	elseif (z <= -1.52e-176)
		tmp = t_0;
	elseif (z <= 2.8e-256)
		tmp = Float64(x + Float64(-1.0 / Float64(-1.1283791670955126 / y)));
	elseif (z <= 3.7e-70)
		tmp = t_0;
	elseif (z <= 1.75e-6)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x - (1.0 / x);
	t_1 = x + (0.8862269254527579 * (y / (z + 1.0)));
	tmp = 0.0;
	if (z <= -0.4)
		tmp = t_0;
	elseif (z <= -1.75e-86)
		tmp = t_1;
	elseif (z <= -1.52e-176)
		tmp = t_0;
	elseif (z <= 2.8e-256)
		tmp = x + (-1.0 / (-1.1283791670955126 / y));
	elseif (z <= 3.7e-70)
		tmp = t_0;
	elseif (z <= 1.75e-6)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(1.0 / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(0.8862269254527579 * N[(y / N[(z + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.4], t$95$0, If[LessEqual[z, -1.75e-86], t$95$1, If[LessEqual[z, -1.52e-176], t$95$0, If[LessEqual[z, 2.8e-256], N[(x + N[(-1.0 / N[(-1.1283791670955126 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-70], t$95$0, If[LessEqual[z, 1.75e-6], t$95$1, x]]]]]]]]

Derivation

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

Alternative 5: 84.3% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{1}{x}\\ t_1 := x - y \cdot -0.8862269254527579\\ \mathbf{if}\;z \leq -0.108:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{-71}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ 1.0 x))) (t_1 (- x (* y -0.8862269254527579))))
   (if (<= z -0.108)
     t_0
     (if (<= z -3.5e-86)
       t_1
       (if (<= z -1.75e-176)
         t_0
         (if (<= z 1.5e-260)
           t_1
           (if (<= z 3.45e-71) t_0 (if (<= z 1e-7) t_1 x))))))))

C

double code(double x, double y, double z) {
	double t_0 = x - (1.0 / x);
	double t_1 = x - (y * -0.8862269254527579);
	double tmp;
	if (z <= -0.108) {
		tmp = t_0;
	} else if (z <= -3.5e-86) {
		tmp = t_1;
	} else if (z <= -1.75e-176) {
		tmp = t_0;
	} else if (z <= 1.5e-260) {
		tmp = t_1;
	} else if (z <= 3.45e-71) {
		tmp = t_0;
	} else if (z <= 1e-7) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x - (1.0d0 / x)
    t_1 = x - (y * (-0.8862269254527579d0))
    if (z <= (-0.108d0)) then
        tmp = t_0
    else if (z <= (-3.5d-86)) then
        tmp = t_1
    else if (z <= (-1.75d-176)) then
        tmp = t_0
    else if (z <= 1.5d-260) then
        tmp = t_1
    else if (z <= 3.45d-71) then
        tmp = t_0
    else if (z <= 1d-7) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x - (1.0 / x);
	double t_1 = x - (y * -0.8862269254527579);
	double tmp;
	if (z <= -0.108) {
		tmp = t_0;
	} else if (z <= -3.5e-86) {
		tmp = t_1;
	} else if (z <= -1.75e-176) {
		tmp = t_0;
	} else if (z <= 1.5e-260) {
		tmp = t_1;
	} else if (z <= 3.45e-71) {
		tmp = t_0;
	} else if (z <= 1e-7) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (1.0 / x)
	t_1 = x - (y * -0.8862269254527579)
	tmp = 0
	if z <= -0.108:
		tmp = t_0
	elif z <= -3.5e-86:
		tmp = t_1
	elif z <= -1.75e-176:
		tmp = t_0
	elif z <= 1.5e-260:
		tmp = t_1
	elif z <= 3.45e-71:
		tmp = t_0
	elif z <= 1e-7:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(1.0 / x))
	t_1 = Float64(x - Float64(y * -0.8862269254527579))
	tmp = 0.0
	if (z <= -0.108)
		tmp = t_0;
	elseif (z <= -3.5e-86)
		tmp = t_1;
	elseif (z <= -1.75e-176)
		tmp = t_0;
	elseif (z <= 1.5e-260)
		tmp = t_1;
	elseif (z <= 3.45e-71)
		tmp = t_0;
	elseif (z <= 1e-7)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x - (1.0 / x);
	t_1 = x - (y * -0.8862269254527579);
	tmp = 0.0;
	if (z <= -0.108)
		tmp = t_0;
	elseif (z <= -3.5e-86)
		tmp = t_1;
	elseif (z <= -1.75e-176)
		tmp = t_0;
	elseif (z <= 1.5e-260)
		tmp = t_1;
	elseif (z <= 3.45e-71)
		tmp = t_0;
	elseif (z <= 1e-7)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(1.0 / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x - N[(y * -0.8862269254527579), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.108], t$95$0, If[LessEqual[z, -3.5e-86], t$95$1, If[LessEqual[z, -1.75e-176], t$95$0, If[LessEqual[z, 1.5e-260], t$95$1, If[LessEqual[z, 3.45e-71], t$95$0, If[LessEqual[z, 1e-7], t$95$1, x]]]]]]]]

Derivation

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

Alternative 6: 84.2% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{1}{x}\\ t_1 := x - \frac{y}{-1.1283791670955126}\\ \mathbf{if}\;z \leq -120:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-71}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-9}:\\ \;\;\;\;x - y \cdot -0.8862269254527579\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ 1.0 x))) (t_1 (- x (/ y -1.1283791670955126))))
   (if (<= z -120.0)
     t_0
     (if (<= z -1.18e-85)
       t_1
       (if (<= z -6e-176)
         t_0
         (if (<= z 3.3e-256)
           t_1
           (if (<= z 4e-71)
             t_0
             (if (<= z 3.2e-9) (- x (* y -0.8862269254527579)) x))))))))

C

double code(double x, double y, double z) {
	double t_0 = x - (1.0 / x);
	double t_1 = x - (y / -1.1283791670955126);
	double tmp;
	if (z <= -120.0) {
		tmp = t_0;
	} else if (z <= -1.18e-85) {
		tmp = t_1;
	} else if (z <= -6e-176) {
		tmp = t_0;
	} else if (z <= 3.3e-256) {
		tmp = t_1;
	} else if (z <= 4e-71) {
		tmp = t_0;
	} else if (z <= 3.2e-9) {
		tmp = x - (y * -0.8862269254527579);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x - (1.0d0 / x)
    t_1 = x - (y / (-1.1283791670955126d0))
    if (z <= (-120.0d0)) then
        tmp = t_0
    else if (z <= (-1.18d-85)) then
        tmp = t_1
    else if (z <= (-6d-176)) then
        tmp = t_0
    else if (z <= 3.3d-256) then
        tmp = t_1
    else if (z <= 4d-71) then
        tmp = t_0
    else if (z <= 3.2d-9) then
        tmp = x - (y * (-0.8862269254527579d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x - (1.0 / x);
	double t_1 = x - (y / -1.1283791670955126);
	double tmp;
	if (z <= -120.0) {
		tmp = t_0;
	} else if (z <= -1.18e-85) {
		tmp = t_1;
	} else if (z <= -6e-176) {
		tmp = t_0;
	} else if (z <= 3.3e-256) {
		tmp = t_1;
	} else if (z <= 4e-71) {
		tmp = t_0;
	} else if (z <= 3.2e-9) {
		tmp = x - (y * -0.8862269254527579);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (1.0 / x)
	t_1 = x - (y / -1.1283791670955126)
	tmp = 0
	if z <= -120.0:
		tmp = t_0
	elif z <= -1.18e-85:
		tmp = t_1
	elif z <= -6e-176:
		tmp = t_0
	elif z <= 3.3e-256:
		tmp = t_1
	elif z <= 4e-71:
		tmp = t_0
	elif z <= 3.2e-9:
		tmp = x - (y * -0.8862269254527579)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(1.0 / x))
	t_1 = Float64(x - Float64(y / -1.1283791670955126))
	tmp = 0.0
	if (z <= -120.0)
		tmp = t_0;
	elseif (z <= -1.18e-85)
		tmp = t_1;
	elseif (z <= -6e-176)
		tmp = t_0;
	elseif (z <= 3.3e-256)
		tmp = t_1;
	elseif (z <= 4e-71)
		tmp = t_0;
	elseif (z <= 3.2e-9)
		tmp = Float64(x - Float64(y * -0.8862269254527579));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x - (1.0 / x);
	t_1 = x - (y / -1.1283791670955126);
	tmp = 0.0;
	if (z <= -120.0)
		tmp = t_0;
	elseif (z <= -1.18e-85)
		tmp = t_1;
	elseif (z <= -6e-176)
		tmp = t_0;
	elseif (z <= 3.3e-256)
		tmp = t_1;
	elseif (z <= 4e-71)
		tmp = t_0;
	elseif (z <= 3.2e-9)
		tmp = x - (y * -0.8862269254527579);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(1.0 / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x - N[(y / -1.1283791670955126), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -120.0], t$95$0, If[LessEqual[z, -1.18e-85], t$95$1, If[LessEqual[z, -6e-176], t$95$0, If[LessEqual[z, 3.3e-256], t$95$1, If[LessEqual[z, 4e-71], t$95$0, If[LessEqual[z, 3.2e-9], N[(x - N[(y * -0.8862269254527579), $MachinePrecision]), $MachinePrecision], x]]]]]]]]

Derivation

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

Alternative 7: 84.2% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{1}{x}\\ \mathbf{if}\;z \leq -23:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-87}:\\ \;\;\;\;x - \frac{y}{-1.1283791670955126}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-256}:\\ \;\;\;\;x + \frac{-1}{\frac{-1.1283791670955126}{y}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-71}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-12}:\\ \;\;\;\;x - y \cdot -0.8862269254527579\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ 1.0 x))))
   (if (<= z -23.0)
     t_0
     (if (<= z -6.5e-87)
       (- x (/ y -1.1283791670955126))
       (if (<= z -5e-176)
         t_0
         (if (<= z 3.8e-256)
           (+ x (/ -1.0 (/ -1.1283791670955126 y)))
           (if (<= z 3.5e-71)
             t_0
             (if (<= z 8e-12) (- x (* y -0.8862269254527579)) x))))))))

C

double code(double x, double y, double z) {
	double t_0 = x - (1.0 / x);
	double tmp;
	if (z <= -23.0) {
		tmp = t_0;
	} else if (z <= -6.5e-87) {
		tmp = x - (y / -1.1283791670955126);
	} else if (z <= -5e-176) {
		tmp = t_0;
	} else if (z <= 3.8e-256) {
		tmp = x + (-1.0 / (-1.1283791670955126 / y));
	} else if (z <= 3.5e-71) {
		tmp = t_0;
	} else if (z <= 8e-12) {
		tmp = x - (y * -0.8862269254527579);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x - (1.0d0 / x)
    if (z <= (-23.0d0)) then
        tmp = t_0
    else if (z <= (-6.5d-87)) then
        tmp = x - (y / (-1.1283791670955126d0))
    else if (z <= (-5d-176)) then
        tmp = t_0
    else if (z <= 3.8d-256) then
        tmp = x + ((-1.0d0) / ((-1.1283791670955126d0) / y))
    else if (z <= 3.5d-71) then
        tmp = t_0
    else if (z <= 8d-12) then
        tmp = x - (y * (-0.8862269254527579d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x - (1.0 / x);
	double tmp;
	if (z <= -23.0) {
		tmp = t_0;
	} else if (z <= -6.5e-87) {
		tmp = x - (y / -1.1283791670955126);
	} else if (z <= -5e-176) {
		tmp = t_0;
	} else if (z <= 3.8e-256) {
		tmp = x + (-1.0 / (-1.1283791670955126 / y));
	} else if (z <= 3.5e-71) {
		tmp = t_0;
	} else if (z <= 8e-12) {
		tmp = x - (y * -0.8862269254527579);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (1.0 / x)
	tmp = 0
	if z <= -23.0:
		tmp = t_0
	elif z <= -6.5e-87:
		tmp = x - (y / -1.1283791670955126)
	elif z <= -5e-176:
		tmp = t_0
	elif z <= 3.8e-256:
		tmp = x + (-1.0 / (-1.1283791670955126 / y))
	elif z <= 3.5e-71:
		tmp = t_0
	elif z <= 8e-12:
		tmp = x - (y * -0.8862269254527579)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(1.0 / x))
	tmp = 0.0
	if (z <= -23.0)
		tmp = t_0;
	elseif (z <= -6.5e-87)
		tmp = Float64(x - Float64(y / -1.1283791670955126));
	elseif (z <= -5e-176)
		tmp = t_0;
	elseif (z <= 3.8e-256)
		tmp = Float64(x + Float64(-1.0 / Float64(-1.1283791670955126 / y)));
	elseif (z <= 3.5e-71)
		tmp = t_0;
	elseif (z <= 8e-12)
		tmp = Float64(x - Float64(y * -0.8862269254527579));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x - (1.0 / x);
	tmp = 0.0;
	if (z <= -23.0)
		tmp = t_0;
	elseif (z <= -6.5e-87)
		tmp = x - (y / -1.1283791670955126);
	elseif (z <= -5e-176)
		tmp = t_0;
	elseif (z <= 3.8e-256)
		tmp = x + (-1.0 / (-1.1283791670955126 / y));
	elseif (z <= 3.5e-71)
		tmp = t_0;
	elseif (z <= 8e-12)
		tmp = x - (y * -0.8862269254527579);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(1.0 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -23.0], t$95$0, If[LessEqual[z, -6.5e-87], N[(x - N[(y / -1.1283791670955126), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e-176], t$95$0, If[LessEqual[z, 3.8e-256], N[(x + N[(-1.0 / N[(-1.1283791670955126 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-71], t$95$0, If[LessEqual[z, 8e-12], N[(x - N[(y * -0.8862269254527579), $MachinePrecision]), $MachinePrecision], x]]]]]]]

Derivation

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

Alternative 8: 99.6% accurate, 6.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -192:\\ \;\;\;\;x - \frac{1}{x}\\ \mathbf{elif}\;z \leq 0.00165:\\ \;\;\;\;x + \frac{y}{\left(1.1283791670955126 + z \cdot 1.1283791670955126\right) - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -192.0)
   (- x (/ 1.0 x))
   (if (<= z 0.00165)
     (+ x (/ y (- (+ 1.1283791670955126 (* z 1.1283791670955126)) (* x y))))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -192.0) {
		tmp = x - (1.0 / x);
	} else if (z <= 0.00165) {
		tmp = x + (y / ((1.1283791670955126 + (z * 1.1283791670955126)) - (x * y)));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-192.0d0)) then
        tmp = x - (1.0d0 / x)
    else if (z <= 0.00165d0) then
        tmp = x + (y / ((1.1283791670955126d0 + (z * 1.1283791670955126d0)) - (x * y)))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -192.0) {
		tmp = x - (1.0 / x);
	} else if (z <= 0.00165) {
		tmp = x + (y / ((1.1283791670955126 + (z * 1.1283791670955126)) - (x * y)));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -192.0:
		tmp = x - (1.0 / x)
	elif z <= 0.00165:
		tmp = x + (y / ((1.1283791670955126 + (z * 1.1283791670955126)) - (x * y)))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -192.0)
		tmp = Float64(x - Float64(1.0 / x));
	elseif (z <= 0.00165)
		tmp = Float64(x + Float64(y / Float64(Float64(1.1283791670955126 + Float64(z * 1.1283791670955126)) - Float64(x * y))));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -192.0)
		tmp = x - (1.0 / x);
	elseif (z <= 0.00165)
		tmp = x + (y / ((1.1283791670955126 + (z * 1.1283791670955126)) - (x * y)));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -192.0], N[(x - N[(1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00165], N[(x + N[(y / N[(N[(1.1283791670955126 + N[(z * 1.1283791670955126), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

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

Alternative 9: 99.5% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -98:\\ \;\;\;\;x - \frac{1}{x}\\ \mathbf{elif}\;z \leq 0.00165:\\ \;\;\;\;x + \frac{y}{1.1283791670955126 - x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -98.0)
   (- x (/ 1.0 x))
   (if (<= z 0.00165) (+ x (/ y (- 1.1283791670955126 (* x y)))) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -98.0) {
		tmp = x - (1.0 / x);
	} else if (z <= 0.00165) {
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-98.0d0)) then
        tmp = x - (1.0d0 / x)
    else if (z <= 0.00165d0) then
        tmp = x + (y / (1.1283791670955126d0 - (x * y)))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -98.0) {
		tmp = x - (1.0 / x);
	} else if (z <= 0.00165) {
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -98.0:
		tmp = x - (1.0 / x)
	elif z <= 0.00165:
		tmp = x + (y / (1.1283791670955126 - (x * y)))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -98.0)
		tmp = Float64(x - Float64(1.0 / x));
	elseif (z <= 0.00165)
		tmp = Float64(x + Float64(y / Float64(1.1283791670955126 - Float64(x * y))));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -98.0)
		tmp = x - (1.0 / x);
	elseif (z <= 0.00165)
		tmp = x + (y / (1.1283791670955126 - (x * y)));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -98.0], N[(x - N[(1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00165], N[(x + N[(y / N[(1.1283791670955126 - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

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

Alternative 10: 99.5% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -250:\\ \;\;\;\;x - \frac{1}{x}\\ \mathbf{elif}\;z \leq 0.00165:\\ \;\;\;\;x + \frac{-1}{x + \frac{-1.1283791670955126}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -250.0)
   (- x (/ 1.0 x))
   (if (<= z 0.00165) (+ x (/ -1.0 (+ x (/ -1.1283791670955126 y)))) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -250.0) {
		tmp = x - (1.0 / x);
	} else if (z <= 0.00165) {
		tmp = x + (-1.0 / (x + (-1.1283791670955126 / y)));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-250.0d0)) then
        tmp = x - (1.0d0 / x)
    else if (z <= 0.00165d0) then
        tmp = x + ((-1.0d0) / (x + ((-1.1283791670955126d0) / y)))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -250.0) {
		tmp = x - (1.0 / x);
	} else if (z <= 0.00165) {
		tmp = x + (-1.0 / (x + (-1.1283791670955126 / y)));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -250.0:
		tmp = x - (1.0 / x)
	elif z <= 0.00165:
		tmp = x + (-1.0 / (x + (-1.1283791670955126 / y)))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -250.0)
		tmp = Float64(x - Float64(1.0 / x));
	elseif (z <= 0.00165)
		tmp = Float64(x + Float64(-1.0 / Float64(x + Float64(-1.1283791670955126 / y))));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -250.0)
		tmp = x - (1.0 / x);
	elseif (z <= 0.00165)
		tmp = x + (-1.0 / (x + (-1.1283791670955126 / y)));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -250.0], N[(x - N[(1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00165], N[(x + N[(-1.0 / N[(x + N[(-1.1283791670955126 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

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

Alternative 11: 72.8% accurate, 12.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-136}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-105}:\\ \;\;\;\;x - y \cdot -0.8862269254527579\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.5e-136)
   x
   (if (<= x 5.4e-105) (- x (* y -0.8862269254527579)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.5e-136) {
		tmp = x;
	} else if (x <= 5.4e-105) {
		tmp = x - (y * -0.8862269254527579);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-9.5d-136)) then
        tmp = x
    else if (x <= 5.4d-105) then
        tmp = x - (y * (-0.8862269254527579d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.5e-136) {
		tmp = x;
	} else if (x <= 5.4e-105) {
		tmp = x - (y * -0.8862269254527579);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.5e-136:
		tmp = x
	elif x <= 5.4e-105:
		tmp = x - (y * -0.8862269254527579)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.5e-136)
		tmp = x;
	elseif (x <= 5.4e-105)
		tmp = Float64(x - Float64(y * -0.8862269254527579));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9.5e-136)
		tmp = x;
	elseif (x <= 5.4e-105)
		tmp = x - (y * -0.8862269254527579);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.5e-136], x, If[LessEqual[x, 5.4e-105], N[(x - N[(y * -0.8862269254527579), $MachinePrecision]), $MachinePrecision], x]]

Derivation

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

Alternative 12: 69.8% accurate, 15.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{-144}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-144}:\\ \;\;\;\;y \cdot 0.8862269254527579\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.28e-144) x (if (<= x 9e-144) (* y 0.8862269254527579) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.28e-144) {
		tmp = x;
	} else if (x <= 9e-144) {
		tmp = y * 0.8862269254527579;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.28d-144)) then
        tmp = x
    else if (x <= 9d-144) then
        tmp = y * 0.8862269254527579d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.28e-144) {
		tmp = x;
	} else if (x <= 9e-144) {
		tmp = y * 0.8862269254527579;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.28e-144:
		tmp = x
	elif x <= 9e-144:
		tmp = y * 0.8862269254527579
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.28e-144)
		tmp = x;
	elseif (x <= 9e-144)
		tmp = Float64(y * 0.8862269254527579);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.28e-144)
		tmp = x;
	elseif (x <= 9e-144)
		tmp = y * 0.8862269254527579;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.28e-144], x, If[LessEqual[x, 9e-144], N[(y * 0.8862269254527579), $MachinePrecision], x]]

Derivation

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

Alternative 13: 69.9% accurate, 15.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{y}{1.1283791670955126}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.8e-143) x (if (<= x 3.2e-144) (/ y 1.1283791670955126) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.8e-143) {
		tmp = x;
	} else if (x <= 3.2e-144) {
		tmp = y / 1.1283791670955126;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.8d-143)) then
        tmp = x
    else if (x <= 3.2d-144) then
        tmp = y / 1.1283791670955126d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.8e-143) {
		tmp = x;
	} else if (x <= 3.2e-144) {
		tmp = y / 1.1283791670955126;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.8e-143:
		tmp = x
	elif x <= 3.2e-144:
		tmp = y / 1.1283791670955126
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.8e-143)
		tmp = x;
	elseif (x <= 3.2e-144)
		tmp = Float64(y / 1.1283791670955126);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.8e-143)
		tmp = x;
	elseif (x <= 3.2e-144)
		tmp = y / 1.1283791670955126;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.8e-143], x, If[LessEqual[x, 3.2e-144], N[(y / 1.1283791670955126), $MachinePrecision], x]]

Derivation

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

Alternative 14: 69.6% accurate, 111.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

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

Developer target: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ 1.0 (- (* (/ 1.1283791670955126 y) (exp z)) x))))

C

double code(double x, double y, double z) {
	return x + (1.0 / (((1.1283791670955126 / y) * exp(z)) - x));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (1.0d0 / (((1.1283791670955126d0 / y) * exp(z)) - x))
end function

Java

public static double code(double x, double y, double z) {
	return x + (1.0 / (((1.1283791670955126 / y) * Math.exp(z)) - x));
}

Python

def code(x, y, z):
	return x + (1.0 / (((1.1283791670955126 / y) * math.exp(z)) - x))

Julia

function code(x, y, z)
	return Float64(x + Float64(1.0 / Float64(Float64(Float64(1.1283791670955126 / y) * exp(z)) - x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (1.0 / (((1.1283791670955126 / y) * exp(z)) - x));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(1.0 / N[(N[(N[(1.1283791670955126 / y), $MachinePrecision] * N[Exp[z], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023343 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ x (/ 1.0 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

  (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))