Data.Colour.Matrix:inverse from colour-2.3.3, B

Percentage Accurate: 91.5% → 96.5%

Time: 8.3s

Alternatives: 12

Speedup: 0.5×

• 28.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - z \cdot t}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- (* x y) (* z t)) a))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - (z * t)) / a
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Python

def code(x, y, z, t, a):
	return ((x * y) - (z * t)) / a

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (z * t)) / a;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]

Initial Program: 91.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - z \cdot t}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- (* x y) (* z t)) a))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - (z * t)) / a
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Python

def code(x, y, z, t, a):
	return ((x * y) - (z * t)) / a

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (z * t)) / a;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]

Alternative 1: 96.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ a_s \cdot \begin{array}{l} \mathbf{if}\;t_1 \leq -1 \cdot 10^{+270}:\\ \;\;\;\;\frac{x}{\sqrt{a_m}} \cdot \frac{y}{\sqrt{a_m}} - \frac{z}{\frac{a_m}{t}}\\ \mathbf{elif}\;t_1 \leq 10^{+304}:\\ \;\;\;\;\frac{t_1}{a_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{y}{t} - \frac{z}{x}}{\frac{a_m}{t}}\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (*
    a_s
    (if (<= t_1 -1e+270)
      (- (* (/ x (sqrt a_m)) (/ y (sqrt a_m))) (/ z (/ a_m t)))
      (if (<= t_1 1e+304)
        (/ t_1 a_m)
        (* x (/ (- (/ y t) (/ z x)) (/ a_m t))))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -1e+270) {
		tmp = ((x / sqrt(a_m)) * (y / sqrt(a_m))) - (z / (a_m / t));
	} else if (t_1 <= 1e+304) {
		tmp = t_1 / a_m;
	} else {
		tmp = x * (((y / t) - (z / x)) / (a_m / t));
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    if (t_1 <= (-1d+270)) then
        tmp = ((x / sqrt(a_m)) * (y / sqrt(a_m))) - (z / (a_m / t))
    else if (t_1 <= 1d+304) then
        tmp = t_1 / a_m
    else
        tmp = x * (((y / t) - (z / x)) / (a_m / t))
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -1e+270) {
		tmp = ((x / Math.sqrt(a_m)) * (y / Math.sqrt(a_m))) - (z / (a_m / t));
	} else if (t_1 <= 1e+304) {
		tmp = t_1 / a_m;
	} else {
		tmp = x * (((y / t) - (z / x)) / (a_m / t));
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -1e+270:
		tmp = ((x / math.sqrt(a_m)) * (y / math.sqrt(a_m))) - (z / (a_m / t))
	elif t_1 <= 1e+304:
		tmp = t_1 / a_m
	else:
		tmp = x * (((y / t) - (z / x)) / (a_m / t))
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= -1e+270)
		tmp = Float64(Float64(Float64(x / sqrt(a_m)) * Float64(y / sqrt(a_m))) - Float64(z / Float64(a_m / t)));
	elseif (t_1 <= 1e+304)
		tmp = Float64(t_1 / a_m);
	else
		tmp = Float64(x * Float64(Float64(Float64(y / t) - Float64(z / x)) / Float64(a_m / t)));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -1e+270)
		tmp = ((x / sqrt(a_m)) * (y / sqrt(a_m))) - (z / (a_m / t));
	elseif (t_1 <= 1e+304)
		tmp = t_1 / a_m;
	else
		tmp = x * (((y / t) - (z / x)) / (a_m / t));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t$95$1, -1e+270], N[(N[(N[(x / N[Sqrt[a$95$m], $MachinePrecision]), $MachinePrecision] * N[(y / N[Sqrt[a$95$m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a$95$m / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+304], N[(t$95$1 / a$95$m), $MachinePrecision], N[(x * N[(N[(N[(y / t), $MachinePrecision] - N[(z / x), $MachinePrecision]), $MachinePrecision] / N[(a$95$m / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

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

Alternative 2: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ a_s \cdot \begin{array}{l} \mathbf{if}\;t_1 \leq -2 \cdot 10^{+297}:\\ \;\;\;\;\frac{x}{\frac{a_m}{y}} - \frac{z}{\frac{a_m}{t}}\\ \mathbf{elif}\;t_1 \leq 10^{+304}:\\ \;\;\;\;\frac{t_1}{a_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{y}{t} - \frac{z}{x}}{\frac{a_m}{t}}\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (*
    a_s
    (if (<= t_1 -2e+297)
      (- (/ x (/ a_m y)) (/ z (/ a_m t)))
      (if (<= t_1 1e+304)
        (/ t_1 a_m)
        (* x (/ (- (/ y t) (/ z x)) (/ a_m t))))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -2e+297) {
		tmp = (x / (a_m / y)) - (z / (a_m / t));
	} else if (t_1 <= 1e+304) {
		tmp = t_1 / a_m;
	} else {
		tmp = x * (((y / t) - (z / x)) / (a_m / t));
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    if (t_1 <= (-2d+297)) then
        tmp = (x / (a_m / y)) - (z / (a_m / t))
    else if (t_1 <= 1d+304) then
        tmp = t_1 / a_m
    else
        tmp = x * (((y / t) - (z / x)) / (a_m / t))
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -2e+297) {
		tmp = (x / (a_m / y)) - (z / (a_m / t));
	} else if (t_1 <= 1e+304) {
		tmp = t_1 / a_m;
	} else {
		tmp = x * (((y / t) - (z / x)) / (a_m / t));
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -2e+297:
		tmp = (x / (a_m / y)) - (z / (a_m / t))
	elif t_1 <= 1e+304:
		tmp = t_1 / a_m
	else:
		tmp = x * (((y / t) - (z / x)) / (a_m / t))
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= -2e+297)
		tmp = Float64(Float64(x / Float64(a_m / y)) - Float64(z / Float64(a_m / t)));
	elseif (t_1 <= 1e+304)
		tmp = Float64(t_1 / a_m);
	else
		tmp = Float64(x * Float64(Float64(Float64(y / t) - Float64(z / x)) / Float64(a_m / t)));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -2e+297)
		tmp = (x / (a_m / y)) - (z / (a_m / t));
	elseif (t_1 <= 1e+304)
		tmp = t_1 / a_m;
	else
		tmp = x * (((y / t) - (z / x)) / (a_m / t));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t$95$1, -2e+297], N[(N[(x / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a$95$m / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+304], N[(t$95$1 / a$95$m), $MachinePrecision], N[(x * N[(N[(N[(y / t), $MachinePrecision] - N[(z / x), $MachinePrecision]), $MachinePrecision] / N[(a$95$m / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

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

Alternative 3: 96.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ a_s \cdot \begin{array}{l} \mathbf{if}\;t_1 \leq -2 \cdot 10^{+297} \lor \neg \left(t_1 \leq 5 \cdot 10^{+265}\right):\\ \;\;\;\;\frac{x}{\frac{a_m}{y}} - z \cdot \frac{t}{a_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a_m}\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (*
    a_s
    (if (or (<= t_1 -2e+297) (not (<= t_1 5e+265)))
      (- (/ x (/ a_m y)) (* z (/ t a_m)))
      (/ t_1 a_m)))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -2e+297) || !(t_1 <= 5e+265)) {
		tmp = (x / (a_m / y)) - (z * (t / a_m));
	} else {
		tmp = t_1 / a_m;
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    if ((t_1 <= (-2d+297)) .or. (.not. (t_1 <= 5d+265))) then
        tmp = (x / (a_m / y)) - (z * (t / a_m))
    else
        tmp = t_1 / a_m
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -2e+297) || !(t_1 <= 5e+265)) {
		tmp = (x / (a_m / y)) - (z * (t / a_m));
	} else {
		tmp = t_1 / a_m;
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -2e+297) or not (t_1 <= 5e+265):
		tmp = (x / (a_m / y)) - (z * (t / a_m))
	else:
		tmp = t_1 / a_m
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= -2e+297) || !(t_1 <= 5e+265))
		tmp = Float64(Float64(x / Float64(a_m / y)) - Float64(z * Float64(t / a_m)));
	else
		tmp = Float64(t_1 / a_m);
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -2e+297) || ~((t_1 <= 5e+265)))
		tmp = (x / (a_m / y)) - (z * (t / a_m));
	else
		tmp = t_1 / a_m;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[Or[LessEqual[t$95$1, -2e+297], N[Not[LessEqual[t$95$1, 5e+265]], $MachinePrecision]], N[(N[(x / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a$95$m), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 4: 96.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{a_m}{y}}\\ t_2 := x \cdot y - z \cdot t\\ a_s \cdot \begin{array}{l} \mathbf{if}\;t_2 \leq -2 \cdot 10^{+297}:\\ \;\;\;\;t_1 - \frac{z}{\frac{a_m}{t}}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+265}:\\ \;\;\;\;\frac{t_2}{a_m}\\ \mathbf{else}:\\ \;\;\;\;t_1 - z \cdot \frac{t}{a_m}\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (/ x (/ a_m y))) (t_2 (- (* x y) (* z t))))
   (*
    a_s
    (if (<= t_2 -2e+297)
      (- t_1 (/ z (/ a_m t)))
      (if (<= t_2 5e+265) (/ t_2 a_m) (- t_1 (* z (/ t a_m))))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = x / (a_m / y);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -2e+297) {
		tmp = t_1 - (z / (a_m / t));
	} else if (t_2 <= 5e+265) {
		tmp = t_2 / a_m;
	} else {
		tmp = t_1 - (z * (t / a_m));
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (a_m / y)
    t_2 = (x * y) - (z * t)
    if (t_2 <= (-2d+297)) then
        tmp = t_1 - (z / (a_m / t))
    else if (t_2 <= 5d+265) then
        tmp = t_2 / a_m
    else
        tmp = t_1 - (z * (t / a_m))
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = x / (a_m / y);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -2e+297) {
		tmp = t_1 - (z / (a_m / t));
	} else if (t_2 <= 5e+265) {
		tmp = t_2 / a_m;
	} else {
		tmp = t_1 - (z * (t / a_m));
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = x / (a_m / y)
	t_2 = (x * y) - (z * t)
	tmp = 0
	if t_2 <= -2e+297:
		tmp = t_1 - (z / (a_m / t))
	elif t_2 <= 5e+265:
		tmp = t_2 / a_m
	else:
		tmp = t_1 - (z * (t / a_m))
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(x / Float64(a_m / y))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_2 <= -2e+297)
		tmp = Float64(t_1 - Float64(z / Float64(a_m / t)));
	elseif (t_2 <= 5e+265)
		tmp = Float64(t_2 / a_m);
	else
		tmp = Float64(t_1 - Float64(z * Float64(t / a_m)));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = x / (a_m / y);
	t_2 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_2 <= -2e+297)
		tmp = t_1 - (z / (a_m / t));
	elseif (t_2 <= 5e+265)
		tmp = t_2 / a_m;
	else
		tmp = t_1 - (z * (t / a_m));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(x / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t$95$2, -2e+297], N[(t$95$1 - N[(z / N[(a$95$m / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+265], N[(t$95$2 / a$95$m), $MachinePrecision], N[(t$95$1 - N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]]

Derivation

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

Alternative 5: 72.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \frac{-t}{\frac{a_m}{z}}\\ t_2 := y \cdot \frac{x}{a_m}\\ a_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-93}:\\ \;\;\;\;\frac{x \cdot y}{a_m}\\ \mathbf{elif}\;x \cdot y \leq 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ a_m z))) (t_2 (* y (/ x a_m))))
   (*
    a_s
    (if (<= (* x y) -2e+136)
      t_2
      (if (<= (* x y) -5e+87)
        t_1
        (if (<= (* x y) -5e-93)
          (/ (* x y) a_m)
          (if (<= (* x y) 1e+14) t_1 t_2)))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = -t / (a_m / z);
	double t_2 = y * (x / a_m);
	double tmp;
	if ((x * y) <= -2e+136) {
		tmp = t_2;
	} else if ((x * y) <= -5e+87) {
		tmp = t_1;
	} else if ((x * y) <= -5e-93) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 1e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -t / (a_m / z)
    t_2 = y * (x / a_m)
    if ((x * y) <= (-2d+136)) then
        tmp = t_2
    else if ((x * y) <= (-5d+87)) then
        tmp = t_1
    else if ((x * y) <= (-5d-93)) then
        tmp = (x * y) / a_m
    else if ((x * y) <= 1d+14) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = -t / (a_m / z);
	double t_2 = y * (x / a_m);
	double tmp;
	if ((x * y) <= -2e+136) {
		tmp = t_2;
	} else if ((x * y) <= -5e+87) {
		tmp = t_1;
	} else if ((x * y) <= -5e-93) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 1e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = -t / (a_m / z)
	t_2 = y * (x / a_m)
	tmp = 0
	if (x * y) <= -2e+136:
		tmp = t_2
	elif (x * y) <= -5e+87:
		tmp = t_1
	elif (x * y) <= -5e-93:
		tmp = (x * y) / a_m
	elif (x * y) <= 1e+14:
		tmp = t_1
	else:
		tmp = t_2
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(-t) / Float64(a_m / z))
	t_2 = Float64(y * Float64(x / a_m))
	tmp = 0.0
	if (Float64(x * y) <= -2e+136)
		tmp = t_2;
	elseif (Float64(x * y) <= -5e+87)
		tmp = t_1;
	elseif (Float64(x * y) <= -5e-93)
		tmp = Float64(Float64(x * y) / a_m);
	elseif (Float64(x * y) <= 1e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = -t / (a_m / z);
	t_2 = y * (x / a_m);
	tmp = 0.0;
	if ((x * y) <= -2e+136)
		tmp = t_2;
	elseif ((x * y) <= -5e+87)
		tmp = t_1;
	elseif ((x * y) <= -5e-93)
		tmp = (x * y) / a_m;
	elseif ((x * y) <= 1e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[((-t) / N[(a$95$m / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -2e+136], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -5e+87], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5e-93], N[(N[(x * y), $MachinePrecision] / a$95$m), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+14], t$95$1, t$95$2]]]]), $MachinePrecision]]]

Derivation

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

Alternative 6: 72.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := y \cdot \frac{x}{a_m}\\ a_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+87}:\\ \;\;\;\;\frac{-t}{\frac{a_m}{z}}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-93}:\\ \;\;\;\;\frac{x \cdot y}{a_m}\\ \mathbf{elif}\;x \cdot y \leq 10^{+14}:\\ \;\;\;\;t \cdot \frac{-z}{a_m}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* y (/ x a_m))))
   (*
    a_s
    (if (<= (* x y) -2e+136)
      t_1
      (if (<= (* x y) -5e+87)
        (/ (- t) (/ a_m z))
        (if (<= (* x y) -5e-93)
          (/ (* x y) a_m)
          (if (<= (* x y) 1e+14) (* t (/ (- z) a_m)) t_1)))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = y * (x / a_m);
	double tmp;
	if ((x * y) <= -2e+136) {
		tmp = t_1;
	} else if ((x * y) <= -5e+87) {
		tmp = -t / (a_m / z);
	} else if ((x * y) <= -5e-93) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 1e+14) {
		tmp = t * (-z / a_m);
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x / a_m)
    if ((x * y) <= (-2d+136)) then
        tmp = t_1
    else if ((x * y) <= (-5d+87)) then
        tmp = -t / (a_m / z)
    else if ((x * y) <= (-5d-93)) then
        tmp = (x * y) / a_m
    else if ((x * y) <= 1d+14) then
        tmp = t * (-z / a_m)
    else
        tmp = t_1
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = y * (x / a_m);
	double tmp;
	if ((x * y) <= -2e+136) {
		tmp = t_1;
	} else if ((x * y) <= -5e+87) {
		tmp = -t / (a_m / z);
	} else if ((x * y) <= -5e-93) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 1e+14) {
		tmp = t * (-z / a_m);
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = y * (x / a_m)
	tmp = 0
	if (x * y) <= -2e+136:
		tmp = t_1
	elif (x * y) <= -5e+87:
		tmp = -t / (a_m / z)
	elif (x * y) <= -5e-93:
		tmp = (x * y) / a_m
	elif (x * y) <= 1e+14:
		tmp = t * (-z / a_m)
	else:
		tmp = t_1
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(y * Float64(x / a_m))
	tmp = 0.0
	if (Float64(x * y) <= -2e+136)
		tmp = t_1;
	elseif (Float64(x * y) <= -5e+87)
		tmp = Float64(Float64(-t) / Float64(a_m / z));
	elseif (Float64(x * y) <= -5e-93)
		tmp = Float64(Float64(x * y) / a_m);
	elseif (Float64(x * y) <= 1e+14)
		tmp = Float64(t * Float64(Float64(-z) / a_m));
	else
		tmp = t_1;
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = y * (x / a_m);
	tmp = 0.0;
	if ((x * y) <= -2e+136)
		tmp = t_1;
	elseif ((x * y) <= -5e+87)
		tmp = -t / (a_m / z);
	elseif ((x * y) <= -5e-93)
		tmp = (x * y) / a_m;
	elseif ((x * y) <= 1e+14)
		tmp = t * (-z / a_m);
	else
		tmp = t_1;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -2e+136], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5e+87], N[((-t) / N[(a$95$m / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e-93], N[(N[(x * y), $MachinePrecision] / a$95$m), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+14], N[(t * N[((-z) / a$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

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

Alternative 7: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := y \cdot \frac{x}{a_m}\\ a_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+87}:\\ \;\;\;\;\frac{-t}{\frac{a_m}{z}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-22}:\\ \;\;\;\;\frac{x \cdot y}{a_m}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a_m}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* y (/ x a_m))))
   (*
    a_s
    (if (<= (* x y) -2e+136)
      t_1
      (if (<= (* x y) -5e+87)
        (/ (- t) (/ a_m z))
        (if (<= (* x y) -2e-22)
          (/ (* x y) a_m)
          (if (<= (* x y) 2e-5) (/ (* z (- t)) a_m) t_1)))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = y * (x / a_m);
	double tmp;
	if ((x * y) <= -2e+136) {
		tmp = t_1;
	} else if ((x * y) <= -5e+87) {
		tmp = -t / (a_m / z);
	} else if ((x * y) <= -2e-22) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 2e-5) {
		tmp = (z * -t) / a_m;
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x / a_m)
    if ((x * y) <= (-2d+136)) then
        tmp = t_1
    else if ((x * y) <= (-5d+87)) then
        tmp = -t / (a_m / z)
    else if ((x * y) <= (-2d-22)) then
        tmp = (x * y) / a_m
    else if ((x * y) <= 2d-5) then
        tmp = (z * -t) / a_m
    else
        tmp = t_1
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = y * (x / a_m);
	double tmp;
	if ((x * y) <= -2e+136) {
		tmp = t_1;
	} else if ((x * y) <= -5e+87) {
		tmp = -t / (a_m / z);
	} else if ((x * y) <= -2e-22) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 2e-5) {
		tmp = (z * -t) / a_m;
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = y * (x / a_m)
	tmp = 0
	if (x * y) <= -2e+136:
		tmp = t_1
	elif (x * y) <= -5e+87:
		tmp = -t / (a_m / z)
	elif (x * y) <= -2e-22:
		tmp = (x * y) / a_m
	elif (x * y) <= 2e-5:
		tmp = (z * -t) / a_m
	else:
		tmp = t_1
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(y * Float64(x / a_m))
	tmp = 0.0
	if (Float64(x * y) <= -2e+136)
		tmp = t_1;
	elseif (Float64(x * y) <= -5e+87)
		tmp = Float64(Float64(-t) / Float64(a_m / z));
	elseif (Float64(x * y) <= -2e-22)
		tmp = Float64(Float64(x * y) / a_m);
	elseif (Float64(x * y) <= 2e-5)
		tmp = Float64(Float64(z * Float64(-t)) / a_m);
	else
		tmp = t_1;
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = y * (x / a_m);
	tmp = 0.0;
	if ((x * y) <= -2e+136)
		tmp = t_1;
	elseif ((x * y) <= -5e+87)
		tmp = -t / (a_m / z);
	elseif ((x * y) <= -2e-22)
		tmp = (x * y) / a_m;
	elseif ((x * y) <= 2e-5)
		tmp = (z * -t) / a_m;
	else
		tmp = t_1;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -2e+136], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5e+87], N[((-t) / N[(a$95$m / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-22], N[(N[(x * y), $MachinePrecision] / a$95$m), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-5], N[(N[(z * (-t)), $MachinePrecision] / a$95$m), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

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

Alternative 8: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+136}:\\ \;\;\;\;\frac{\frac{x}{a_m}}{\frac{1}{y}}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+87}:\\ \;\;\;\;\frac{-t}{\frac{a_m}{z}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-22}:\\ \;\;\;\;\frac{x \cdot y}{a_m}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a_m}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a_m}\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* x y) -2e+136)
    (/ (/ x a_m) (/ 1.0 y))
    (if (<= (* x y) -5e+87)
      (/ (- t) (/ a_m z))
      (if (<= (* x y) -2e-22)
        (/ (* x y) a_m)
        (if (<= (* x y) 2e-5) (/ (* z (- t)) a_m) (* y (/ x a_m))))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -2e+136) {
		tmp = (x / a_m) / (1.0 / y);
	} else if ((x * y) <= -5e+87) {
		tmp = -t / (a_m / z);
	} else if ((x * y) <= -2e-22) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 2e-5) {
		tmp = (z * -t) / a_m;
	} else {
		tmp = y * (x / a_m);
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: tmp
    if ((x * y) <= (-2d+136)) then
        tmp = (x / a_m) / (1.0d0 / y)
    else if ((x * y) <= (-5d+87)) then
        tmp = -t / (a_m / z)
    else if ((x * y) <= (-2d-22)) then
        tmp = (x * y) / a_m
    else if ((x * y) <= 2d-5) then
        tmp = (z * -t) / a_m
    else
        tmp = y * (x / a_m)
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -2e+136) {
		tmp = (x / a_m) / (1.0 / y);
	} else if ((x * y) <= -5e+87) {
		tmp = -t / (a_m / z);
	} else if ((x * y) <= -2e-22) {
		tmp = (x * y) / a_m;
	} else if ((x * y) <= 2e-5) {
		tmp = (z * -t) / a_m;
	} else {
		tmp = y * (x / a_m);
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (x * y) <= -2e+136:
		tmp = (x / a_m) / (1.0 / y)
	elif (x * y) <= -5e+87:
		tmp = -t / (a_m / z)
	elif (x * y) <= -2e-22:
		tmp = (x * y) / a_m
	elif (x * y) <= 2e-5:
		tmp = (z * -t) / a_m
	else:
		tmp = y * (x / a_m)
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(x * y) <= -2e+136)
		tmp = Float64(Float64(x / a_m) / Float64(1.0 / y));
	elseif (Float64(x * y) <= -5e+87)
		tmp = Float64(Float64(-t) / Float64(a_m / z));
	elseif (Float64(x * y) <= -2e-22)
		tmp = Float64(Float64(x * y) / a_m);
	elseif (Float64(x * y) <= 2e-5)
		tmp = Float64(Float64(z * Float64(-t)) / a_m);
	else
		tmp = Float64(y * Float64(x / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((x * y) <= -2e+136)
		tmp = (x / a_m) / (1.0 / y);
	elseif ((x * y) <= -5e+87)
		tmp = -t / (a_m / z);
	elseif ((x * y) <= -2e-22)
		tmp = (x * y) / a_m;
	elseif ((x * y) <= 2e-5)
		tmp = (z * -t) / a_m;
	else
		tmp = y * (x / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -2e+136], N[(N[(x / a$95$m), $MachinePrecision] / N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e+87], N[((-t) / N[(a$95$m / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-22], N[(N[(x * y), $MachinePrecision] / a$95$m), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-5], N[(N[(z * (-t)), $MachinePrecision] / a$95$m), $MachinePrecision], N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

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

Alternative 9: 94.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+297}:\\ \;\;\;\;\frac{x}{\frac{a_m}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+230}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a_m}\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* x y) -2e+297)
    (/ x (/ a_m y))
    (if (<= (* x y) 5e+230) (/ (- (* x y) (* z t)) a_m) (* x (/ y a_m))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -2e+297) {
		tmp = x / (a_m / y);
	} else if ((x * y) <= 5e+230) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = x * (y / a_m);
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: tmp
    if ((x * y) <= (-2d+297)) then
        tmp = x / (a_m / y)
    else if ((x * y) <= 5d+230) then
        tmp = ((x * y) - (z * t)) / a_m
    else
        tmp = x * (y / a_m)
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= -2e+297) {
		tmp = x / (a_m / y);
	} else if ((x * y) <= 5e+230) {
		tmp = ((x * y) - (z * t)) / a_m;
	} else {
		tmp = x * (y / a_m);
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (x * y) <= -2e+297:
		tmp = x / (a_m / y)
	elif (x * y) <= 5e+230:
		tmp = ((x * y) - (z * t)) / a_m
	else:
		tmp = x * (y / a_m)
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(x * y) <= -2e+297)
		tmp = Float64(x / Float64(a_m / y));
	elseif (Float64(x * y) <= 5e+230)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a_m);
	else
		tmp = Float64(x * Float64(y / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((x * y) <= -2e+297)
		tmp = x / (a_m / y);
	elseif ((x * y) <= 5e+230)
		tmp = ((x * y) - (z * t)) / a_m;
	else
		tmp = x * (y / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -2e+297], N[(x / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+230], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a$95$m), $MachinePrecision], N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 10: 51.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \begin{array}{l} \mathbf{if}\;t \leq 1.1 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \frac{y}{a_m}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a_m}\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (* a_s (if (<= t 1.1e-248) (* x (/ y a_m)) (* y (/ x a_m)))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= 1.1e-248) {
		tmp = x * (y / a_m);
	} else {
		tmp = y * (x / a_m);
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: tmp
    if (t <= 1.1d-248) then
        tmp = x * (y / a_m)
    else
        tmp = y * (x / a_m)
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= 1.1e-248) {
		tmp = x * (y / a_m);
	} else {
		tmp = y * (x / a_m);
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if t <= 1.1e-248:
		tmp = x * (y / a_m)
	else:
		tmp = y * (x / a_m)
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (t <= 1.1e-248)
		tmp = Float64(x * Float64(y / a_m));
	else
		tmp = Float64(y * Float64(x / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (t <= 1.1e-248)
		tmp = x * (y / a_m);
	else
		tmp = y * (x / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[t, 1.1e-248], N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 11: 51.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \begin{array}{l} \mathbf{if}\;t \leq 1.06 \cdot 10^{-209}:\\ \;\;\;\;\frac{x}{\frac{a_m}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a_m}\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (* a_s (if (<= t 1.06e-209) (/ x (/ a_m y)) (* y (/ x a_m)))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= 1.06e-209) {
		tmp = x / (a_m / y);
	} else {
		tmp = y * (x / a_m);
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: tmp
    if (t <= 1.06d-209) then
        tmp = x / (a_m / y)
    else
        tmp = y * (x / a_m)
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (t <= 1.06e-209) {
		tmp = x / (a_m / y);
	} else {
		tmp = y * (x / a_m);
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if t <= 1.06e-209:
		tmp = x / (a_m / y)
	else:
		tmp = y * (x / a_m)
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (t <= 1.06e-209)
		tmp = Float64(x / Float64(a_m / y));
	else
		tmp = Float64(y * Float64(x / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (t <= 1.06e-209)
		tmp = x / (a_m / y);
	else
		tmp = y * (x / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[t, 1.06e-209], N[(x / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 12: 51.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \left(x \cdot \frac{y}{a_m}\right) \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m) :precision binary64 (* a_s (* x (/ y a_m))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (x * (y / a_m));
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    code = a_s * (x * (y / a_m))
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (x * (y / a_m));
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	return a_s * (x * (y / a_m))

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	return Float64(a_s * Float64(x * Float64(y / a_m)))
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp = code(a_s, x, y, z, t, a_m)
	tmp = a_s * (x * (y / a_m));
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Developer target: 91.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* (/ y a) x) (* (/ t a) z))))
   (if (< z -2.468684968699548e+170)
     t_1
     (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y / a) * x) - ((t / a) * z)
    if (z < (-2.468684968699548d+170)) then
        tmp = t_1
    else if (z < 6.309831121978371d-71) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y / a) * x) - ((t / a) * z)
	tmp = 0
	if z < -2.468684968699548e+170:
		tmp = t_1
	elif z < 6.309831121978371e-71:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y / a) * x) - Float64(Float64(t / a) * z))
	tmp = 0.0
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y / a) * x) - ((t / a) * z);
	tmp = 0.0;
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -2.468684968699548e+170], t$95$1, If[Less[z, 6.309831121978371e-71], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023347 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (if (< z -2.468684968699548e+170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

  (/ (- (* x y) (* z t)) a))