Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, I

Percentage Accurate: 91.4% → 92.6%

Time: 9.7s

Alternatives: 12

Speedup: 0.7×

• 28.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

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 * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 91.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

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 * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 92.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+213}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, z \cdot \frac{t}{a}, \frac{x \cdot \left(y \cdot 0.5\right)}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* (* z 9.0) t) 2e+213)
   (/ (fma x y (* z (* t -9.0))) (* a 2.0))
   (fma -4.5 (* z (/ t a)) (/ (* x (* y 0.5)) a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * 9.0) * t) <= 2e+213) {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = fma(-4.5, (z * (t / a)), ((x * (y * 0.5)) / a));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(z * 9.0) * t) <= 2e+213)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = fma(-4.5, Float64(z * Float64(t / a)), Float64(Float64(x * Float64(y * 0.5)) / a));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision], 2e+213], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 92.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+213}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* (* z 9.0) t) 2e+213)
   (/ (fma x y (* z (* t -9.0))) (* a 2.0))
   (* z (* t (/ -4.5 a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * 9.0) * t) <= 2e+213) {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = z * (t * (-4.5 / a));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(z * 9.0) * t) <= 2e+213)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision], 2e+213], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 3: 92.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+213}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* (* z 9.0) t) 2e+213)
   (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
   (* z (* t (/ -4.5 a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * 9.0) * t) <= 2e+213) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = z * (t * (-4.5 / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) :: tmp
    if (((z * 9.0d0) * t) <= 2d+213) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = z * (t * ((-4.5d0) / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * 9.0) * t) <= 2e+213) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = z * (t * (-4.5 / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((z * 9.0) * t) <= 2e+213:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = z * (t * (-4.5 / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(z * 9.0) * t) <= 2e+213)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z * 9.0) * t) <= 2e+213)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = z * (t * (-4.5 / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision], 2e+213], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 4: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+44}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+33} \lor \neg \left(x \leq 7.8 \cdot 10^{-74}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (* x (/ y a)))))
   (if (<= x -1.8e+72)
     t_1
     (if (<= x -7.5e+44)
       (* -4.5 (* t (/ z a)))
       (if (or (<= x -3.8e+33) (not (<= x 7.8e-74)))
         t_1
         (* -4.5 (/ (* z t) a)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x * (y / a));
	double tmp;
	if (x <= -1.8e+72) {
		tmp = t_1;
	} else if (x <= -7.5e+44) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x <= -3.8e+33) || !(x <= 7.8e-74)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = 0.5d0 * (x * (y / a))
    if (x <= (-1.8d+72)) then
        tmp = t_1
    else if (x <= (-7.5d+44)) then
        tmp = (-4.5d0) * (t * (z / a))
    else if ((x <= (-3.8d+33)) .or. (.not. (x <= 7.8d-74))) then
        tmp = t_1
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x * (y / a));
	double tmp;
	if (x <= -1.8e+72) {
		tmp = t_1;
	} else if (x <= -7.5e+44) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x <= -3.8e+33) || !(x <= 7.8e-74)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = 0.5 * (x * (y / a))
	tmp = 0
	if x <= -1.8e+72:
		tmp = t_1
	elif x <= -7.5e+44:
		tmp = -4.5 * (t * (z / a))
	elif (x <= -3.8e+33) or not (x <= 7.8e-74):
		tmp = t_1
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(x * Float64(y / a)))
	tmp = 0.0
	if (x <= -1.8e+72)
		tmp = t_1;
	elseif (x <= -7.5e+44)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif ((x <= -3.8e+33) || !(x <= 7.8e-74))
		tmp = t_1;
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (x * (y / a));
	tmp = 0.0;
	if (x <= -1.8e+72)
		tmp = t_1;
	elseif (x <= -7.5e+44)
		tmp = -4.5 * (t * (z / a));
	elseif ((x <= -3.8e+33) || ~((x <= 7.8e-74)))
		tmp = t_1;
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.8e+72], t$95$1, If[LessEqual[x, -7.5e+44], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -3.8e+33], N[Not[LessEqual[x, 7.8e-74]], $MachinePrecision]], t$95$1, N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 5: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{-67}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-85}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-73}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (* x (/ y a)))))
   (if (<= x -1.2e+76)
     t_1
     (if (<= x -2.75e-67)
       (* -4.5 (* z (/ t a)))
       (if (<= x -1.9e-85)
         (* 0.5 (/ x (/ a y)))
         (if (<= x 1.85e-73) (* -4.5 (/ (* z t) a)) t_1))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x * (y / a));
	double tmp;
	if (x <= -1.2e+76) {
		tmp = t_1;
	} else if (x <= -2.75e-67) {
		tmp = -4.5 * (z * (t / a));
	} else if (x <= -1.9e-85) {
		tmp = 0.5 * (x / (a / y));
	} else if (x <= 1.85e-73) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = 0.5d0 * (x * (y / a))
    if (x <= (-1.2d+76)) then
        tmp = t_1
    else if (x <= (-2.75d-67)) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (x <= (-1.9d-85)) then
        tmp = 0.5d0 * (x / (a / y))
    else if (x <= 1.85d-73) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x * (y / a));
	double tmp;
	if (x <= -1.2e+76) {
		tmp = t_1;
	} else if (x <= -2.75e-67) {
		tmp = -4.5 * (z * (t / a));
	} else if (x <= -1.9e-85) {
		tmp = 0.5 * (x / (a / y));
	} else if (x <= 1.85e-73) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = 0.5 * (x * (y / a))
	tmp = 0
	if x <= -1.2e+76:
		tmp = t_1
	elif x <= -2.75e-67:
		tmp = -4.5 * (z * (t / a))
	elif x <= -1.9e-85:
		tmp = 0.5 * (x / (a / y))
	elif x <= 1.85e-73:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(x * Float64(y / a)))
	tmp = 0.0
	if (x <= -1.2e+76)
		tmp = t_1;
	elseif (x <= -2.75e-67)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (x <= -1.9e-85)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (x <= 1.85e-73)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (x * (y / a));
	tmp = 0.0;
	if (x <= -1.2e+76)
		tmp = t_1;
	elseif (x <= -2.75e-67)
		tmp = -4.5 * (z * (t / a));
	elseif (x <= -1.9e-85)
		tmp = 0.5 * (x / (a / y));
	elseif (x <= 1.85e-73)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+76], t$95$1, If[LessEqual[x, -2.75e-67], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.9e-85], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e-73], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

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

Alternative 6: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-85}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-74}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (* x (/ y a)))))
   (if (<= x -8.5e+74)
     t_1
     (if (<= x -1.55e-67)
       (* z (* t (/ -4.5 a)))
       (if (<= x -1.4e-85)
         (* 0.5 (/ x (/ a y)))
         (if (<= x 7.5e-74) (* -4.5 (/ (* z t) a)) t_1))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x * (y / a));
	double tmp;
	if (x <= -8.5e+74) {
		tmp = t_1;
	} else if (x <= -1.55e-67) {
		tmp = z * (t * (-4.5 / a));
	} else if (x <= -1.4e-85) {
		tmp = 0.5 * (x / (a / y));
	} else if (x <= 7.5e-74) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = 0.5d0 * (x * (y / a))
    if (x <= (-8.5d+74)) then
        tmp = t_1
    else if (x <= (-1.55d-67)) then
        tmp = z * (t * ((-4.5d0) / a))
    else if (x <= (-1.4d-85)) then
        tmp = 0.5d0 * (x / (a / y))
    else if (x <= 7.5d-74) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x * (y / a));
	double tmp;
	if (x <= -8.5e+74) {
		tmp = t_1;
	} else if (x <= -1.55e-67) {
		tmp = z * (t * (-4.5 / a));
	} else if (x <= -1.4e-85) {
		tmp = 0.5 * (x / (a / y));
	} else if (x <= 7.5e-74) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = 0.5 * (x * (y / a))
	tmp = 0
	if x <= -8.5e+74:
		tmp = t_1
	elif x <= -1.55e-67:
		tmp = z * (t * (-4.5 / a))
	elif x <= -1.4e-85:
		tmp = 0.5 * (x / (a / y))
	elif x <= 7.5e-74:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(x * Float64(y / a)))
	tmp = 0.0
	if (x <= -8.5e+74)
		tmp = t_1;
	elseif (x <= -1.55e-67)
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	elseif (x <= -1.4e-85)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (x <= 7.5e-74)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (x * (y / a));
	tmp = 0.0;
	if (x <= -8.5e+74)
		tmp = t_1;
	elseif (x <= -1.55e-67)
		tmp = z * (t * (-4.5 / a));
	elseif (x <= -1.4e-85)
		tmp = 0.5 * (x / (a / y));
	elseif (x <= 7.5e-74)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e+74], t$95$1, If[LessEqual[x, -1.55e-67], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.4e-85], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-74], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

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

Alternative 7: 65.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-85}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-80}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.9e+73)
   (* x (* y (/ 0.5 a)))
   (if (<= x -1.8e-67)
     (* z (* t (/ -4.5 a)))
     (if (<= x -2.1e-85)
       (* 0.5 (/ x (/ a y)))
       (if (<= x 9.8e-80) (* -4.5 (/ (* z t) a)) (* 0.5 (* x (/ y a))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.9e+73) {
		tmp = x * (y * (0.5 / a));
	} else if (x <= -1.8e-67) {
		tmp = z * (t * (-4.5 / a));
	} else if (x <= -2.1e-85) {
		tmp = 0.5 * (x / (a / y));
	} else if (x <= 9.8e-80) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) :: tmp
    if (x <= (-2.9d+73)) then
        tmp = x * (y * (0.5d0 / a))
    else if (x <= (-1.8d-67)) then
        tmp = z * (t * ((-4.5d0) / a))
    else if (x <= (-2.1d-85)) then
        tmp = 0.5d0 * (x / (a / y))
    else if (x <= 9.8d-80) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = 0.5d0 * (x * (y / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.9e+73) {
		tmp = x * (y * (0.5 / a));
	} else if (x <= -1.8e-67) {
		tmp = z * (t * (-4.5 / a));
	} else if (x <= -2.1e-85) {
		tmp = 0.5 * (x / (a / y));
	} else if (x <= 9.8e-80) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.9e+73:
		tmp = x * (y * (0.5 / a))
	elif x <= -1.8e-67:
		tmp = z * (t * (-4.5 / a))
	elif x <= -2.1e-85:
		tmp = 0.5 * (x / (a / y))
	elif x <= 9.8e-80:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = 0.5 * (x * (y / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.9e+73)
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	elseif (x <= -1.8e-67)
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	elseif (x <= -2.1e-85)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (x <= 9.8e-80)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.9e+73)
		tmp = x * (y * (0.5 / a));
	elseif (x <= -1.8e-67)
		tmp = z * (t * (-4.5 / a));
	elseif (x <= -2.1e-85)
		tmp = 0.5 * (x / (a / y));
	elseif (x <= 9.8e-80)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = 0.5 * (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.9e+73], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.8e-67], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e-85], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e-80], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 8: 66.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{if}\;x \leq -2.25 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-81}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (* x 0.5) a))))
   (if (<= x -2.25e+72)
     t_1
     (if (<= x -1.95e-66)
       (* z (* t (/ -4.5 a)))
       (if (<= x -1.3e-85)
         t_1
         (if (<= x 2.65e-81) (* -4.5 (/ (* z t) a)) (* 0.5 (* x (/ y a)))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x * 0.5) / a);
	double tmp;
	if (x <= -2.25e+72) {
		tmp = t_1;
	} else if (x <= -1.95e-66) {
		tmp = z * (t * (-4.5 / a));
	} else if (x <= -1.3e-85) {
		tmp = t_1;
	} else if (x <= 2.65e-81) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 * ((x * 0.5d0) / a)
    if (x <= (-2.25d+72)) then
        tmp = t_1
    else if (x <= (-1.95d-66)) then
        tmp = z * (t * ((-4.5d0) / a))
    else if (x <= (-1.3d-85)) then
        tmp = t_1
    else if (x <= 2.65d-81) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = 0.5d0 * (x * (y / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x * 0.5) / a);
	double tmp;
	if (x <= -2.25e+72) {
		tmp = t_1;
	} else if (x <= -1.95e-66) {
		tmp = z * (t * (-4.5 / a));
	} else if (x <= -1.3e-85) {
		tmp = t_1;
	} else if (x <= 2.65e-81) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = y * ((x * 0.5) / a)
	tmp = 0
	if x <= -2.25e+72:
		tmp = t_1
	elif x <= -1.95e-66:
		tmp = z * (t * (-4.5 / a))
	elif x <= -1.3e-85:
		tmp = t_1
	elif x <= 2.65e-81:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = 0.5 * (x * (y / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(x * 0.5) / a))
	tmp = 0.0
	if (x <= -2.25e+72)
		tmp = t_1;
	elseif (x <= -1.95e-66)
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	elseif (x <= -1.3e-85)
		tmp = t_1;
	elseif (x <= 2.65e-81)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((x * 0.5) / a);
	tmp = 0.0;
	if (x <= -2.25e+72)
		tmp = t_1;
	elseif (x <= -1.95e-66)
		tmp = z * (t * (-4.5 / a));
	elseif (x <= -1.3e-85)
		tmp = t_1;
	elseif (x <= 2.65e-81)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = 0.5 * (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(x * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.25e+72], t$95$1, If[LessEqual[x, -1.95e-66], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.3e-85], t$95$1, If[LessEqual[x, 2.65e-81], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 9: 66.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-76}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (* x 0.5) a))))
   (if (<= x -1.9e+72)
     t_1
     (if (<= x -4.3e-66)
       (* z (* t (/ -4.5 a)))
       (if (<= x -2.05e-85)
         t_1
         (if (<= x 1.5e-76) (/ (* t (* z -4.5)) a) (* 0.5 (* x (/ y a)))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x * 0.5) / a);
	double tmp;
	if (x <= -1.9e+72) {
		tmp = t_1;
	} else if (x <= -4.3e-66) {
		tmp = z * (t * (-4.5 / a));
	} else if (x <= -2.05e-85) {
		tmp = t_1;
	} else if (x <= 1.5e-76) {
		tmp = (t * (z * -4.5)) / a;
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 * ((x * 0.5d0) / a)
    if (x <= (-1.9d+72)) then
        tmp = t_1
    else if (x <= (-4.3d-66)) then
        tmp = z * (t * ((-4.5d0) / a))
    else if (x <= (-2.05d-85)) then
        tmp = t_1
    else if (x <= 1.5d-76) then
        tmp = (t * (z * (-4.5d0))) / a
    else
        tmp = 0.5d0 * (x * (y / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x * 0.5) / a);
	double tmp;
	if (x <= -1.9e+72) {
		tmp = t_1;
	} else if (x <= -4.3e-66) {
		tmp = z * (t * (-4.5 / a));
	} else if (x <= -2.05e-85) {
		tmp = t_1;
	} else if (x <= 1.5e-76) {
		tmp = (t * (z * -4.5)) / a;
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = y * ((x * 0.5) / a)
	tmp = 0
	if x <= -1.9e+72:
		tmp = t_1
	elif x <= -4.3e-66:
		tmp = z * (t * (-4.5 / a))
	elif x <= -2.05e-85:
		tmp = t_1
	elif x <= 1.5e-76:
		tmp = (t * (z * -4.5)) / a
	else:
		tmp = 0.5 * (x * (y / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(x * 0.5) / a))
	tmp = 0.0
	if (x <= -1.9e+72)
		tmp = t_1;
	elseif (x <= -4.3e-66)
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	elseif (x <= -2.05e-85)
		tmp = t_1;
	elseif (x <= 1.5e-76)
		tmp = Float64(Float64(t * Float64(z * -4.5)) / a);
	else
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((x * 0.5) / a);
	tmp = 0.0;
	if (x <= -1.9e+72)
		tmp = t_1;
	elseif (x <= -4.3e-66)
		tmp = z * (t * (-4.5 / a));
	elseif (x <= -2.05e-85)
		tmp = t_1;
	elseif (x <= 1.5e-76)
		tmp = (t * (z * -4.5)) / a;
	else
		tmp = 0.5 * (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(x * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9e+72], t$95$1, If[LessEqual[x, -4.3e-66], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.05e-85], t$95$1, If[LessEqual[x, 1.5e-76], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 10: 66.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-86}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-82}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.36e+75)
   (* y (/ (* x 0.5) a))
   (if (<= x -3.5e-66)
     (* z (* t (/ -4.5 a)))
     (if (<= x -4.4e-86)
       (/ (* x (* y 0.5)) a)
       (if (<= x 8.2e-82) (/ (* t (* z -4.5)) a) (* 0.5 (* x (/ y a))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.36e+75) {
		tmp = y * ((x * 0.5) / a);
	} else if (x <= -3.5e-66) {
		tmp = z * (t * (-4.5 / a));
	} else if (x <= -4.4e-86) {
		tmp = (x * (y * 0.5)) / a;
	} else if (x <= 8.2e-82) {
		tmp = (t * (z * -4.5)) / a;
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) :: tmp
    if (x <= (-1.36d+75)) then
        tmp = y * ((x * 0.5d0) / a)
    else if (x <= (-3.5d-66)) then
        tmp = z * (t * ((-4.5d0) / a))
    else if (x <= (-4.4d-86)) then
        tmp = (x * (y * 0.5d0)) / a
    else if (x <= 8.2d-82) then
        tmp = (t * (z * (-4.5d0))) / a
    else
        tmp = 0.5d0 * (x * (y / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.36e+75) {
		tmp = y * ((x * 0.5) / a);
	} else if (x <= -3.5e-66) {
		tmp = z * (t * (-4.5 / a));
	} else if (x <= -4.4e-86) {
		tmp = (x * (y * 0.5)) / a;
	} else if (x <= 8.2e-82) {
		tmp = (t * (z * -4.5)) / a;
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.36e+75:
		tmp = y * ((x * 0.5) / a)
	elif x <= -3.5e-66:
		tmp = z * (t * (-4.5 / a))
	elif x <= -4.4e-86:
		tmp = (x * (y * 0.5)) / a
	elif x <= 8.2e-82:
		tmp = (t * (z * -4.5)) / a
	else:
		tmp = 0.5 * (x * (y / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.36e+75)
		tmp = Float64(y * Float64(Float64(x * 0.5) / a));
	elseif (x <= -3.5e-66)
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	elseif (x <= -4.4e-86)
		tmp = Float64(Float64(x * Float64(y * 0.5)) / a);
	elseif (x <= 8.2e-82)
		tmp = Float64(Float64(t * Float64(z * -4.5)) / a);
	else
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.36e+75)
		tmp = y * ((x * 0.5) / a);
	elseif (x <= -3.5e-66)
		tmp = z * (t * (-4.5 / a));
	elseif (x <= -4.4e-86)
		tmp = (x * (y * 0.5)) / a;
	elseif (x <= 8.2e-82)
		tmp = (t * (z * -4.5)) / a;
	else
		tmp = 0.5 * (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.36e+75], N[(y * N[(N[(x * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.5e-66], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.4e-86], N[(N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[x, 8.2e-82], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 11: 52.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-105}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e-105) (* -4.5 (* t (/ z a))) (* -4.5 (* z (/ t a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e-105) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) :: tmp
    if (z <= (-3d-105)) then
        tmp = (-4.5d0) * (t * (z / a))
    else
        tmp = (-4.5d0) * (z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e-105) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e-105:
		tmp = -4.5 * (t * (z / a))
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e-105)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3e-105)
		tmp = -4.5 * (t * (z / a));
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e-105], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 12: 51.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ -4.5 \cdot \left(z \cdot \frac{t}{a}\right) \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* -4.5 (* z (/ t a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return -4.5 * (z * (t / a));
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = (-4.5d0) * (z * (t / a))
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * (z * (t / a));
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return -4.5 * (z * (t / a))

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(-4.5 * Float64(z * Float64(t / a)))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (z * (t / a));
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Developer target: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (< a -2.090464557976709e+86)
   (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z))))
   (if (< a 2.144030707833976e+99)
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
     (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	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) :: tmp
    if (a < (-2.090464557976709d+86)) then
        tmp = (0.5d0 * ((y * x) / a)) - (4.5d0 * (t / (a / z)))
    else if (a < 2.144030707833976d+99) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = ((y / a) * (x * 0.5d0)) - ((t / a) * (z * 4.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a < -2.090464557976709e+86:
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)))
	elif a < 2.144030707833976e+99:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a < -2.090464557976709e+86)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / a)) - Float64(4.5 * Float64(t / Float64(a / z))));
	elseif (a < 2.144030707833976e+99)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(y / a) * Float64(x * 0.5)) - Float64(Float64(t / a) * Float64(z * 4.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a < -2.090464557976709e+86)
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	elseif (a < 2.144030707833976e+99)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Less[a, -2.090464557976709e+86], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[a, 2.144030707833976e+99], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023347 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :herbie-target
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))