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

Percentage Accurate: 91.3% → 94.1%

Time: 10.9s

Alternatives: 12

Speedup: 1.0×

• 28.1% 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: 91.3% 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: 94.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-9, z \cdot t, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{a}}{2} - t \cdot \frac{z}{\frac{a}{4.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- (* x y) (* (* z 9.0) t)) 5e+288)
   (/ (fma -9.0 (* z t) (* x y)) (* a 2.0))
   (- (/ (* x (/ y a)) 2.0) (* t (/ z (/ a 4.5))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) - ((z * 9.0) * t)) <= 5e+288) {
		tmp = fma(-9.0, (z * t), (x * y)) / (a * 2.0);
	} else {
		tmp = ((x * (y / a)) / 2.0) - (t * (z / (a / 4.5)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) <= 5e+288)
		tmp = Float64(fma(-9.0, Float64(z * t), Float64(x * y)) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(x * Float64(y / a)) / 2.0) - Float64(t * Float64(z / Float64(a / 4.5))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], 5e+288], N[(N[(-9.0 * N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision] - N[(t * N[(z / N[(a / 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 93.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+273}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{a}}{2} - t \cdot \frac{z}{\frac{a}{4.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- (* x y) (* (* z 9.0) t)) 5e+273)
   (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
   (- (/ (* x (/ y a)) 2.0) (* t (/ z (/ a 4.5))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) - ((z * 9.0) * t)) <= 5e+273) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((x * (y / a)) / 2.0) - (t * (z / (a / 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 (((x * y) - ((z * 9.0d0) * t)) <= 5d+273) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = ((x * (y / a)) / 2.0d0) - (t * (z / (a / 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 (((x * y) - ((z * 9.0) * t)) <= 5e+273) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((x * (y / a)) / 2.0) - (t * (z / (a / 4.5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) - ((z * 9.0) * t)) <= 5e+273:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = ((x * (y / a)) / 2.0) - (t * (z / (a / 4.5)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) <= 5e+273)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(x * Float64(y / a)) / 2.0) - Float64(t * Float64(z / Float64(a / 4.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) - ((z * 9.0) * t)) <= 5e+273)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = ((x * (y / a)) / 2.0) - (t * (z / (a / 4.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], 5e+273], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision] - N[(t * N[(z / N[(a / 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 3: 63.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.66 \cdot 10^{+38}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \leq -1650000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-37}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-67} \lor \neg \left(x \leq 3.4 \cdot 10^{-141}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* x (/ y a)) 0.5)))
   (if (<= x -6.2e+166)
     t_1
     (if (<= x -1.66e+38)
       (* -4.5 (* z (/ t a)))
       (if (<= x -1650000000.0)
         t_1
         (if (<= x -4.2e-37)
           (* -4.5 (/ t (/ a z)))
           (if (or (<= x -5e-67) (not (<= x 3.4e-141)))
             t_1
             (* -4.5 (/ (* z t) a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * (y / a)) * 0.5;
	double tmp;
	if (x <= -6.2e+166) {
		tmp = t_1;
	} else if (x <= -1.66e+38) {
		tmp = -4.5 * (z * (t / a));
	} else if (x <= -1650000000.0) {
		tmp = t_1;
	} else if (x <= -4.2e-37) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x <= -5e-67) || !(x <= 3.4e-141)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	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 = (x * (y / a)) * 0.5d0
    if (x <= (-6.2d+166)) then
        tmp = t_1
    else if (x <= (-1.66d+38)) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (x <= (-1650000000.0d0)) then
        tmp = t_1
    else if (x <= (-4.2d-37)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if ((x <= (-5d-67)) .or. (.not. (x <= 3.4d-141))) then
        tmp = t_1
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * (y / a)) * 0.5;
	double tmp;
	if (x <= -6.2e+166) {
		tmp = t_1;
	} else if (x <= -1.66e+38) {
		tmp = -4.5 * (z * (t / a));
	} else if (x <= -1650000000.0) {
		tmp = t_1;
	} else if (x <= -4.2e-37) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x <= -5e-67) || !(x <= 3.4e-141)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * (y / a)) * 0.5
	tmp = 0
	if x <= -6.2e+166:
		tmp = t_1
	elif x <= -1.66e+38:
		tmp = -4.5 * (z * (t / a))
	elif x <= -1650000000.0:
		tmp = t_1
	elif x <= -4.2e-37:
		tmp = -4.5 * (t / (a / z))
	elif (x <= -5e-67) or not (x <= 3.4e-141):
		tmp = t_1
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * Float64(y / a)) * 0.5)
	tmp = 0.0
	if (x <= -6.2e+166)
		tmp = t_1;
	elseif (x <= -1.66e+38)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (x <= -1650000000.0)
		tmp = t_1;
	elseif (x <= -4.2e-37)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif ((x <= -5e-67) || !(x <= 3.4e-141))
		tmp = t_1;
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * (y / a)) * 0.5;
	tmp = 0.0;
	if (x <= -6.2e+166)
		tmp = t_1;
	elseif (x <= -1.66e+38)
		tmp = -4.5 * (z * (t / a));
	elseif (x <= -1650000000.0)
		tmp = t_1;
	elseif (x <= -4.2e-37)
		tmp = -4.5 * (t / (a / z));
	elseif ((x <= -5e-67) || ~((x <= 3.4e-141)))
		tmp = t_1;
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]}, If[LessEqual[x, -6.2e+166], t$95$1, If[LessEqual[x, -1.66e+38], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1650000000.0], t$95$1, If[LessEqual[x, -4.2e-37], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -5e-67], N[Not[LessEqual[x, 3.4e-141]], $MachinePrecision]], t$95$1, N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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

Alternative 4: 63.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+40}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \leq -1350000000:\\ \;\;\;\;\left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-37}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-67} \lor \neg \left(x \leq 3.4 \cdot 10^{-141}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ x (/ a y)))))
   (if (<= x -6.2e+166)
     t_1
     (if (<= x -2.4e+40)
       (* -4.5 (* z (/ t a)))
       (if (<= x -1350000000.0)
         (* (* x (/ y a)) 0.5)
         (if (<= x -5.4e-37)
           (* -4.5 (/ t (/ a z)))
           (if (or (<= x -5.2e-67) (not (<= x 3.4e-141)))
             t_1
             (* -4.5 (/ (* z t) a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x / (a / y));
	double tmp;
	if (x <= -6.2e+166) {
		tmp = t_1;
	} else if (x <= -2.4e+40) {
		tmp = -4.5 * (z * (t / a));
	} else if (x <= -1350000000.0) {
		tmp = (x * (y / a)) * 0.5;
	} else if (x <= -5.4e-37) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x <= -5.2e-67) || !(x <= 3.4e-141)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	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 = 0.5d0 * (x / (a / y))
    if (x <= (-6.2d+166)) then
        tmp = t_1
    else if (x <= (-2.4d+40)) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (x <= (-1350000000.0d0)) then
        tmp = (x * (y / a)) * 0.5d0
    else if (x <= (-5.4d-37)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if ((x <= (-5.2d-67)) .or. (.not. (x <= 3.4d-141))) then
        tmp = t_1
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x / (a / y));
	double tmp;
	if (x <= -6.2e+166) {
		tmp = t_1;
	} else if (x <= -2.4e+40) {
		tmp = -4.5 * (z * (t / a));
	} else if (x <= -1350000000.0) {
		tmp = (x * (y / a)) * 0.5;
	} else if (x <= -5.4e-37) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x <= -5.2e-67) || !(x <= 3.4e-141)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 0.5 * (x / (a / y))
	tmp = 0
	if x <= -6.2e+166:
		tmp = t_1
	elif x <= -2.4e+40:
		tmp = -4.5 * (z * (t / a))
	elif x <= -1350000000.0:
		tmp = (x * (y / a)) * 0.5
	elif x <= -5.4e-37:
		tmp = -4.5 * (t / (a / z))
	elif (x <= -5.2e-67) or not (x <= 3.4e-141):
		tmp = t_1
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(x / Float64(a / y)))
	tmp = 0.0
	if (x <= -6.2e+166)
		tmp = t_1;
	elseif (x <= -2.4e+40)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (x <= -1350000000.0)
		tmp = Float64(Float64(x * Float64(y / a)) * 0.5);
	elseif (x <= -5.4e-37)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif ((x <= -5.2e-67) || !(x <= 3.4e-141))
		tmp = t_1;
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (x / (a / y));
	tmp = 0.0;
	if (x <= -6.2e+166)
		tmp = t_1;
	elseif (x <= -2.4e+40)
		tmp = -4.5 * (z * (t / a));
	elseif (x <= -1350000000.0)
		tmp = (x * (y / a)) * 0.5;
	elseif (x <= -5.4e-37)
		tmp = -4.5 * (t / (a / z));
	elseif ((x <= -5.2e-67) || ~((x <= 3.4e-141)))
		tmp = t_1;
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+166], t$95$1, If[LessEqual[x, -2.4e+40], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1350000000.0], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision], If[LessEqual[x, -5.4e-37], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -5.2e-67], N[Not[LessEqual[x, 3.4e-141]], $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: 64.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+29}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \leq -1550000000:\\ \;\;\;\;\left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-37}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-113}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ x (/ a y)))))
   (if (<= x -6.2e+166)
     t_1
     (if (<= x -5.6e+29)
       (* -4.5 (* z (/ t a)))
       (if (<= x -1550000000.0)
         (* (* x (/ y a)) 0.5)
         (if (<= x -3.8e-37)
           (* -4.5 (/ t (/ a z)))
           (if (<= x -1.75e-67)
             t_1
             (if (<= x 2.7e-113)
               (* -4.5 (/ (* z t) a))
               (* (* y 0.5) (/ x a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x / (a / y));
	double tmp;
	if (x <= -6.2e+166) {
		tmp = t_1;
	} else if (x <= -5.6e+29) {
		tmp = -4.5 * (z * (t / a));
	} else if (x <= -1550000000.0) {
		tmp = (x * (y / a)) * 0.5;
	} else if (x <= -3.8e-37) {
		tmp = -4.5 * (t / (a / z));
	} else if (x <= -1.75e-67) {
		tmp = t_1;
	} else if (x <= 2.7e-113) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = (y * 0.5) * (x / a);
	}
	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 = 0.5d0 * (x / (a / y))
    if (x <= (-6.2d+166)) then
        tmp = t_1
    else if (x <= (-5.6d+29)) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (x <= (-1550000000.0d0)) then
        tmp = (x * (y / a)) * 0.5d0
    else if (x <= (-3.8d-37)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if (x <= (-1.75d-67)) then
        tmp = t_1
    else if (x <= 2.7d-113) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = (y * 0.5d0) * (x / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x / (a / y));
	double tmp;
	if (x <= -6.2e+166) {
		tmp = t_1;
	} else if (x <= -5.6e+29) {
		tmp = -4.5 * (z * (t / a));
	} else if (x <= -1550000000.0) {
		tmp = (x * (y / a)) * 0.5;
	} else if (x <= -3.8e-37) {
		tmp = -4.5 * (t / (a / z));
	} else if (x <= -1.75e-67) {
		tmp = t_1;
	} else if (x <= 2.7e-113) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = (y * 0.5) * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 0.5 * (x / (a / y))
	tmp = 0
	if x <= -6.2e+166:
		tmp = t_1
	elif x <= -5.6e+29:
		tmp = -4.5 * (z * (t / a))
	elif x <= -1550000000.0:
		tmp = (x * (y / a)) * 0.5
	elif x <= -3.8e-37:
		tmp = -4.5 * (t / (a / z))
	elif x <= -1.75e-67:
		tmp = t_1
	elif x <= 2.7e-113:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = (y * 0.5) * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(x / Float64(a / y)))
	tmp = 0.0
	if (x <= -6.2e+166)
		tmp = t_1;
	elseif (x <= -5.6e+29)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (x <= -1550000000.0)
		tmp = Float64(Float64(x * Float64(y / a)) * 0.5);
	elseif (x <= -3.8e-37)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (x <= -1.75e-67)
		tmp = t_1;
	elseif (x <= 2.7e-113)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(Float64(y * 0.5) * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (x / (a / y));
	tmp = 0.0;
	if (x <= -6.2e+166)
		tmp = t_1;
	elseif (x <= -5.6e+29)
		tmp = -4.5 * (z * (t / a));
	elseif (x <= -1550000000.0)
		tmp = (x * (y / a)) * 0.5;
	elseif (x <= -3.8e-37)
		tmp = -4.5 * (t / (a / z));
	elseif (x <= -1.75e-67)
		tmp = t_1;
	elseif (x <= 2.7e-113)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = (y * 0.5) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+166], t$95$1, If[LessEqual[x, -5.6e+29], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1550000000.0], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision], If[LessEqual[x, -3.8e-37], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.75e-67], t$95$1, If[LessEqual[x, 2.7e-113], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 6: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -20000:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+38}:\\ \;\;\;\;-4.5 \cdot \frac{1}{a \cdot \frac{\frac{1}{z}}{t}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -20000.0)
   (* (* y 0.5) (/ x a))
   (if (<= (* x y) 1e+38)
     (* -4.5 (/ 1.0 (* a (/ (/ 1.0 z) t))))
     (* 0.5 (/ x (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -20000.0) {
		tmp = (y * 0.5) * (x / a);
	} else if ((x * y) <= 1e+38) {
		tmp = -4.5 * (1.0 / (a * ((1.0 / z) / t)));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	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 ((x * y) <= (-20000.0d0)) then
        tmp = (y * 0.5d0) * (x / a)
    else if ((x * y) <= 1d+38) then
        tmp = (-4.5d0) * (1.0d0 / (a * ((1.0d0 / z) / t)))
    else
        tmp = 0.5d0 * (x / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -20000.0) {
		tmp = (y * 0.5) * (x / a);
	} else if ((x * y) <= 1e+38) {
		tmp = -4.5 * (1.0 / (a * ((1.0 / z) / t)));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -20000.0:
		tmp = (y * 0.5) * (x / a)
	elif (x * y) <= 1e+38:
		tmp = -4.5 * (1.0 / (a * ((1.0 / z) / t)))
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -20000.0)
		tmp = Float64(Float64(y * 0.5) * Float64(x / a));
	elseif (Float64(x * y) <= 1e+38)
		tmp = Float64(-4.5 * Float64(1.0 / Float64(a * Float64(Float64(1.0 / z) / t))));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -20000.0)
		tmp = (y * 0.5) * (x / a);
	elseif ((x * y) <= 1e+38)
		tmp = -4.5 * (1.0 / (a * ((1.0 / z) / t)));
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -20000.0], N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+38], N[(-4.5 * N[(1.0 / N[(a * N[(N[(1.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 7: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -20000:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+38}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -20000.0)
   (* (* y 0.5) (/ x a))
   (if (<= (* x y) 1e+38)
     (/ (* z (* t -9.0)) (* a 2.0))
     (* 0.5 (/ x (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -20000.0) {
		tmp = (y * 0.5) * (x / a);
	} else if ((x * y) <= 1e+38) {
		tmp = (z * (t * -9.0)) / (a * 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	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 ((x * y) <= (-20000.0d0)) then
        tmp = (y * 0.5d0) * (x / a)
    else if ((x * y) <= 1d+38) then
        tmp = (z * (t * (-9.0d0))) / (a * 2.0d0)
    else
        tmp = 0.5d0 * (x / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -20000.0) {
		tmp = (y * 0.5) * (x / a);
	} else if ((x * y) <= 1e+38) {
		tmp = (z * (t * -9.0)) / (a * 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -20000.0:
		tmp = (y * 0.5) * (x / a)
	elif (x * y) <= 1e+38:
		tmp = (z * (t * -9.0)) / (a * 2.0)
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -20000.0)
		tmp = Float64(Float64(y * 0.5) * Float64(x / a));
	elseif (Float64(x * y) <= 1e+38)
		tmp = Float64(Float64(z * Float64(t * -9.0)) / Float64(a * 2.0));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -20000.0)
		tmp = (y * 0.5) * (x / a);
	elseif ((x * y) <= 1e+38)
		tmp = (z * (t * -9.0)) / (a * 2.0);
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -20000.0], N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+38], N[(N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 8: 91.3% accurate, 1.0× speedup

Math

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

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(z * Float64(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[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 9: 63.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-146}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+65}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.5e-146)
   (* -4.5 (/ (* z t) a))
   (if (<= t 2.3e+65) (/ (* x (* y 0.5)) a) (* z (/ (* t -4.5) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e-146) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 2.3e+65) {
		tmp = (x * (y * 0.5)) / a;
	} else {
		tmp = z * ((t * -4.5) / a);
	}
	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 (t <= (-9.5d-146)) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (t <= 2.3d+65) then
        tmp = (x * (y * 0.5d0)) / a
    else
        tmp = z * ((t * (-4.5d0)) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e-146) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 2.3e+65) {
		tmp = (x * (y * 0.5)) / a;
	} else {
		tmp = z * ((t * -4.5) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.5e-146:
		tmp = -4.5 * ((z * t) / a)
	elif t <= 2.3e+65:
		tmp = (x * (y * 0.5)) / a
	else:
		tmp = z * ((t * -4.5) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.5e-146)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (t <= 2.3e+65)
		tmp = Float64(Float64(x * Float64(y * 0.5)) / a);
	else
		tmp = Float64(z * Float64(Float64(t * -4.5) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.5e-146)
		tmp = -4.5 * ((z * t) / a);
	elseif (t <= 2.3e+65)
		tmp = (x * (y * 0.5)) / a;
	else
		tmp = z * ((t * -4.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.5e-146], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+65], N[(N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 10: 63.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-146}:\\ \;\;\;\;\frac{-9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{+65}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.5e-146)
   (/ (* -9.0 (* z t)) (* a 2.0))
   (if (<= t 1.56e+65) (/ (* x (* y 0.5)) a) (* z (/ (* t -4.5) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e-146) {
		tmp = (-9.0 * (z * t)) / (a * 2.0);
	} else if (t <= 1.56e+65) {
		tmp = (x * (y * 0.5)) / a;
	} else {
		tmp = z * ((t * -4.5) / a);
	}
	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 (t <= (-9.5d-146)) then
        tmp = ((-9.0d0) * (z * t)) / (a * 2.0d0)
    else if (t <= 1.56d+65) then
        tmp = (x * (y * 0.5d0)) / a
    else
        tmp = z * ((t * (-4.5d0)) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e-146) {
		tmp = (-9.0 * (z * t)) / (a * 2.0);
	} else if (t <= 1.56e+65) {
		tmp = (x * (y * 0.5)) / a;
	} else {
		tmp = z * ((t * -4.5) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.5e-146:
		tmp = (-9.0 * (z * t)) / (a * 2.0)
	elif t <= 1.56e+65:
		tmp = (x * (y * 0.5)) / a
	else:
		tmp = z * ((t * -4.5) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.5e-146)
		tmp = Float64(Float64(-9.0 * Float64(z * t)) / Float64(a * 2.0));
	elseif (t <= 1.56e+65)
		tmp = Float64(Float64(x * Float64(y * 0.5)) / a);
	else
		tmp = Float64(z * Float64(Float64(t * -4.5) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.5e-146)
		tmp = (-9.0 * (z * t)) / (a * 2.0);
	elseif (t <= 1.56e+65)
		tmp = (x * (y * 0.5)) / a;
	else
		tmp = z * ((t * -4.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.5e-146], N[(N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.56e+65], N[(N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 11: 52.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ -4.5 \cdot \left(z \cdot \frac{t}{a}\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* -4.5 (* z (/ t a))))

C

double code(double x, double y, double z, double t, double a) {
	return -4.5 * (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 = (-4.5d0) * (z * (t / a))
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (z * (t / a));
end

Wolfram

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

Alternative 12: 51.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ -4.5 \cdot \frac{z \cdot t}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* -4.5 (/ (* z t) a)))

C

double code(double x, double y, double z, double t, double a) {
	return -4.5 * ((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 = (-4.5d0) * ((z * t) / a)
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = -4.5 * ((z * t) / a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]

Derivation

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

Developer target: 94.2% 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 2024008 
(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)))