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

Percentage Accurate: 91.4% → 94.4%

Time: 9.8s

Alternatives: 13

Speedup: 0.8×

• 28.2% 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: 94.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \begin{array}{l} \mathbf{if}\;a_m \cdot 2 \leq 3.1 \cdot 10^{+58}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{y}{a_m}\right) \cdot 0.5 - t \cdot \frac{z \cdot 4.5}{a_m}\\ \end{array} \end{array} \]

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 (<= (* a_m 2.0) 3.1e+58)
    (/ (fma x y (* z (* t -9.0))) (* a_m 2.0))
    (- (* (* x (/ y a_m)) 0.5) (* t (/ (* z 4.5) 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 ((a_m * 2.0) <= 3.1e+58) {
		tmp = fma(x, y, (z * (t * -9.0))) / (a_m * 2.0);
	} else {
		tmp = ((x * (y / a_m)) * 0.5) - (t * ((z * 4.5) / 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(a_m * 2.0) <= 3.1e+58)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a_m * 2.0));
	else
		tmp = Float64(Float64(Float64(x * Float64(y / a_m)) * 0.5) - Float64(t * Float64(Float64(z * 4.5) / a_m)));
	end
	return Float64(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[(a$95$m * 2.0), $MachinePrecision], 3.1e+58], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision] - N[(t * N[(N[(z * 4.5), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 2: 94.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \begin{array}{l} \mathbf{if}\;a_m \cdot 2 \leq 3.1 \cdot 10^{+58}:\\ \;\;\;\;\frac{0.5}{\frac{a_m}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{y}{a_m}\right) \cdot 0.5 - t \cdot \frac{z \cdot 4.5}{a_m}\\ \end{array} \end{array} \]

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 (<= (* a_m 2.0) 3.1e+58)
    (/ 0.5 (/ a_m (fma x y (* t (* z -9.0)))))
    (- (* (* x (/ y a_m)) 0.5) (* t (/ (* z 4.5) 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 ((a_m * 2.0) <= 3.1e+58) {
		tmp = 0.5 / (a_m / fma(x, y, (t * (z * -9.0))));
	} else {
		tmp = ((x * (y / a_m)) * 0.5) - (t * ((z * 4.5) / 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(a_m * 2.0) <= 3.1e+58)
		tmp = Float64(0.5 / Float64(a_m / fma(x, y, Float64(t * Float64(z * -9.0)))));
	else
		tmp = Float64(Float64(Float64(x * Float64(y / a_m)) * 0.5) - Float64(t * Float64(Float64(z * 4.5) / a_m)));
	end
	return Float64(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[(a$95$m * 2.0), $MachinePrecision], 3.1e+58], N[(0.5 / N[(a$95$m / N[(x * y + N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision] - N[(t * N[(N[(z * 4.5), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 3: 71.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x}{\frac{a_m}{y}}\\ t_2 := \frac{x \cdot y}{a_m \cdot 2}\\ a_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+57}:\\ \;\;\;\;\left(z \cdot -4.5\right) \cdot \frac{t}{a_m}\\ \mathbf{elif}\;x \cdot y \leq -2000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a_m}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+102}:\\ \;\;\;\;-4.5 \cdot \left(\left(z \cdot t\right) \cdot \frac{1}{a_m}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \end{array} \]

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 (* 0.5 (/ x (/ a_m y)))) (t_2 (/ (* x y) (* a_m 2.0))))
   (*
    a_s
    (if (<= (* x y) -5e+150)
      t_1
      (if (<= (* x y) -1e+57)
        (* (* z -4.5) (/ t a_m))
        (if (<= (* x y) -2000000.0)
          t_2
          (if (<= (* x y) 3e-16)
            (* t (* z (/ -4.5 a_m)))
            (if (<= (* x y) 2e+89)
              t_2
              (if (<= (* x y) 2e+102)
                (* -4.5 (* (* z t) (/ 1.0 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 = 0.5 * (x / (a_m / y));
	double t_2 = (x * y) / (a_m * 2.0);
	double tmp;
	if ((x * y) <= -5e+150) {
		tmp = t_1;
	} else if ((x * y) <= -1e+57) {
		tmp = (z * -4.5) * (t / a_m);
	} else if ((x * y) <= -2000000.0) {
		tmp = t_2;
	} else if ((x * y) <= 3e-16) {
		tmp = t * (z * (-4.5 / a_m));
	} else if ((x * y) <= 2e+89) {
		tmp = t_2;
	} else if ((x * y) <= 2e+102) {
		tmp = -4.5 * ((z * t) * (1.0 / 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) :: t_2
    real(8) :: tmp
    t_1 = 0.5d0 * (x / (a_m / y))
    t_2 = (x * y) / (a_m * 2.0d0)
    if ((x * y) <= (-5d+150)) then
        tmp = t_1
    else if ((x * y) <= (-1d+57)) then
        tmp = (z * (-4.5d0)) * (t / a_m)
    else if ((x * y) <= (-2000000.0d0)) then
        tmp = t_2
    else if ((x * y) <= 3d-16) then
        tmp = t * (z * ((-4.5d0) / a_m))
    else if ((x * y) <= 2d+89) then
        tmp = t_2
    else if ((x * y) <= 2d+102) then
        tmp = (-4.5d0) * ((z * t) * (1.0d0 / 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 = 0.5 * (x / (a_m / y));
	double t_2 = (x * y) / (a_m * 2.0);
	double tmp;
	if ((x * y) <= -5e+150) {
		tmp = t_1;
	} else if ((x * y) <= -1e+57) {
		tmp = (z * -4.5) * (t / a_m);
	} else if ((x * y) <= -2000000.0) {
		tmp = t_2;
	} else if ((x * y) <= 3e-16) {
		tmp = t * (z * (-4.5 / a_m));
	} else if ((x * y) <= 2e+89) {
		tmp = t_2;
	} else if ((x * y) <= 2e+102) {
		tmp = -4.5 * ((z * t) * (1.0 / 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 = 0.5 * (x / (a_m / y))
	t_2 = (x * y) / (a_m * 2.0)
	tmp = 0
	if (x * y) <= -5e+150:
		tmp = t_1
	elif (x * y) <= -1e+57:
		tmp = (z * -4.5) * (t / a_m)
	elif (x * y) <= -2000000.0:
		tmp = t_2
	elif (x * y) <= 3e-16:
		tmp = t * (z * (-4.5 / a_m))
	elif (x * y) <= 2e+89:
		tmp = t_2
	elif (x * y) <= 2e+102:
		tmp = -4.5 * ((z * t) * (1.0 / 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(0.5 * Float64(x / Float64(a_m / y)))
	t_2 = Float64(Float64(x * y) / Float64(a_m * 2.0))
	tmp = 0.0
	if (Float64(x * y) <= -5e+150)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e+57)
		tmp = Float64(Float64(z * -4.5) * Float64(t / a_m));
	elseif (Float64(x * y) <= -2000000.0)
		tmp = t_2;
	elseif (Float64(x * y) <= 3e-16)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a_m)));
	elseif (Float64(x * y) <= 2e+89)
		tmp = t_2;
	elseif (Float64(x * y) <= 2e+102)
		tmp = Float64(-4.5 * Float64(Float64(z * t) * Float64(1.0 / 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 = 0.5 * (x / (a_m / y));
	t_2 = (x * y) / (a_m * 2.0);
	tmp = 0.0;
	if ((x * y) <= -5e+150)
		tmp = t_1;
	elseif ((x * y) <= -1e+57)
		tmp = (z * -4.5) * (t / a_m);
	elseif ((x * y) <= -2000000.0)
		tmp = t_2;
	elseif ((x * y) <= 3e-16)
		tmp = t * (z * (-4.5 / a_m));
	elseif ((x * y) <= 2e+89)
		tmp = t_2;
	elseif ((x * y) <= 2e+102)
		tmp = -4.5 * ((z * t) * (1.0 / 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[(0.5 * N[(x / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -5e+150], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e+57], N[(N[(z * -4.5), $MachinePrecision] * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2000000.0], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 3e-16], N[(t * N[(z * N[(-4.5 / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+89], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2e+102], N[(-4.5 * N[(N[(z * t), $MachinePrecision] * N[(1.0 / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]), $MachinePrecision]]]

Derivation

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

Alternative 4: 71.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x}{\frac{a_m}{y}}\\ t_2 := \frac{x \cdot y}{a_m \cdot 2}\\ a_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{+57}:\\ \;\;\;\;\left(z \cdot -4.5\right) \cdot \frac{t}{a_m}\\ \mathbf{elif}\;x \cdot y \leq -2000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a_m}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+102}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a_m}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \end{array} \]

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 (* 0.5 (/ x (/ a_m y)))) (t_2 (/ (* x y) (* a_m 2.0))))
   (*
    a_s
    (if (<= (* x y) -5e+150)
      t_1
      (if (<= (* x y) -1e+57)
        (* (* z -4.5) (/ t a_m))
        (if (<= (* x y) -2000000.0)
          t_2
          (if (<= (* x y) 3e-16)
            (* t (* z (/ -4.5 a_m)))
            (if (<= (* x y) 2e+89)
              t_2
              (if (<= (* x y) 2e+102) (* -4.5 (/ t (/ a_m z))) 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 = 0.5 * (x / (a_m / y));
	double t_2 = (x * y) / (a_m * 2.0);
	double tmp;
	if ((x * y) <= -5e+150) {
		tmp = t_1;
	} else if ((x * y) <= -1e+57) {
		tmp = (z * -4.5) * (t / a_m);
	} else if ((x * y) <= -2000000.0) {
		tmp = t_2;
	} else if ((x * y) <= 3e-16) {
		tmp = t * (z * (-4.5 / a_m));
	} else if ((x * y) <= 2e+89) {
		tmp = t_2;
	} else if ((x * y) <= 2e+102) {
		tmp = -4.5 * (t / (a_m / z));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = 0.5d0 * (x / (a_m / y))
    t_2 = (x * y) / (a_m * 2.0d0)
    if ((x * y) <= (-5d+150)) then
        tmp = t_1
    else if ((x * y) <= (-1d+57)) then
        tmp = (z * (-4.5d0)) * (t / a_m)
    else if ((x * y) <= (-2000000.0d0)) then
        tmp = t_2
    else if ((x * y) <= 3d-16) then
        tmp = t * (z * ((-4.5d0) / a_m))
    else if ((x * y) <= 2d+89) then
        tmp = t_2
    else if ((x * y) <= 2d+102) then
        tmp = (-4.5d0) * (t / (a_m / z))
    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 = 0.5 * (x / (a_m / y));
	double t_2 = (x * y) / (a_m * 2.0);
	double tmp;
	if ((x * y) <= -5e+150) {
		tmp = t_1;
	} else if ((x * y) <= -1e+57) {
		tmp = (z * -4.5) * (t / a_m);
	} else if ((x * y) <= -2000000.0) {
		tmp = t_2;
	} else if ((x * y) <= 3e-16) {
		tmp = t * (z * (-4.5 / a_m));
	} else if ((x * y) <= 2e+89) {
		tmp = t_2;
	} else if ((x * y) <= 2e+102) {
		tmp = -4.5 * (t / (a_m / z));
	} 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 = 0.5 * (x / (a_m / y))
	t_2 = (x * y) / (a_m * 2.0)
	tmp = 0
	if (x * y) <= -5e+150:
		tmp = t_1
	elif (x * y) <= -1e+57:
		tmp = (z * -4.5) * (t / a_m)
	elif (x * y) <= -2000000.0:
		tmp = t_2
	elif (x * y) <= 3e-16:
		tmp = t * (z * (-4.5 / a_m))
	elif (x * y) <= 2e+89:
		tmp = t_2
	elif (x * y) <= 2e+102:
		tmp = -4.5 * (t / (a_m / z))
	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(0.5 * Float64(x / Float64(a_m / y)))
	t_2 = Float64(Float64(x * y) / Float64(a_m * 2.0))
	tmp = 0.0
	if (Float64(x * y) <= -5e+150)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e+57)
		tmp = Float64(Float64(z * -4.5) * Float64(t / a_m));
	elseif (Float64(x * y) <= -2000000.0)
		tmp = t_2;
	elseif (Float64(x * y) <= 3e-16)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a_m)));
	elseif (Float64(x * y) <= 2e+89)
		tmp = t_2;
	elseif (Float64(x * y) <= 2e+102)
		tmp = Float64(-4.5 * Float64(t / Float64(a_m / z)));
	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 = 0.5 * (x / (a_m / y));
	t_2 = (x * y) / (a_m * 2.0);
	tmp = 0.0;
	if ((x * y) <= -5e+150)
		tmp = t_1;
	elseif ((x * y) <= -1e+57)
		tmp = (z * -4.5) * (t / a_m);
	elseif ((x * y) <= -2000000.0)
		tmp = t_2;
	elseif ((x * y) <= 3e-16)
		tmp = t * (z * (-4.5 / a_m));
	elseif ((x * y) <= 2e+89)
		tmp = t_2;
	elseif ((x * y) <= 2e+102)
		tmp = -4.5 * (t / (a_m / z));
	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[(0.5 * N[(x / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -5e+150], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e+57], N[(N[(z * -4.5), $MachinePrecision] * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2000000.0], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 3e-16], N[(t * N[(z * N[(-4.5 / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+89], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2e+102], N[(-4.5 * N[(t / N[(a$95$m / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]), $MachinePrecision]]]

Derivation

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

Alternative 5: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot 9\right) \leq 5 \cdot 10^{+294}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a_m}{z}}\\ \end{array} \end{array} \]

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 (* z 9.0)) 5e+294)
    (/ (- (* x y) (* z (* t 9.0))) (* a_m 2.0))
    (* -4.5 (/ t (/ a_m z))))))

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 * (z * 9.0)) <= 5e+294) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0);
	} else {
		tmp = -4.5 * (t / (a_m / z));
	}
	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 * (z * 9.0d0)) <= 5d+294) then
        tmp = ((x * y) - (z * (t * 9.0d0))) / (a_m * 2.0d0)
    else
        tmp = (-4.5d0) * (t / (a_m / z))
    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 * (z * 9.0)) <= 5e+294) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0);
	} else {
		tmp = -4.5 * (t / (a_m / z));
	}
	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 * (z * 9.0)) <= 5e+294:
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0)
	else:
		tmp = -4.5 * (t / (a_m / z))
	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(t * Float64(z * 9.0)) <= 5e+294)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a_m * 2.0));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a_m / z)));
	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 * (z * 9.0)) <= 5e+294)
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0);
	else
		tmp = -4.5 * (t / (a_m / z));
	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[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision], 5e+294], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a$95$m / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 6: 94.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \begin{array}{l} \mathbf{if}\;a_m \cdot 2 \leq 5 \cdot 10^{-60}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{y}{a_m}\right) \cdot 0.5 - t \cdot \frac{z \cdot 4.5}{a_m}\\ \end{array} \end{array} \]

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 (<= (* a_m 2.0) 5e-60)
    (/ (- (* x y) (* z (* t 9.0))) (* a_m 2.0))
    (- (* (* x (/ y a_m)) 0.5) (* t (/ (* z 4.5) 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 ((a_m * 2.0) <= 5e-60) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0);
	} else {
		tmp = ((x * (y / a_m)) * 0.5) - (t * ((z * 4.5) / 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 ((a_m * 2.0d0) <= 5d-60) then
        tmp = ((x * y) - (z * (t * 9.0d0))) / (a_m * 2.0d0)
    else
        tmp = ((x * (y / a_m)) * 0.5d0) - (t * ((z * 4.5d0) / 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 ((a_m * 2.0) <= 5e-60) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0);
	} else {
		tmp = ((x * (y / a_m)) * 0.5) - (t * ((z * 4.5) / 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 (a_m * 2.0) <= 5e-60:
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0)
	else:
		tmp = ((x * (y / a_m)) * 0.5) - (t * ((z * 4.5) / 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(a_m * 2.0) <= 5e-60)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a_m * 2.0));
	else
		tmp = Float64(Float64(Float64(x * Float64(y / a_m)) * 0.5) - Float64(t * Float64(Float64(z * 4.5) / 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 ((a_m * 2.0) <= 5e-60)
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0);
	else
		tmp = ((x * (y / a_m)) * 0.5) - (t * ((z * 4.5) / 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[(a$95$m * 2.0), $MachinePrecision], 5e-60], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision] - N[(t * N[(N[(z * 4.5), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 7: 92.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+254}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a_m}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{a_m}{x \cdot y + -9 \cdot \left(z \cdot t\right)}}\\ \end{array} \end{array} \]

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) -1e+254)
    (* 0.5 (/ x (/ a_m y)))
    (/ 0.5 (/ a_m (+ (* x y) (* -9.0 (* z 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 tmp;
	if ((x * y) <= -1e+254) {
		tmp = 0.5 * (x / (a_m / y));
	} else {
		tmp = 0.5 / (a_m / ((x * y) + (-9.0 * (z * 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) :: tmp
    if ((x * y) <= (-1d+254)) then
        tmp = 0.5d0 * (x / (a_m / y))
    else
        tmp = 0.5d0 / (a_m / ((x * y) + ((-9.0d0) * (z * 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 tmp;
	if ((x * y) <= -1e+254) {
		tmp = 0.5 * (x / (a_m / y));
	} else {
		tmp = 0.5 / (a_m / ((x * y) + (-9.0 * (z * 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):
	tmp = 0
	if (x * y) <= -1e+254:
		tmp = 0.5 * (x / (a_m / y))
	else:
		tmp = 0.5 / (a_m / ((x * y) + (-9.0 * (z * 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)
	tmp = 0.0
	if (Float64(x * y) <= -1e+254)
		tmp = Float64(0.5 * Float64(x / Float64(a_m / y)));
	else
		tmp = Float64(0.5 / Float64(a_m / Float64(Float64(x * y) + Float64(-9.0 * Float64(z * 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)
	tmp = 0.0;
	if ((x * y) <= -1e+254)
		tmp = 0.5 * (x / (a_m / y));
	else
		tmp = 0.5 / (a_m / ((x * y) + (-9.0 * (z * 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_] := N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -1e+254], N[(0.5 * N[(x / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(a$95$m / N[(N[(x * y), $MachinePrecision] + N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 8: 64.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-143} \lor \neg \left(t \leq 3.4 \cdot 10^{-18}\right):\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{y}{a_m}\right) \cdot 0.5\\ \end{array} \end{array} \]

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 (or (<= t -1.65e-143) (not (<= t 3.4e-18)))
    (* t (* -4.5 (/ z a_m)))
    (* (* x (/ y a_m)) 0.5))))

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 <= -1.65e-143) || !(t <= 3.4e-18)) {
		tmp = t * (-4.5 * (z / a_m));
	} else {
		tmp = (x * (y / a_m)) * 0.5;
	}
	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 <= (-1.65d-143)) .or. (.not. (t <= 3.4d-18))) then
        tmp = t * ((-4.5d0) * (z / a_m))
    else
        tmp = (x * (y / a_m)) * 0.5d0
    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 <= -1.65e-143) || !(t <= 3.4e-18)) {
		tmp = t * (-4.5 * (z / a_m));
	} else {
		tmp = (x * (y / a_m)) * 0.5;
	}
	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 <= -1.65e-143) or not (t <= 3.4e-18):
		tmp = t * (-4.5 * (z / a_m))
	else:
		tmp = (x * (y / a_m)) * 0.5
	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 <= -1.65e-143) || !(t <= 3.4e-18))
		tmp = Float64(t * Float64(-4.5 * Float64(z / a_m)));
	else
		tmp = Float64(Float64(x * Float64(y / a_m)) * 0.5);
	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 <= -1.65e-143) || ~((t <= 3.4e-18)))
		tmp = t * (-4.5 * (z / a_m));
	else
		tmp = (x * (y / a_m)) * 0.5;
	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[Or[LessEqual[t, -1.65e-143], N[Not[LessEqual[t, 3.4e-18]], $MachinePrecision]], N[(t * N[(-4.5 * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 9: 64.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-143}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a_m}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-18}:\\ \;\;\;\;\left(x \cdot \frac{y}{a_m}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a_m}{z}}\\ \end{array} \end{array} \]

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 -1.65e-143)
    (* -4.5 (* z (/ t a_m)))
    (if (<= t 6e-18) (* (* x (/ y a_m)) 0.5) (* -4.5 (/ t (/ a_m z)))))))

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 <= -1.65e-143) {
		tmp = -4.5 * (z * (t / a_m));
	} else if (t <= 6e-18) {
		tmp = (x * (y / a_m)) * 0.5;
	} else {
		tmp = -4.5 * (t / (a_m / z));
	}
	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 <= (-1.65d-143)) then
        tmp = (-4.5d0) * (z * (t / a_m))
    else if (t <= 6d-18) then
        tmp = (x * (y / a_m)) * 0.5d0
    else
        tmp = (-4.5d0) * (t / (a_m / z))
    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 <= -1.65e-143) {
		tmp = -4.5 * (z * (t / a_m));
	} else if (t <= 6e-18) {
		tmp = (x * (y / a_m)) * 0.5;
	} else {
		tmp = -4.5 * (t / (a_m / z));
	}
	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 <= -1.65e-143:
		tmp = -4.5 * (z * (t / a_m))
	elif t <= 6e-18:
		tmp = (x * (y / a_m)) * 0.5
	else:
		tmp = -4.5 * (t / (a_m / z))
	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 <= -1.65e-143)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a_m)));
	elseif (t <= 6e-18)
		tmp = Float64(Float64(x * Float64(y / a_m)) * 0.5);
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a_m / z)));
	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 <= -1.65e-143)
		tmp = -4.5 * (z * (t / a_m));
	elseif (t <= 6e-18)
		tmp = (x * (y / a_m)) * 0.5;
	else
		tmp = -4.5 * (t / (a_m / z));
	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, -1.65e-143], N[(-4.5 * N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-18], N[(N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision], N[(-4.5 * N[(t / N[(a$95$m / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 10: 64.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a_m}\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-18}:\\ \;\;\;\;\left(x \cdot \frac{y}{a_m}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a_m}\right)\\ \end{array} \end{array} \]

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 -1.4e-147)
    (* t (* -4.5 (/ z a_m)))
    (if (<= t 4.5e-18) (* (* x (/ y a_m)) 0.5) (* t (* z (/ -4.5 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 <= -1.4e-147) {
		tmp = t * (-4.5 * (z / a_m));
	} else if (t <= 4.5e-18) {
		tmp = (x * (y / a_m)) * 0.5;
	} else {
		tmp = t * (z * (-4.5 / 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 <= (-1.4d-147)) then
        tmp = t * ((-4.5d0) * (z / a_m))
    else if (t <= 4.5d-18) then
        tmp = (x * (y / a_m)) * 0.5d0
    else
        tmp = t * (z * ((-4.5d0) / 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 <= -1.4e-147) {
		tmp = t * (-4.5 * (z / a_m));
	} else if (t <= 4.5e-18) {
		tmp = (x * (y / a_m)) * 0.5;
	} else {
		tmp = t * (z * (-4.5 / 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 <= -1.4e-147:
		tmp = t * (-4.5 * (z / a_m))
	elif t <= 4.5e-18:
		tmp = (x * (y / a_m)) * 0.5
	else:
		tmp = t * (z * (-4.5 / 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 <= -1.4e-147)
		tmp = Float64(t * Float64(-4.5 * Float64(z / a_m)));
	elseif (t <= 4.5e-18)
		tmp = Float64(Float64(x * Float64(y / a_m)) * 0.5);
	else
		tmp = Float64(t * Float64(z * Float64(-4.5 / 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 <= -1.4e-147)
		tmp = t * (-4.5 * (z / a_m));
	elseif (t <= 4.5e-18)
		tmp = (x * (y / a_m)) * 0.5;
	else
		tmp = t * (z * (-4.5 / 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, -1.4e-147], N[(t * N[(-4.5 * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-18], N[(N[(x * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision], N[(t * N[(z * N[(-4.5 / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 11: 51.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \begin{array}{l} \mathbf{if}\;a_m \leq 1.6 \cdot 10^{+183}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a_m}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a_m}{z}}\\ \end{array} \end{array} \]

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 (<= a_m 1.6e+183) (* -4.5 (/ (* z t) a_m)) (* -4.5 (/ t (/ a_m z))))))

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 (a_m <= 1.6e+183) {
		tmp = -4.5 * ((z * t) / a_m);
	} else {
		tmp = -4.5 * (t / (a_m / z));
	}
	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 (a_m <= 1.6d+183) then
        tmp = (-4.5d0) * ((z * t) / a_m)
    else
        tmp = (-4.5d0) * (t / (a_m / z))
    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 (a_m <= 1.6e+183) {
		tmp = -4.5 * ((z * t) / a_m);
	} else {
		tmp = -4.5 * (t / (a_m / z));
	}
	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 a_m <= 1.6e+183:
		tmp = -4.5 * ((z * t) / a_m)
	else:
		tmp = -4.5 * (t / (a_m / z))
	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 (a_m <= 1.6e+183)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a_m));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a_m / z)));
	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 (a_m <= 1.6e+183)
		tmp = -4.5 * ((z * t) / a_m);
	else
		tmp = -4.5 * (t / (a_m / z));
	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[a$95$m, 1.6e+183], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a$95$m / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 12: 50.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \left(-4.5 \cdot \left(z \cdot \frac{t}{a_m}\right)\right) \end{array} \]

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 (* -4.5 (* 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) {
	return a_s * (-4.5 * (z * (t / 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 * ((-4.5d0) * (z * (t / 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 * (-4.5 * (z * (t / 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 * (-4.5 * (z * (t / 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(-4.5 * Float64(z * Float64(t / 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 * (-4.5 * (z * (t / 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[(-4.5 * N[(z * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 13: 50.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a_s \cdot \left(-4.5 \cdot \frac{t}{\frac{a_m}{z}}\right) \end{array} \]

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 (* -4.5 (/ t (/ a_m z)))))

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 * (-4.5 * (t / (a_m / z)));
}

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 * ((-4.5d0) * (t / (a_m / z)))
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 * (-4.5 * (t / (a_m / z)));
}

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 * (-4.5 * (t / (a_m / z)))

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(-4.5 * Float64(t / Float64(a_m / z))))
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 * (-4.5 * (t / (a_m / z)));
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[(-4.5 * N[(t / N[(a$95$m / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Developer target: 93.9% 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 2024003 
(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)))