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

Percentage Accurate: 91.1% → 93.2%

Time: 7.5s

Alternatives: 8

Speedup: 0.4×

• 28.3% 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: 91.1% 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: 93.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \left(-4.5 \cdot \frac{z \cdot t}{y \cdot a} + 0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+231}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a} + 0.5 \cdot \frac{x \cdot y}{z \cdot a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 (- INFINITY))
     (* y (+ (* -4.5 (/ (* z t) (* y a))) (* 0.5 (/ x a))))
     (if (<= t_1 5e+231)
       (/ (- (* x y) (* 9.0 (* z t))) (* a 2.0))
       (* z (+ (* -4.5 (/ t a)) (* 0.5 (/ (* x y) (* z a)))))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / a)));
	} else if (t_1 <= 5e+231) {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = z * ((-4.5 * (t / a)) + (0.5 * ((x * y) / (z * a))));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / a)));
	} else if (t_1 <= 5e+231) {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = z * ((-4.5 * (t / a)) + (0.5 * ((x * y) / (z * a))));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / a)))
	elif t_1 <= 5e+231:
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0)
	else:
		tmp = z * ((-4.5 * (t / a)) + (0.5 * ((x * y) / (z * a))))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(-4.5 * Float64(Float64(z * t) / Float64(y * a))) + Float64(0.5 * Float64(x / a))));
	elseif (t_1 <= 5e+231)
		tmp = Float64(Float64(Float64(x * y) - Float64(9.0 * Float64(z * t))) / Float64(a * 2.0));
	else
		tmp = Float64(z * Float64(Float64(-4.5 * Float64(t / a)) + Float64(0.5 * Float64(Float64(x * y) / Float64(z * a)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / a)));
	elseif (t_1 <= 5e+231)
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	else
		tmp = z * ((-4.5 * (t / a)) + (0.5 * ((x * y) / (z * a))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(N[(-4.5 * N[(N[(z * t), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+231], N[(N[(N[(x * y), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[(x * y), $MachinePrecision] / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -inf.0

   1. Initial program 57.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.2%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 5.00000000000000028e231

   1. Initial program 99.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.1%

      \[\leadsto \frac{\color{blue}{x \cdot y - 9 \cdot \left(t \cdot z\right)}}{a \cdot 2} \]

   if 5.00000000000000028e231 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 66.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.1%

      \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a} + 0.5 \cdot \frac{x \cdot y}{a \cdot z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;y \cdot \left(-4.5 \cdot \frac{z \cdot t}{y \cdot a} + 0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+231}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a} + 0.5 \cdot \frac{x \cdot y}{z \cdot a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \left(-4.5 \cdot \frac{z \cdot t}{y \cdot a} + 0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+303}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a} + 0.5 \cdot \frac{x \cdot y}{t \cdot a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 (- INFINITY))
     (* y (+ (* -4.5 (/ (* z t) (* y a))) (* 0.5 (/ x a))))
     (if (<= t_1 5e+303)
       (/ (- (* x y) (* 9.0 (* z t))) (* a 2.0))
       (* t (+ (* -4.5 (/ z a)) (* 0.5 (/ (* x y) (* t a)))))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / a)));
	} else if (t_1 <= 5e+303) {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = t * ((-4.5 * (z / a)) + (0.5 * ((x * y) / (t * a))));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / a)));
	} else if (t_1 <= 5e+303) {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = t * ((-4.5 * (z / a)) + (0.5 * ((x * y) / (t * a))));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / a)))
	elif t_1 <= 5e+303:
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0)
	else:
		tmp = t * ((-4.5 * (z / a)) + (0.5 * ((x * y) / (t * a))))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(-4.5 * Float64(Float64(z * t) / Float64(y * a))) + Float64(0.5 * Float64(x / a))));
	elseif (t_1 <= 5e+303)
		tmp = Float64(Float64(Float64(x * y) - Float64(9.0 * Float64(z * t))) / Float64(a * 2.0));
	else
		tmp = Float64(t * Float64(Float64(-4.5 * Float64(z / a)) + Float64(0.5 * Float64(Float64(x * y) / Float64(t * a)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / a)));
	elseif (t_1 <= 5e+303)
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	else
		tmp = t * ((-4.5 * (z / a)) + (0.5 * ((x * y) / (t * a))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(N[(-4.5 * N[(N[(z * t), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+303], N[(N[(N[(x * y), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(-4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[(x * y), $MachinePrecision] / N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -inf.0

   1. Initial program 57.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.2%

      \[\leadsto \color{blue}{y \cdot \left(-4.5 \cdot \frac{t \cdot z}{a \cdot y} + 0.5 \cdot \frac{x}{a}\right)} \]

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 4.9999999999999997e303

   1. Initial program 99.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.2%

      \[\leadsto \frac{\color{blue}{x \cdot y - 9 \cdot \left(t \cdot z\right)}}{a \cdot 2} \]

   if 4.9999999999999997e303 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 51.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 81.1%

      \[\leadsto \color{blue}{t \cdot \left(-4.5 \cdot \frac{z}{a} + 0.5 \cdot \frac{x \cdot y}{a \cdot t}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;y \cdot \left(-4.5 \cdot \frac{z \cdot t}{y \cdot a} + 0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+303}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a} + 0.5 \cdot \frac{x \cdot y}{t \cdot a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;z \cdot \frac{-4.5}{\frac{a}{t}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+251}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 (- INFINITY))
     (* z (/ -4.5 (/ a t)))
     (if (<= t_1 2e+251)
       (/ (- (* x y) (* 9.0 (* z t))) (* a 2.0))
       (* z (* t (/ -4.5 a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z * (-4.5 / (a / t));
	} else if (t_1 <= 2e+251) {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = z * (t * (-4.5 / a));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (-4.5 / (a / t));
	} else if (t_1 <= 2e+251) {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = z * (t * (-4.5 / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z * (-4.5 / (a / t))
	elif t_1 <= 2e+251:
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0)
	else:
		tmp = z * (t * (-4.5 / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z * Float64(-4.5 / Float64(a / t)));
	elseif (t_1 <= 2e+251)
		tmp = Float64(Float64(Float64(x * y) - Float64(9.0 * Float64(z * t))) / Float64(a * 2.0));
	else
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z * (-4.5 / (a / t));
	elseif (t_1 <= 2e+251)
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	else
		tmp = z * (t * (-4.5 / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z * N[(-4.5 / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+251], N[(N[(N[(x * y), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -inf.0

   1. Initial program 37.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 37.1%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 37.1%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 37.1%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 99.7%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 99.7%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 99.6%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 99.6%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]
   6. Step-by-step derivation

      1. clear-num 99.6%

         \[\leadsto z \cdot \color{blue}{\frac{1}{\frac{a}{-4.5 \cdot t}}} \]

      2. inv-pow 99.6%

         \[\leadsto z \cdot \color{blue}{{\left(\frac{a}{-4.5 \cdot t}\right)}^{-1}} \]

      3. *-un-lft-identity 99.6%

         \[\leadsto z \cdot {\left(\frac{\color{blue}{1 \cdot a}}{-4.5 \cdot t}\right)}^{-1} \]

      4. times-frac 99.7%

         \[\leadsto z \cdot {\color{blue}{\left(\frac{1}{-4.5} \cdot \frac{a}{t}\right)}}^{-1} \]

      5. metadata-eval 99.7%

         \[\leadsto z \cdot {\left(\color{blue}{-0.2222222222222222} \cdot \frac{a}{t}\right)}^{-1} \]

   7. Applied egg-rr 99.7%

      \[\leadsto z \cdot \color{blue}{{\left(-0.2222222222222222 \cdot \frac{a}{t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 99.7%

         \[\leadsto z \cdot \color{blue}{\frac{1}{-0.2222222222222222 \cdot \frac{a}{t}}} \]

      2. associate-/r* 99.9%

         \[\leadsto z \cdot \color{blue}{\frac{\frac{1}{-0.2222222222222222}}{\frac{a}{t}}} \]

      3. metadata-eval 99.9%

         \[\leadsto z \cdot \frac{\color{blue}{-4.5}}{\frac{a}{t}} \]

   9. Simplified 99.9%

      \[\leadsto z \cdot \color{blue}{\frac{-4.5}{\frac{a}{t}}} \]

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 2.0000000000000001e251

   1. Initial program 93.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 93.0%

      \[\leadsto \frac{\color{blue}{x \cdot y - 9 \cdot \left(t \cdot z\right)}}{a \cdot 2} \]

   if 2.0000000000000001e251 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 55.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 55.4%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 55.3%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 55.3%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 93.9%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 94.0%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 94.0%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 93.9%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 93.9%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]

   6. Taylor expanded in t around 0 94.0%

      \[\leadsto z \cdot \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 93.9%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

      2. *-commutative 93.9%

         \[\leadsto z \cdot \frac{\color{blue}{t \cdot -4.5}}{a} \]

      3. associate-*r/ 93.9%

         \[\leadsto z \cdot \color{blue}{\left(t \cdot \frac{-4.5}{a}\right)} \]

   8. Simplified 93.9%

      \[\leadsto z \cdot \color{blue}{\left(t \cdot \frac{-4.5}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;z \cdot \frac{-4.5}{\frac{a}{t}}\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+251}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-54}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y \cdot 0.5}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+78)
   (* x (/ (* y 0.5) a))
   (if (<= (* x y) 5e-54) (* -4.5 (* t (/ z a))) (/ x (/ a (* y 0.5))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+78) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= 5e-54) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = x / (a / (y * 0.5));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-5d+78)) then
        tmp = x * ((y * 0.5d0) / a)
    else if ((x * y) <= 5d-54) then
        tmp = (-4.5d0) * (t * (z / a))
    else
        tmp = x / (a / (y * 0.5d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+78) {
		tmp = x * ((y * 0.5) / a);
	} else if ((x * y) <= 5e-54) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = x / (a / (y * 0.5));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+78:
		tmp = x * ((y * 0.5) / a)
	elif (x * y) <= 5e-54:
		tmp = -4.5 * (t * (z / a))
	else:
		tmp = x / (a / (y * 0.5))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+78)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	elseif (Float64(x * y) <= 5e-54)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	else
		tmp = Float64(x / Float64(a / Float64(y * 0.5)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+78)
		tmp = x * ((y * 0.5) / a);
	elseif ((x * y) <= 5e-54)
		tmp = -4.5 * (t * (z / a));
	else
		tmp = x / (a / (y * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+78], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-54], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.99999999999999984e78

   1. Initial program 76.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 70.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 70.7%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 87.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 87.7%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 87.7%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 87.7%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 87.7%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if -4.99999999999999984e78 < (*.f64 x y) < 5.00000000000000015e-54

   1. Initial program 91.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 69.8%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 71.4%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 71.4%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]

   if 5.00000000000000015e-54 < (*.f64 x y)

   1. Initial program 88.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 72.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 72.7%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 78.2%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 78.2%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 78.2%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 78.2%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 78.2%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
   6. Step-by-step derivation

      1. clear-num 78.1%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{a}{0.5 \cdot y}}} \]

      2. un-div-inv 78.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{0.5 \cdot y}}} \]

      3. *-commutative 78.2%

         \[\leadsto \frac{x}{\frac{a}{\color{blue}{y \cdot 0.5}}} \]

   7. Applied egg-rr 78.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y \cdot 0.5}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-54}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y \cdot 0.5}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-91} \lor \neg \left(t \leq 2.4 \cdot 10^{+31}\right):\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e-91) (not (<= t 2.4e+31)))
   (* -4.5 (* t (/ z a)))
   (* x (/ (* y 0.5) a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e-91) || !(t <= 2.4e+31)) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.4d-91)) .or. (.not. (t <= 2.4d+31))) then
        tmp = (-4.5d0) * (t * (z / a))
    else
        tmp = x * ((y * 0.5d0) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e-91) || !(t <= 2.4e+31)) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.4e-91) or not (t <= 2.4e+31):
		tmp = -4.5 * (t * (z / a))
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e-91) || !(t <= 2.4e+31))
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.4e-91) || ~((t <= 2.4e+31)))
		tmp = -4.5 * (t * (z / a));
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e-91], N[Not[LessEqual[t, 2.4e+31]], $MachinePrecision]], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.40000000000000011e-91 or 2.39999999999999982e31 < t

   1. Initial program 81.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 58.4%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 66.6%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 66.6%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]

   if -2.40000000000000011e-91 < t < 2.39999999999999982e31

   1. Initial program 92.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 72.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 72.0%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 76.0%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 76.0%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 76.0%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 76.0%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 76.0%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-91} \lor \neg \left(t \leq 2.4 \cdot 10^{+31}\right):\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-90}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.88 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.5e-90)
   (* -4.5 (* t (/ z a)))
   (if (<= t 1.88e+31) (* x (/ (* y 0.5) a)) (* z (* t (/ -4.5 a))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e-90) {
		tmp = -4.5 * (t * (z / a));
	} else if (t <= 1.88e+31) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = z * (t * (-4.5 / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.5d-90)) then
        tmp = (-4.5d0) * (t * (z / a))
    else if (t <= 1.88d+31) then
        tmp = x * ((y * 0.5d0) / a)
    else
        tmp = z * (t * ((-4.5d0) / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e-90) {
		tmp = -4.5 * (t * (z / a));
	} else if (t <= 1.88e+31) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = z * (t * (-4.5 / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.5e-90:
		tmp = -4.5 * (t * (z / a))
	elif t <= 1.88e+31:
		tmp = x * ((y * 0.5) / a)
	else:
		tmp = z * (t * (-4.5 / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.5e-90)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (t <= 1.88e+31)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.5e-90)
		tmp = -4.5 * (t * (z / a));
	elseif (t <= 1.88e+31)
		tmp = x * ((y * 0.5) / a);
	else
		tmp = z * (t * (-4.5 / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.5e-90], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.88e+31], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5000000000000003e-90

   1. Initial program 82.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 59.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 65.6%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 65.6%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]

   if -5.5000000000000003e-90 < t < 1.87999999999999996e31

   1. Initial program 92.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 72.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 72.2%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 76.2%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 76.2%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 76.2%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 76.2%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 76.2%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if 1.87999999999999996e31 < t

   1. Initial program 80.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 57.5%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 57.5%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 57.5%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 78.3%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 78.3%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 78.3%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 78.3%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 78.3%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]

   6. Taylor expanded in t around 0 78.3%

      \[\leadsto z \cdot \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 78.3%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

      2. *-commutative 78.3%

         \[\leadsto z \cdot \frac{\color{blue}{t \cdot -4.5}}{a} \]

      3. associate-*r/ 78.3%

         \[\leadsto z \cdot \color{blue}{\left(t \cdot \frac{-4.5}{a}\right)} \]

   8. Simplified 78.3%

      \[\leadsto z \cdot \color{blue}{\left(t \cdot \frac{-4.5}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-90}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.88 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-90}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-4.5}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.5e-90)
   (* -4.5 (* t (/ z a)))
   (if (<= t 2e+31) (* x (/ (* y 0.5) a)) (* z (/ -4.5 (/ a t))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e-90) {
		tmp = -4.5 * (t * (z / a));
	} else if (t <= 2e+31) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = z * (-4.5 / (a / t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.5d-90)) then
        tmp = (-4.5d0) * (t * (z / a))
    else if (t <= 2d+31) then
        tmp = x * ((y * 0.5d0) / a)
    else
        tmp = z * ((-4.5d0) / (a / t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e-90) {
		tmp = -4.5 * (t * (z / a));
	} else if (t <= 2e+31) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = z * (-4.5 / (a / t));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.5e-90:
		tmp = -4.5 * (t * (z / a))
	elif t <= 2e+31:
		tmp = x * ((y * 0.5) / a)
	else:
		tmp = z * (-4.5 / (a / t))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.5e-90)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (t <= 2e+31)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = Float64(z * Float64(-4.5 / Float64(a / t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.5e-90)
		tmp = -4.5 * (t * (z / a));
	elseif (t <= 2e+31)
		tmp = x * ((y * 0.5) / a);
	else
		tmp = z * (-4.5 / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.5e-90], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+31], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(z * N[(-4.5 / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5000000000000003e-90

   1. Initial program 82.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 59.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 65.6%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 65.6%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]

   if -5.5000000000000003e-90 < t < 1.9999999999999999e31

   1. Initial program 92.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 72.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 72.2%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 76.2%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 76.2%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 76.2%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 76.2%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 76.2%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if 1.9999999999999999e31 < t

   1. Initial program 80.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 57.5%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-*r/ 57.5%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. associate-*r* 57.5%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      3. associate-*l/ 78.3%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{a} \cdot z} \]

      4. associate-*r/ 78.3%

         \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right)} \cdot z \]

      5. *-commutative 78.3%

         \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a}\right)} \]

      6. associate-*r/ 78.3%

         \[\leadsto z \cdot \color{blue}{\frac{-4.5 \cdot t}{a}} \]

   5. Simplified 78.3%

      \[\leadsto \color{blue}{z \cdot \frac{-4.5 \cdot t}{a}} \]
   6. Step-by-step derivation

      1. clear-num 78.2%

         \[\leadsto z \cdot \color{blue}{\frac{1}{\frac{a}{-4.5 \cdot t}}} \]

      2. inv-pow 78.2%

         \[\leadsto z \cdot \color{blue}{{\left(\frac{a}{-4.5 \cdot t}\right)}^{-1}} \]

      3. *-un-lft-identity 78.2%

         \[\leadsto z \cdot {\left(\frac{\color{blue}{1 \cdot a}}{-4.5 \cdot t}\right)}^{-1} \]

      4. times-frac 78.2%

         \[\leadsto z \cdot {\color{blue}{\left(\frac{1}{-4.5} \cdot \frac{a}{t}\right)}}^{-1} \]

      5. metadata-eval 78.2%

         \[\leadsto z \cdot {\left(\color{blue}{-0.2222222222222222} \cdot \frac{a}{t}\right)}^{-1} \]

   7. Applied egg-rr 78.2%

      \[\leadsto z \cdot \color{blue}{{\left(-0.2222222222222222 \cdot \frac{a}{t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 78.2%

         \[\leadsto z \cdot \color{blue}{\frac{1}{-0.2222222222222222 \cdot \frac{a}{t}}} \]

      2. associate-/r* 78.4%

         \[\leadsto z \cdot \color{blue}{\frac{\frac{1}{-0.2222222222222222}}{\frac{a}{t}}} \]

      3. metadata-eval 78.4%

         \[\leadsto z \cdot \frac{\color{blue}{-4.5}}{\frac{a}{t}} \]

   9. Simplified 78.4%

      \[\leadsto z \cdot \color{blue}{\frac{-4.5}{\frac{a}{t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-90}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-4.5}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.1% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (-4.5d0) * (t * (z / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.2%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 44.7%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
4. Step-by-step derivation

   1. associate-/l* 49.1%

      \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

5. Simplified 49.1%

   \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]

6. Final simplification 49.1%

   \[\leadsto -4.5 \cdot \left(t \cdot \frac{z}{a}\right) \]
7. Add Preprocessing

Developer target: 93.3% accurate, 0.5× 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 2024115 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :alt
  (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)))