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

Percentage Accurate: 90.9% → 92.7%

Time: 10.3s

Alternatives: 10

Speedup: 0.6×

• 28.4% 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: 90.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{0.5}{a} \cdot \left(x \cdot y - 9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+266}:\\ \;\;\;\;\frac{y}{a} \cdot \frac{x}{2}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-237}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+237}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2}\\ \end{array} \end{array} \]

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 (* (/ 0.5 a) (- (* x y) (* 9.0 (* z t))))))
   (if (<= (* x y) -4e+266)
     (* (/ y a) (/ x 2.0))
     (if (<= (* x y) -1e-170)
       t_1
       (if (<= (* x y) 1e-237)
         (* (/ z a) (* t -4.5))
         (if (<= (* x y) 2e+237) t_1 (* (/ x a) (/ y 2.0))))))))

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 = (0.5 / a) * ((x * y) - (9.0 * (z * t)));
	double tmp;
	if ((x * y) <= -4e+266) {
		tmp = (y / a) * (x / 2.0);
	} else if ((x * y) <= -1e-170) {
		tmp = t_1;
	} else if ((x * y) <= 1e-237) {
		tmp = (z / a) * (t * -4.5);
	} else if ((x * y) <= 2e+237) {
		tmp = t_1;
	} else {
		tmp = (x / a) * (y / 2.0);
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (0.5d0 / a) * ((x * y) - (9.0d0 * (z * t)))
    if ((x * y) <= (-4d+266)) then
        tmp = (y / a) * (x / 2.0d0)
    else if ((x * y) <= (-1d-170)) then
        tmp = t_1
    else if ((x * y) <= 1d-237) then
        tmp = (z / a) * (t * (-4.5d0))
    else if ((x * y) <= 2d+237) then
        tmp = t_1
    else
        tmp = (x / a) * (y / 2.0d0)
    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 t_1 = (0.5 / a) * ((x * y) - (9.0 * (z * t)));
	double tmp;
	if ((x * y) <= -4e+266) {
		tmp = (y / a) * (x / 2.0);
	} else if ((x * y) <= -1e-170) {
		tmp = t_1;
	} else if ((x * y) <= 1e-237) {
		tmp = (z / a) * (t * -4.5);
	} else if ((x * y) <= 2e+237) {
		tmp = t_1;
	} else {
		tmp = (x / a) * (y / 2.0);
	}
	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 = (0.5 / a) * ((x * y) - (9.0 * (z * t)))
	tmp = 0
	if (x * y) <= -4e+266:
		tmp = (y / a) * (x / 2.0)
	elif (x * y) <= -1e-170:
		tmp = t_1
	elif (x * y) <= 1e-237:
		tmp = (z / a) * (t * -4.5)
	elif (x * y) <= 2e+237:
		tmp = t_1
	else:
		tmp = (x / a) * (y / 2.0)
	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(0.5 / a) * Float64(Float64(x * y) - Float64(9.0 * Float64(z * t))))
	tmp = 0.0
	if (Float64(x * y) <= -4e+266)
		tmp = Float64(Float64(y / a) * Float64(x / 2.0));
	elseif (Float64(x * y) <= -1e-170)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-237)
		tmp = Float64(Float64(z / a) * Float64(t * -4.5));
	elseif (Float64(x * y) <= 2e+237)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / a) * Float64(y / 2.0));
	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 = (0.5 / a) * ((x * y) - (9.0 * (z * t)));
	tmp = 0.0;
	if ((x * y) <= -4e+266)
		tmp = (y / a) * (x / 2.0);
	elseif ((x * y) <= -1e-170)
		tmp = t_1;
	elseif ((x * y) <= 1e-237)
		tmp = (z / a) * (t * -4.5);
	elseif ((x * y) <= 2e+237)
		tmp = t_1;
	else
		tmp = (x / a) * (y / 2.0);
	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[(0.5 / a), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e+266], N[(N[(y / a), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-170], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-237], N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+237], t$95$1, N[(N[(x / a), $MachinePrecision] * N[(y / 2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.0000000000000001e266

   1. Initial program 54.4%

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

   3. Taylor expanded in x around inf 59.7%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 59.7%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]

      2. times-frac 90.6%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \frac{x}{2}} \]

   5. Applied egg-rr 90.6%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \frac{x}{2}} \]

   if -4.0000000000000001e266 < (*.f64 x y) < -9.99999999999999983e-171 or 9.9999999999999999e-238 < (*.f64 x y) < 1.99999999999999988e237

   1. Initial program 97.2%

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

      1. div-inv 97.1%

         \[\leadsto \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{1}{a \cdot 2}} \]

      2. *-commutative 97.1%

         \[\leadsto \color{blue}{\frac{1}{a \cdot 2} \cdot \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)} \]

      3. *-commutative 97.1%

         \[\leadsto \frac{1}{\color{blue}{2 \cdot a}} \cdot \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \]

      4. associate-/r* 97.1%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{a}} \cdot \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \]

      5. metadata-eval 97.1%

         \[\leadsto \frac{\color{blue}{0.5}}{a} \cdot \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \]

      6. *-commutative 97.1%

         \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y - \color{blue}{\left(9 \cdot z\right)} \cdot t\right) \]

      7. associate-*l* 97.2%

         \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y - \color{blue}{9 \cdot \left(z \cdot t\right)}\right) \]

   4. Applied egg-rr 97.2%

      \[\leadsto \color{blue}{\frac{0.5}{a} \cdot \left(x \cdot y - 9 \cdot \left(z \cdot t\right)\right)} \]

   if -9.99999999999999983e-171 < (*.f64 x y) < 9.9999999999999999e-238

   1. Initial program 89.0%

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

   3. Taylor expanded in x around 0 88.7%

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

      1. associate-/l* 96.3%

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

   5. Simplified 96.3%

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

      1. associate-*r* 96.4%

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

   7. Applied egg-rr 96.4%

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

   if 1.99999999999999988e237 < (*.f64 x y)

   1. Initial program 78.2%

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

   3. Taylor expanded in x around inf 78.2%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 78.2%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]

      2. *-commutative 78.2%

         \[\leadsto \frac{y \cdot x}{\color{blue}{2 \cdot a}} \]

      3. times-frac 96.1%

         \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   5. Applied egg-rr 96.1%

      \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+266}:\\ \;\;\;\;\frac{y}{a} \cdot \frac{x}{2}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-170}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y - 9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-237}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+237}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y - 9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+224}\right):\\ \;\;\;\;\frac{x \cdot \frac{y}{z} + t \cdot -9}{a} \cdot \frac{z}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \end{array} \]

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)) (* a 2.0))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+224)))
     (* (/ (+ (* x (/ y z)) (* t -9.0)) a) (/ z 2.0))
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)))))

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)) / (a * 2.0);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+224)) {
		tmp = (((x * (y / z)) + (t * -9.0)) / a) * (z / 2.0);
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	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)) / (a * 2.0);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+224)) {
		tmp = (((x * (y / z)) + (t * -9.0)) / a) * (z / 2.0);
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	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)) / (a * 2.0)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+224):
		tmp = (((x * (y / z)) + (t * -9.0)) / a) * (z / 2.0)
	else:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	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(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+224))
		tmp = Float64(Float64(Float64(Float64(x * Float64(y / z)) + Float64(t * -9.0)) / a) * Float64(z / 2.0));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	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)) / (a * 2.0);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+224)))
		tmp = (((x * (y / z)) + (t * -9.0)) / a) * (z / 2.0);
	else
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	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[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+224]], $MachinePrecision]], N[(N[(N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(t * -9.0), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * N[(z / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) (*.f64 a #s(literal 2 binary64))) < -inf.0 or 4.99999999999999964e224 < (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) (*.f64 a #s(literal 2 binary64)))

   1. Initial program 79.1%

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

   3. Taylor expanded in z around inf 79.2%

      \[\leadsto \frac{\color{blue}{z \cdot \left(\frac{x \cdot y}{z} - 9 \cdot t\right)}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 79.2%

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

      2. times-frac 86.7%

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

      3. cancel-sign-sub-inv 86.7%

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

      4. associate-/l* 92.6%

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

      5. metadata-eval 92.6%

         \[\leadsto \frac{x \cdot \frac{y}{z} + \color{blue}{-9} \cdot t}{a} \cdot \frac{z}{2} \]

   5. Applied egg-rr 92.6%

      \[\leadsto \color{blue}{\frac{x \cdot \frac{y}{z} + -9 \cdot t}{a} \cdot \frac{z}{2}} \]

   if -inf.0 < (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) (*.f64 a #s(literal 2 binary64))) < 4.99999999999999964e224

   1. Initial program 98.3%

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

      1. associate-*l* 98.3%

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

      2. *-commutative 98.3%

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

   4. Applied egg-rr 98.3%

      \[\leadsto \frac{x \cdot y - \color{blue}{\left(9 \cdot t\right) \cdot z}}{a \cdot 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \leq -\infty \lor \neg \left(\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \leq 5 \cdot 10^{+224}\right):\\ \;\;\;\;\frac{x \cdot \frac{y}{z} + t \cdot -9}{a} \cdot \frac{z}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1.5 \cdot 10^{+253}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right) - \left(t \cdot \frac{z}{a}\right) \cdot 4.5\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+281}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z} + t \cdot -9}{a} \cdot \frac{z}{2}\\ \end{array} \end{array} \]

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 -1.5e+253)
     (- (* y (* 0.5 (/ x a))) (* (* t (/ z a)) 4.5))
     (if (<= t_1 5e+281)
       (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
       (* (/ (+ (* x (/ y z)) (* t -9.0)) a) (/ z 2.0))))))

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 <= -1.5e+253) {
		tmp = (y * (0.5 * (x / a))) - ((t * (z / a)) * 4.5);
	} else if (t_1 <= 5e+281) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = (((x * (y / z)) + (t * -9.0)) / a) * (z / 2.0);
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - ((z * 9.0d0) * t)
    if (t_1 <= (-1.5d+253)) then
        tmp = (y * (0.5d0 * (x / a))) - ((t * (z / a)) * 4.5d0)
    else if (t_1 <= 5d+281) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = (((x * (y / z)) + (t * (-9.0d0))) / a) * (z / 2.0d0)
    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 t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -1.5e+253) {
		tmp = (y * (0.5 * (x / a))) - ((t * (z / a)) * 4.5);
	} else if (t_1 <= 5e+281) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = (((x * (y / z)) + (t * -9.0)) / a) * (z / 2.0);
	}
	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 <= -1.5e+253:
		tmp = (y * (0.5 * (x / a))) - ((t * (z / a)) * 4.5)
	elif t_1 <= 5e+281:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = (((x * (y / z)) + (t * -9.0)) / a) * (z / 2.0)
	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 <= -1.5e+253)
		tmp = Float64(Float64(y * Float64(0.5 * Float64(x / a))) - Float64(Float64(t * Float64(z / a)) * 4.5));
	elseif (t_1 <= 5e+281)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(Float64(x * Float64(y / z)) + Float64(t * -9.0)) / a) * Float64(z / 2.0));
	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 <= -1.5e+253)
		tmp = (y * (0.5 * (x / a))) - ((t * (z / a)) * 4.5);
	elseif (t_1 <= 5e+281)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = (((x * (y / z)) + (t * -9.0)) / a) * (z / 2.0);
	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, -1.5e+253], N[(N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] * 4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+281], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(t * -9.0), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * N[(z / 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -1.4999999999999999e253

   1. Initial program 67.2%

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

      1. associate-*l* 67.2%

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

      2. *-commutative 67.2%

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

   4. Applied egg-rr 67.2%

      \[\leadsto \frac{x \cdot y - \color{blue}{\left(9 \cdot t\right) \cdot z}}{a \cdot 2} \]
   5. Step-by-step derivation

      1. div-sub 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-*r/ 76.2%

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

      4. *-un-lft-identity 76.2%

         \[\leadsto y \cdot \frac{\color{blue}{1 \cdot x}}{a \cdot 2} - \frac{\left(9 \cdot t\right) \cdot z}{a \cdot 2} \]

      5. *-commutative 76.2%

         \[\leadsto y \cdot \frac{1 \cdot x}{\color{blue}{2 \cdot a}} - \frac{\left(9 \cdot t\right) \cdot z}{a \cdot 2} \]

      6. times-frac 76.2%

         \[\leadsto y \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{x}{a}\right)} - \frac{\left(9 \cdot t\right) \cdot z}{a \cdot 2} \]

      7. metadata-eval 76.2%

         \[\leadsto y \cdot \left(\color{blue}{0.5} \cdot \frac{x}{a}\right) - \frac{\left(9 \cdot t\right) \cdot z}{a \cdot 2} \]

      8. associate-*l* 76.3%

         \[\leadsto y \cdot \left(0.5 \cdot \frac{x}{a}\right) - \frac{\color{blue}{9 \cdot \left(t \cdot z\right)}}{a \cdot 2} \]

      9. *-commutative 76.3%

         \[\leadsto y \cdot \left(0.5 \cdot \frac{x}{a}\right) - \frac{9 \cdot \color{blue}{\left(z \cdot t\right)}}{a \cdot 2} \]

      10. *-commutative 76.3%

          \[\leadsto y \cdot \left(0.5 \cdot \frac{x}{a}\right) - \frac{\color{blue}{\left(z \cdot t\right) \cdot 9}}{a \cdot 2} \]

      11. times-frac 76.3%

          \[\leadsto y \cdot \left(0.5 \cdot \frac{x}{a}\right) - \color{blue}{\frac{z \cdot t}{a} \cdot \frac{9}{2}} \]

      12. *-commutative 76.3%

          \[\leadsto y \cdot \left(0.5 \cdot \frac{x}{a}\right) - \frac{\color{blue}{t \cdot z}}{a} \cdot \frac{9}{2} \]

      13. associate-*r/ 94.8%

          \[\leadsto y \cdot \left(0.5 \cdot \frac{x}{a}\right) - \color{blue}{\left(t \cdot \frac{z}{a}\right)} \cdot \frac{9}{2} \]

      14. metadata-eval 94.8%

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

   6. Applied egg-rr 94.8%

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

   if -1.4999999999999999e253 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 5.00000000000000016e281

   1. Initial program 98.6%

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

      1. associate-*l* 98.6%

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

      2. *-commutative 98.6%

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

   4. Applied egg-rr 98.6%

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

   if 5.00000000000000016e281 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 73.6%

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

   3. Taylor expanded in z around inf 76.4%

      \[\leadsto \frac{\color{blue}{z \cdot \left(\frac{x \cdot y}{z} - 9 \cdot t\right)}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 76.4%

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

      2. times-frac 81.0%

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

      3. cancel-sign-sub-inv 81.0%

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

      4. associate-/l* 92.9%

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

      5. metadata-eval 92.9%

         \[\leadsto \frac{x \cdot \frac{y}{z} + \color{blue}{-9} \cdot t}{a} \cdot \frac{z}{2} \]

   5. Applied egg-rr 92.9%

      \[\leadsto \color{blue}{\frac{x \cdot \frac{y}{z} + -9 \cdot t}{a} \cdot \frac{z}{2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -1.5 \cdot 10^{+253}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right) - \left(t \cdot \frac{z}{a}\right) \cdot 4.5\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+281}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z} + t \cdot -9}{a} \cdot \frac{z}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 4 \cdot 10^{+244}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \end{array} \end{array} \]

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 (<= (* (* z 9.0) t) 4e+244)
   (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
   (* (* t (/ z a)) -4.5)))

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 (((z * 9.0) * t) <= 4e+244) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = (t * (z / a)) * -4.5;
	}
	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 (((z * 9.0d0) * t) <= 4d+244) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = (t * (z / a)) * (-4.5d0)
    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 (((z * 9.0) * t) <= 4e+244) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = (t * (z / a)) * -4.5;
	}
	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 ((z * 9.0) * t) <= 4e+244:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = (t * (z / a)) * -4.5
	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(Float64(z * 9.0) * t) <= 4e+244)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(t * Float64(z / a)) * -4.5);
	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 (((z * 9.0) * t) <= 4e+244)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = (t * (z / a)) * -4.5;
	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[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision], 4e+244], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 4.0000000000000003e244

   1. Initial program 92.4%

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

      1. associate-*l* 92.4%

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

      2. *-commutative 92.4%

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

   4. Applied egg-rr 92.4%

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

   if 4.0000000000000003e244 < (*.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 x around 0 70.2%

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

      1. associate-/l* 99.8%

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

   5. Simplified 99.8%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 4 \cdot 10^{+244}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+74} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-69}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \end{array} \end{array} \]

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 (or (<= (* x y) -1e+74) (not (<= (* x y) 5e-69)))
   (* 0.5 (/ x (/ a y)))
   (* (/ z a) (* t -4.5))))

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) <= -1e+74) || !((x * y) <= 5e-69)) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = (z / a) * (t * -4.5);
	}
	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) <= (-1d+74)) .or. (.not. ((x * y) <= 5d-69))) then
        tmp = 0.5d0 * (x / (a / y))
    else
        tmp = (z / a) * (t * (-4.5d0))
    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) <= -1e+74) || !((x * y) <= 5e-69)) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = (z / a) * (t * -4.5);
	}
	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) <= -1e+74) or not ((x * y) <= 5e-69):
		tmp = 0.5 * (x / (a / y))
	else:
		tmp = (z / a) * (t * -4.5)
	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) <= -1e+74) || !(Float64(x * y) <= 5e-69))
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	else
		tmp = Float64(Float64(z / a) * Float64(t * -4.5));
	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) <= -1e+74) || ~(((x * y) <= 5e-69)))
		tmp = 0.5 * (x / (a / y));
	else
		tmp = (z / a) * (t * -4.5);
	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[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+74], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e-69]], $MachinePrecision]], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.99999999999999952e73 or 5.00000000000000033e-69 < (*.f64 x y)

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf 67.1%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 67.1%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]

      2. *-commutative 67.1%

         \[\leadsto \frac{y \cdot x}{\color{blue}{2 \cdot a}} \]

      3. times-frac 72.1%

         \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   5. Applied egg-rr 72.1%

      \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   6. Taylor expanded in y around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*r/ 72.1%

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

      3. *-commutative 72.1%

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

      4. /-rgt-identity 72.1%

         \[\leadsto 0.5 \cdot \left(\color{blue}{\frac{\frac{x}{a}}{1}} \cdot y\right) \]

      5. associate-/r/ 72.0%

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

      6. associate-/l/ 73.5%

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

      7. associate-*l/ 73.6%

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

      8. *-lft-identity 73.6%

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

   8. Simplified 73.6%

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

   if -9.99999999999999952e73 < (*.f64 x y) < 5.00000000000000033e-69

   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 78.0%

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

      1. associate-/l* 80.8%

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

   5. Simplified 80.8%

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

      1. associate-*r* 80.9%

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

   7. Applied egg-rr 80.9%

      \[\leadsto \color{blue}{\left(-4.5 \cdot t\right) \cdot \frac{z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+74} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-69}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+74}:\\ \;\;\;\;\frac{y}{a} \cdot \frac{x}{2}\\ \mathbf{elif}\;x \cdot y \leq 0.2:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \end{array} \end{array} \]

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) -1e+74)
   (* (/ y a) (/ x 2.0))
   (if (<= (* x y) 0.2) (* (/ z a) (* t -4.5)) (/ (* y 0.5) (/ a x)))))

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) <= -1e+74) {
		tmp = (y / a) * (x / 2.0);
	} else if ((x * y) <= 0.2) {
		tmp = (z / a) * (t * -4.5);
	} else {
		tmp = (y * 0.5) / (a / x);
	}
	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) <= (-1d+74)) then
        tmp = (y / a) * (x / 2.0d0)
    else if ((x * y) <= 0.2d0) then
        tmp = (z / a) * (t * (-4.5d0))
    else
        tmp = (y * 0.5d0) / (a / x)
    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) <= -1e+74) {
		tmp = (y / a) * (x / 2.0);
	} else if ((x * y) <= 0.2) {
		tmp = (z / a) * (t * -4.5);
	} else {
		tmp = (y * 0.5) / (a / x);
	}
	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) <= -1e+74:
		tmp = (y / a) * (x / 2.0)
	elif (x * y) <= 0.2:
		tmp = (z / a) * (t * -4.5)
	else:
		tmp = (y * 0.5) / (a / x)
	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) <= -1e+74)
		tmp = Float64(Float64(y / a) * Float64(x / 2.0));
	elseif (Float64(x * y) <= 0.2)
		tmp = Float64(Float64(z / a) * Float64(t * -4.5));
	else
		tmp = Float64(Float64(y * 0.5) / Float64(a / x));
	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) <= -1e+74)
		tmp = (y / a) * (x / 2.0);
	elseif ((x * y) <= 0.2)
		tmp = (z / a) * (t * -4.5);
	else
		tmp = (y * 0.5) / (a / x);
	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], -1e+74], N[(N[(y / a), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.2], N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999952e73

   1. Initial program 79.9%

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

   3. Taylor expanded in x around inf 63.9%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 63.9%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]

      2. times-frac 77.4%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \frac{x}{2}} \]

   5. Applied egg-rr 77.4%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \frac{x}{2}} \]

   if -9.99999999999999952e73 < (*.f64 x y) < 0.20000000000000001

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0 74.2%

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

      1. associate-/l* 77.4%

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

   5. Simplified 77.4%

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

      1. associate-*r* 77.4%

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

   7. Applied egg-rr 77.4%

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

   if 0.20000000000000001 < (*.f64 x y)

   1. Initial program 89.6%

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

   3. Taylor expanded in x around inf 74.8%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 74.8%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]

      2. *-commutative 74.8%

         \[\leadsto \frac{y \cdot x}{\color{blue}{2 \cdot a}} \]

      3. times-frac 77.7%

         \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   5. Applied egg-rr 77.7%

      \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]
   6. Step-by-step derivation

      1. clear-num 77.7%

         \[\leadsto \frac{y}{2} \cdot \color{blue}{\frac{1}{\frac{a}{x}}} \]

      2. un-div-inv 77.7%

         \[\leadsto \color{blue}{\frac{\frac{y}{2}}{\frac{a}{x}}} \]

      3. div-inv 77.7%

         \[\leadsto \frac{\color{blue}{y \cdot \frac{1}{2}}}{\frac{a}{x}} \]

      4. metadata-eval 77.7%

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

   7. Applied egg-rr 77.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+74}:\\ \;\;\;\;\frac{y}{a} \cdot \frac{x}{2}\\ \mathbf{elif}\;x \cdot y \leq 0.2:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+74}:\\ \;\;\;\;\frac{y}{a} \cdot \frac{x}{2}\\ \mathbf{elif}\;x \cdot y \leq 0.2:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2}\\ \end{array} \end{array} \]

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) -1e+74)
   (* (/ y a) (/ x 2.0))
   (if (<= (* x y) 0.2) (* (/ z a) (* t -4.5)) (* (/ x a) (/ y 2.0)))))

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) <= -1e+74) {
		tmp = (y / a) * (x / 2.0);
	} else if ((x * y) <= 0.2) {
		tmp = (z / a) * (t * -4.5);
	} else {
		tmp = (x / a) * (y / 2.0);
	}
	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) <= (-1d+74)) then
        tmp = (y / a) * (x / 2.0d0)
    else if ((x * y) <= 0.2d0) then
        tmp = (z / a) * (t * (-4.5d0))
    else
        tmp = (x / a) * (y / 2.0d0)
    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) <= -1e+74) {
		tmp = (y / a) * (x / 2.0);
	} else if ((x * y) <= 0.2) {
		tmp = (z / a) * (t * -4.5);
	} else {
		tmp = (x / a) * (y / 2.0);
	}
	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) <= -1e+74:
		tmp = (y / a) * (x / 2.0)
	elif (x * y) <= 0.2:
		tmp = (z / a) * (t * -4.5)
	else:
		tmp = (x / a) * (y / 2.0)
	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) <= -1e+74)
		tmp = Float64(Float64(y / a) * Float64(x / 2.0));
	elseif (Float64(x * y) <= 0.2)
		tmp = Float64(Float64(z / a) * Float64(t * -4.5));
	else
		tmp = Float64(Float64(x / a) * Float64(y / 2.0));
	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) <= -1e+74)
		tmp = (y / a) * (x / 2.0);
	elseif ((x * y) <= 0.2)
		tmp = (z / a) * (t * -4.5);
	else
		tmp = (x / a) * (y / 2.0);
	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], -1e+74], N[(N[(y / a), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.2], N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * N[(y / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999952e73

   1. Initial program 79.9%

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

   3. Taylor expanded in x around inf 63.9%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 63.9%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]

      2. times-frac 77.4%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \frac{x}{2}} \]

   5. Applied egg-rr 77.4%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \frac{x}{2}} \]

   if -9.99999999999999952e73 < (*.f64 x y) < 0.20000000000000001

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0 74.2%

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

      1. associate-/l* 77.4%

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

   5. Simplified 77.4%

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

      1. associate-*r* 77.4%

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

   7. Applied egg-rr 77.4%

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

   if 0.20000000000000001 < (*.f64 x y)

   1. Initial program 89.6%

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

   3. Taylor expanded in x around inf 74.8%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 74.8%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]

      2. *-commutative 74.8%

         \[\leadsto \frac{y \cdot x}{\color{blue}{2 \cdot a}} \]

      3. times-frac 77.7%

         \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   5. Applied egg-rr 77.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+74}:\\ \;\;\;\;\frac{y}{a} \cdot \frac{x}{2}\\ \mathbf{elif}\;x \cdot y \leq 0.2:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+74}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 0.2:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2}\\ \end{array} \end{array} \]

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) -1e+74)
   (* 0.5 (/ x (/ a y)))
   (if (<= (* x y) 0.2) (* (/ z a) (* t -4.5)) (* (/ x a) (/ y 2.0)))))

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) <= -1e+74) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= 0.2) {
		tmp = (z / a) * (t * -4.5);
	} else {
		tmp = (x / a) * (y / 2.0);
	}
	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) <= (-1d+74)) then
        tmp = 0.5d0 * (x / (a / y))
    else if ((x * y) <= 0.2d0) then
        tmp = (z / a) * (t * (-4.5d0))
    else
        tmp = (x / a) * (y / 2.0d0)
    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) <= -1e+74) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= 0.2) {
		tmp = (z / a) * (t * -4.5);
	} else {
		tmp = (x / a) * (y / 2.0);
	}
	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) <= -1e+74:
		tmp = 0.5 * (x / (a / y))
	elif (x * y) <= 0.2:
		tmp = (z / a) * (t * -4.5)
	else:
		tmp = (x / a) * (y / 2.0)
	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) <= -1e+74)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (Float64(x * y) <= 0.2)
		tmp = Float64(Float64(z / a) * Float64(t * -4.5));
	else
		tmp = Float64(Float64(x / a) * Float64(y / 2.0));
	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) <= -1e+74)
		tmp = 0.5 * (x / (a / y));
	elseif ((x * y) <= 0.2)
		tmp = (z / a) * (t * -4.5);
	else
		tmp = (x / a) * (y / 2.0);
	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], -1e+74], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.2], N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * N[(y / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999952e73

   1. Initial program 79.9%

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

   3. Taylor expanded in x around inf 63.9%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 63.9%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]

      2. *-commutative 63.9%

         \[\leadsto \frac{y \cdot x}{\color{blue}{2 \cdot a}} \]

      3. times-frac 75.4%

         \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   5. Applied egg-rr 75.4%

      \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   6. Taylor expanded in y around 0 63.9%

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

      1. *-commutative 63.9%

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

      2. associate-*r/ 75.4%

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

      3. *-commutative 75.4%

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

      4. /-rgt-identity 75.4%

         \[\leadsto 0.5 \cdot \left(\color{blue}{\frac{\frac{x}{a}}{1}} \cdot y\right) \]

      5. associate-/r/ 75.4%

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

      6. associate-/l/ 77.4%

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

      7. associate-*l/ 77.5%

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

      8. *-lft-identity 77.5%

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

   8. Simplified 77.5%

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

   if -9.99999999999999952e73 < (*.f64 x y) < 0.20000000000000001

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0 74.2%

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

      1. associate-/l* 77.4%

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

   5. Simplified 77.4%

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

      1. associate-*r* 77.4%

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

   7. Applied egg-rr 77.4%

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

   if 0.20000000000000001 < (*.f64 x y)

   1. Initial program 89.6%

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

   3. Taylor expanded in x around inf 74.8%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 74.8%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]

      2. *-commutative 74.8%

         \[\leadsto \frac{y \cdot x}{\color{blue}{2 \cdot a}} \]

      3. times-frac 77.7%

         \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   5. Applied egg-rr 77.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+74}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 0.2:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+103} \lor \neg \left(x \leq 1.8 \cdot 10^{-150}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \end{array} \end{array} \]

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 (or (<= x -2.3e+103) (not (<= x 1.8e-150)))
   (* 0.5 (/ x (/ a y)))
   (* (* t (/ z a)) -4.5)))

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 <= -2.3e+103) || !(x <= 1.8e-150)) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = (t * (z / a)) * -4.5;
	}
	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 <= (-2.3d+103)) .or. (.not. (x <= 1.8d-150))) then
        tmp = 0.5d0 * (x / (a / y))
    else
        tmp = (t * (z / a)) * (-4.5d0)
    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 <= -2.3e+103) || !(x <= 1.8e-150)) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = (t * (z / a)) * -4.5;
	}
	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 <= -2.3e+103) or not (x <= 1.8e-150):
		tmp = 0.5 * (x / (a / y))
	else:
		tmp = (t * (z / a)) * -4.5
	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 ((x <= -2.3e+103) || !(x <= 1.8e-150))
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	else
		tmp = Float64(Float64(t * Float64(z / a)) * -4.5);
	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 <= -2.3e+103) || ~((x <= 1.8e-150)))
		tmp = 0.5 * (x / (a / y));
	else
		tmp = (t * (z / a)) * -4.5;
	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[Or[LessEqual[x, -2.3e+103], N[Not[LessEqual[x, 1.8e-150]], $MachinePrecision]], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.30000000000000008e103 or 1.8000000000000001e-150 < x

   1. Initial program 86.5%

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

   3. Taylor expanded in x around inf 54.4%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]
   4. Step-by-step derivation

      1. *-commutative 54.4%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]

      2. *-commutative 54.4%

         \[\leadsto \frac{y \cdot x}{\color{blue}{2 \cdot a}} \]

      3. times-frac 61.3%

         \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   5. Applied egg-rr 61.3%

      \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   6. Taylor expanded in y around 0 54.4%

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

      1. *-commutative 54.4%

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

      2. associate-*r/ 61.3%

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

      3. *-commutative 61.3%

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

      4. /-rgt-identity 61.3%

         \[\leadsto 0.5 \cdot \left(\color{blue}{\frac{\frac{x}{a}}{1}} \cdot y\right) \]

      5. associate-/r/ 61.3%

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

      6. associate-/l/ 57.7%

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

      7. associate-*l/ 57.7%

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

      8. *-lft-identity 57.7%

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

   8. Simplified 57.7%

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

   if -2.30000000000000008e103 < x < 1.8000000000000001e-150

   1. Initial program 93.9%

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

   3. Taylor expanded in x around 0 69.5%

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

      1. associate-/l* 71.8%

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

   5. Simplified 71.8%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+103} \lor \neg \left(x \leq 1.8 \cdot 10^{-150}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.3% accurate, 1.9× speedup

Math

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

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

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) {
	return (t * (z / a)) * -4.5;
}

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 = (t * (z / a)) * (-4.5d0)
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 (t * (z / a)) * -4.5;
}

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

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

Derivation

1. Initial program 89.8%

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

3. Taylor expanded in x around 0 53.9%

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

   1. associate-/l* 56.4%

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

5. Simplified 56.4%

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

6. Final simplification 56.4%

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

Developer target: 93.1% 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 2024097 
(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)))