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

Percentage Accurate: 91.1% → 95.4%

Time: 8.6s

Alternatives: 9

Speedup: 0.5×

• 28.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.1% 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: 95.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+302}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - z \cdot \frac{t \cdot 4.5}{a}\\ \mathbf{elif}\;t\_1 \leq 10^{+306}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-4.5 \cdot \frac{z \cdot t}{y \cdot a} + 0.5 \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

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 -1e+302)
     (- (* x (/ y (* a 2.0))) (* z (/ (* t 4.5) a)))
     (if (<= t_1 1e+306)
       (/ t_1 (* a 2.0))
       (* y (+ (* -4.5 (/ (* z t) (* y a))) (* 0.5 (/ x 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 <= -1e+302) {
		tmp = (x * (y / (a * 2.0))) - (z * ((t * 4.5) / a));
	} else if (t_1 <= 1e+306) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - ((z * 9.0d0) * t)
    if (t_1 <= (-1d+302)) then
        tmp = (x * (y / (a * 2.0d0))) - (z * ((t * 4.5d0) / a))
    else if (t_1 <= 1d+306) then
        tmp = t_1 / (a * 2.0d0)
    else
        tmp = y * (((-4.5d0) * ((z * t) / (y * a))) + (0.5d0 * (x / 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 t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -1e+302) {
		tmp = (x * (y / (a * 2.0))) - (z * ((t * 4.5) / a));
	} else if (t_1 <= 1e+306) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / 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 <= -1e+302:
		tmp = (x * (y / (a * 2.0))) - (z * ((t * 4.5) / a))
	elif t_1 <= 1e+306:
		tmp = t_1 / (a * 2.0)
	else:
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / 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 <= -1e+302)
		tmp = Float64(Float64(x * Float64(y / Float64(a * 2.0))) - Float64(z * Float64(Float64(t * 4.5) / a)));
	elseif (t_1 <= 1e+306)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = Float64(y * Float64(Float64(-4.5 * Float64(Float64(z * t) / Float64(y * a))) + Float64(0.5 * Float64(x / 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 <= -1e+302)
		tmp = (x * (y / (a * 2.0))) - (z * ((t * 4.5) / a));
	elseif (t_1 <= 1e+306)
		tmp = t_1 / (a * 2.0);
	else
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / 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, -1e+302], N[(N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(t * 4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+306], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], 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]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -1.0000000000000001e302

   1. Initial program 68.5%

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

      1. div-sub 65.7%

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

      2. associate-/l* 81.2%

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

      3. associate-/l* 94.2%

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

   4. Applied egg-rr 94.2%

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

   5. Taylor expanded in z around 0 81.2%

      \[\leadsto x \cdot \frac{y}{a \cdot 2} - \color{blue}{4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \color{blue}{\frac{4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. metadata-eval 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{\color{blue}{\left(--4.5\right)} \cdot \left(t \cdot z\right)}{a} \]

      3. distribute-lft-neg-in 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{\color{blue}{--4.5 \cdot \left(t \cdot z\right)}}{a} \]

      4. associate-*r* 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{-\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      5. *-commutative 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{-\color{blue}{\left(t \cdot -4.5\right)} \cdot z}{a} \]

      6. *-commutative 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{-\color{blue}{z \cdot \left(t \cdot -4.5\right)}}{a} \]

      7. distribute-rgt-neg-in 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{\color{blue}{z \cdot \left(-t \cdot -4.5\right)}}{a} \]

      8. distribute-rgt-neg-in 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{z \cdot \color{blue}{\left(t \cdot \left(--4.5\right)\right)}}{a} \]

      9. metadata-eval 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{z \cdot \left(t \cdot \color{blue}{4.5}\right)}{a} \]

      10. associate-*r/ 94.3%

          \[\leadsto x \cdot \frac{y}{a \cdot 2} - \color{blue}{z \cdot \frac{t \cdot 4.5}{a}} \]

   7. Simplified 94.3%

      \[\leadsto x \cdot \frac{y}{a \cdot 2} - \color{blue}{z \cdot \frac{t \cdot 4.5}{a}} \]

   if -1.0000000000000001e302 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 1.00000000000000002e306

   1. Initial program 98.2%

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

   if 1.00000000000000002e306 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 62.6%

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

   3. Taylor expanded in y around inf 82.9%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -1 \cdot 10^{+302}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - z \cdot \frac{t \cdot 4.5}{a}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+306}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-4.5 \cdot \frac{z \cdot t}{y \cdot a} + 0.5 \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -1 \cdot 10^{+302}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - z \cdot \frac{t \cdot 4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \end{array} \end{array} \]

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
 (if (<= (- (* x y) (* (* z 9.0) t)) -1e+302)
   (- (* x (/ y (* a 2.0))) (* z (/ (* t 4.5) a)))
   (/ (fma x y (* z (* t -9.0))) (* 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 tmp;
	if (((x * y) - ((z * 9.0) * t)) <= -1e+302) {
		tmp = (x * (y / (a * 2.0))) - (z * ((t * 4.5) / a));
	} else {
		tmp = fma(x, y, (z * (t * -9.0))) / (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)
	tmp = 0.0
	if (Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) <= -1e+302)
		tmp = Float64(Float64(x * Float64(y / Float64(a * 2.0))) - Float64(z * Float64(Float64(t * 4.5) / a)));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	end
	return 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[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], -1e+302], N[(N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(t * 4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -1.0000000000000001e302

   1. Initial program 68.5%

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

      1. div-sub 65.7%

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

      2. associate-/l* 81.2%

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

      3. associate-/l* 94.2%

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

   4. Applied egg-rr 94.2%

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

   5. Taylor expanded in z around 0 81.2%

      \[\leadsto x \cdot \frac{y}{a \cdot 2} - \color{blue}{4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \color{blue}{\frac{4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. metadata-eval 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{\color{blue}{\left(--4.5\right)} \cdot \left(t \cdot z\right)}{a} \]

      3. distribute-lft-neg-in 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{\color{blue}{--4.5 \cdot \left(t \cdot z\right)}}{a} \]

      4. associate-*r* 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{-\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      5. *-commutative 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{-\color{blue}{\left(t \cdot -4.5\right)} \cdot z}{a} \]

      6. *-commutative 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{-\color{blue}{z \cdot \left(t \cdot -4.5\right)}}{a} \]

      7. distribute-rgt-neg-in 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{\color{blue}{z \cdot \left(-t \cdot -4.5\right)}}{a} \]

      8. distribute-rgt-neg-in 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{z \cdot \color{blue}{\left(t \cdot \left(--4.5\right)\right)}}{a} \]

      9. metadata-eval 81.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{z \cdot \left(t \cdot \color{blue}{4.5}\right)}{a} \]

      10. associate-*r/ 94.3%

          \[\leadsto x \cdot \frac{y}{a \cdot 2} - \color{blue}{z \cdot \frac{t \cdot 4.5}{a}} \]

   7. Simplified 94.3%

      \[\leadsto x \cdot \frac{y}{a \cdot 2} - \color{blue}{z \cdot \frac{t \cdot 4.5}{a}} \]

   if -1.0000000000000001e302 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 94.5%

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

      1. div-sub 92.2%

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

      2. *-commutative 92.2%

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

      3. div-sub 94.5%

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

      4. cancel-sign-sub-inv 94.5%

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

      5. *-commutative 94.5%

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

      6. fma-define 94.9%

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

      7. distribute-rgt-neg-in 94.9%

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

      8. associate-*r* 94.5%

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

      9. distribute-lft-neg-in 94.5%

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

      10. *-commutative 94.5%

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

      11. distribute-rgt-neg-in 94.5%

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

      12. metadata-eval 94.5%

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

   3. Simplified 94.5%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -1 \cdot 10^{+302}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - z \cdot \frac{t \cdot 4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+302} \lor \neg \left(t\_1 \leq 10^{+306}\right):\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - z \cdot \frac{t \cdot 4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \end{array} \end{array} \]

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))))
   (if (or (<= t_1 -1e+302) (not (<= t_1 1e+306)))
     (- (* x (/ y (* a 2.0))) (* z (/ (* t 4.5) a)))
     (/ t_1 (* 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);
	double tmp;
	if ((t_1 <= -1e+302) || !(t_1 <= 1e+306)) {
		tmp = (x * (y / (a * 2.0))) - (z * ((t * 4.5) / a));
	} else {
		tmp = t_1 / (a * 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 <= (-1d+302)) .or. (.not. (t_1 <= 1d+306))) then
        tmp = (x * (y / (a * 2.0d0))) - (z * ((t * 4.5d0) / a))
    else
        tmp = t_1 / (a * 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 <= -1e+302) || !(t_1 <= 1e+306)) {
		tmp = (x * (y / (a * 2.0))) - (z * ((t * 4.5) / a));
	} else {
		tmp = t_1 / (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)
	tmp = 0
	if (t_1 <= -1e+302) or not (t_1 <= 1e+306):
		tmp = (x * (y / (a * 2.0))) - (z * ((t * 4.5) / a))
	else:
		tmp = t_1 / (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(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= -1e+302) || !(t_1 <= 1e+306))
		tmp = Float64(Float64(x * Float64(y / Float64(a * 2.0))) - Float64(z * Float64(Float64(t * 4.5) / a)));
	else
		tmp = Float64(t_1 / 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);
	tmp = 0.0;
	if ((t_1 <= -1e+302) || ~((t_1 <= 1e+306)))
		tmp = (x * (y / (a * 2.0))) - (z * ((t * 4.5) / a));
	else
		tmp = t_1 / (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[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+302], N[Not[LessEqual[t$95$1, 1e+306]], $MachinePrecision]], N[(N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(t * 4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -1.0000000000000001e302 or 1.00000000000000002e306 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 66.2%

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

      1. div-sub 62.8%

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

      2. associate-/l* 80.2%

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

      3. associate-/l* 91.4%

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

   4. Applied egg-rr 91.4%

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

   5. Taylor expanded in z around 0 80.2%

      \[\leadsto x \cdot \frac{y}{a \cdot 2} - \color{blue}{4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 80.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \color{blue}{\frac{4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. metadata-eval 80.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{\color{blue}{\left(--4.5\right)} \cdot \left(t \cdot z\right)}{a} \]

      3. distribute-lft-neg-in 80.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{\color{blue}{--4.5 \cdot \left(t \cdot z\right)}}{a} \]

      4. associate-*r* 80.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{-\color{blue}{\left(-4.5 \cdot t\right) \cdot z}}{a} \]

      5. *-commutative 80.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{-\color{blue}{\left(t \cdot -4.5\right)} \cdot z}{a} \]

      6. *-commutative 80.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{-\color{blue}{z \cdot \left(t \cdot -4.5\right)}}{a} \]

      7. distribute-rgt-neg-in 80.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{\color{blue}{z \cdot \left(-t \cdot -4.5\right)}}{a} \]

      8. distribute-rgt-neg-in 80.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{z \cdot \color{blue}{\left(t \cdot \left(--4.5\right)\right)}}{a} \]

      9. metadata-eval 80.2%

         \[\leadsto x \cdot \frac{y}{a \cdot 2} - \frac{z \cdot \left(t \cdot \color{blue}{4.5}\right)}{a} \]

      10. associate-*r/ 91.4%

          \[\leadsto x \cdot \frac{y}{a \cdot 2} - \color{blue}{z \cdot \frac{t \cdot 4.5}{a}} \]

   7. Simplified 91.4%

      \[\leadsto x \cdot \frac{y}{a \cdot 2} - \color{blue}{z \cdot \frac{t \cdot 4.5}{a}} \]

   if -1.0000000000000001e302 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 1.00000000000000002e306

   1. Initial program 98.2%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -1 \cdot 10^{+302} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+306}\right):\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - z \cdot \frac{t \cdot 4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+82} \lor \neg \left(x \cdot y \leq -2 \cdot 10^{-40} \lor \neg \left(x \cdot y \leq -5 \cdot 10^{-70}\right) \land x \cdot y \leq 10^{-19}\right):\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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+82)
         (not
          (or (<= (* x y) -2e-40)
              (and (not (<= (* x y) -5e-70)) (<= (* x y) 1e-19)))))
   (* (/ x a) (/ y 2.0))
   (* -4.5 (/ (* z 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 tmp;
	if (((x * y) <= -1e+82) || !(((x * y) <= -2e-40) || (!((x * y) <= -5e-70) && ((x * y) <= 1e-19)))) {
		tmp = (x / a) * (y / 2.0);
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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+82)) .or. (.not. ((x * y) <= (-2d-40)) .or. (.not. ((x * y) <= (-5d-70))) .and. ((x * y) <= 1d-19))) then
        tmp = (x / a) * (y / 2.0d0)
    else
        tmp = (-4.5d0) * ((z * t) / 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 (((x * y) <= -1e+82) || !(((x * y) <= -2e-40) || (!((x * y) <= -5e-70) && ((x * y) <= 1e-19)))) {
		tmp = (x / a) * (y / 2.0);
	} else {
		tmp = -4.5 * ((z * 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):
	tmp = 0
	if ((x * y) <= -1e+82) or not (((x * y) <= -2e-40) or (not ((x * y) <= -5e-70) and ((x * y) <= 1e-19))):
		tmp = (x / a) * (y / 2.0)
	else:
		tmp = -4.5 * ((z * 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)
	tmp = 0.0
	if ((Float64(x * y) <= -1e+82) || !((Float64(x * y) <= -2e-40) || (!(Float64(x * y) <= -5e-70) && (Float64(x * y) <= 1e-19))))
		tmp = Float64(Float64(x / a) * Float64(y / 2.0));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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+82) || ~((((x * y) <= -2e-40) || (~(((x * y) <= -5e-70)) && ((x * y) <= 1e-19)))))
		tmp = (x / a) * (y / 2.0);
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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+82], N[Not[Or[LessEqual[N[(x * y), $MachinePrecision], -2e-40], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -5e-70]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 1e-19]]]], $MachinePrecision]], N[(N[(x / a), $MachinePrecision] * N[(y / 2.0), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.9999999999999996e81 or -1.9999999999999999e-40 < (*.f64 x y) < -4.9999999999999998e-70 or 9.9999999999999998e-20 < (*.f64 x y)

   1. Initial program 83.6%

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

      1. fma-neg 84.4%

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

      2. distribute-lft-neg-in 84.4%

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

      3. distribute-rgt-neg-in 84.4%

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

      4. metadata-eval 84.4%

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

      5. associate-*r* 84.4%

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

      6. *-commutative 84.4%

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

      7. *-un-lft-identity 84.4%

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

      8. add-sqr-sqrt 40.7%

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

      9. times-frac 40.8%

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

      10. *-commutative 40.8%

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

      11. associate-*r* 40.8%

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

      12. metadata-eval 40.8%

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

      13. distribute-rgt-neg-in 40.8%

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

      14. *-commutative 40.8%

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

      15. distribute-rgt-neg-in 40.8%

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

      16. metadata-eval 40.8%

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

   4. Applied egg-rr 40.8%

      \[\leadsto \color{blue}{\frac{1}{\sqrt{a \cdot 2}} \cdot \frac{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}{\sqrt{a \cdot 2}}} \]
   5. Step-by-step derivation

      1. associate-*l/ 40.8%

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

      2. *-lft-identity 40.8%

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

      3. associate-*r* 40.8%

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

      4. *-commutative 40.8%

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

      5. metadata-eval 40.8%

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

      6. distribute-lft-neg-in 40.8%

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

      7. distribute-lft-neg-in 40.8%

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

      8. metadata-eval 40.8%

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

      9. associate-*r* 40.8%

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

      10. *-commutative 40.8%

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

      11. *-commutative 40.8%

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

   6. Simplified 40.8%

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

   7. Taylor expanded in x around inf 69.8%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot {\left(\sqrt{2}\right)}^{2}}} \]
   8. Step-by-step derivation

      1. times-frac 74.7%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{y}{{\left(\sqrt{2}\right)}^{2}}} \]

      2. unpow2 74.7%

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

      3. rem-square-sqrt 75.4%

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

   9. Simplified 75.4%

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

   if -9.9999999999999996e81 < (*.f64 x y) < -1.9999999999999999e-40 or -4.9999999999999998e-70 < (*.f64 x y) < 9.9999999999999998e-20

   1. Initial program 97.4%

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

   3. Taylor expanded in x around 0 79.7%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+82} \lor \neg \left(x \cdot y \leq -2 \cdot 10^{-40} \lor \neg \left(x \cdot y \leq -5 \cdot 10^{-70}\right) \land x \cdot y \leq 10^{-19}\right):\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{a} \cdot \frac{y}{2}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-40}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;\neg \left(x \cdot y \leq -5 \cdot 10^{-70}\right) \land x \cdot y \leq 10^{-19}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 a) (/ y 2.0))))
   (if (<= (* x y) -1e+82)
     t_1
     (if (<= (* x y) -2e-40)
       (* -4.5 (/ (* z t) a))
       (if (and (not (<= (* x y) -5e-70)) (<= (* x y) 1e-19))
         (/ (* z (* t -4.5)) a)
         t_1)))))

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 / a) * (y / 2.0);
	double tmp;
	if ((x * y) <= -1e+82) {
		tmp = t_1;
	} else if ((x * y) <= -2e-40) {
		tmp = -4.5 * ((z * t) / a);
	} else if (!((x * y) <= -5e-70) && ((x * y) <= 1e-19)) {
		tmp = (z * (t * -4.5)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 / a) * (y / 2.0d0)
    if ((x * y) <= (-1d+82)) then
        tmp = t_1
    else if ((x * y) <= (-2d-40)) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if ((.not. ((x * y) <= (-5d-70))) .and. ((x * y) <= 1d-19)) then
        tmp = (z * (t * (-4.5d0))) / a
    else
        tmp = t_1
    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 / a) * (y / 2.0);
	double tmp;
	if ((x * y) <= -1e+82) {
		tmp = t_1;
	} else if ((x * y) <= -2e-40) {
		tmp = -4.5 * ((z * t) / a);
	} else if (!((x * y) <= -5e-70) && ((x * y) <= 1e-19)) {
		tmp = (z * (t * -4.5)) / a;
	} else {
		tmp = t_1;
	}
	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 / a) * (y / 2.0)
	tmp = 0
	if (x * y) <= -1e+82:
		tmp = t_1
	elif (x * y) <= -2e-40:
		tmp = -4.5 * ((z * t) / a)
	elif not ((x * y) <= -5e-70) and ((x * y) <= 1e-19):
		tmp = (z * (t * -4.5)) / a
	else:
		tmp = t_1
	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 / a) * Float64(y / 2.0))
	tmp = 0.0
	if (Float64(x * y) <= -1e+82)
		tmp = t_1;
	elseif (Float64(x * y) <= -2e-40)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (!(Float64(x * y) <= -5e-70) && (Float64(x * y) <= 1e-19))
		tmp = Float64(Float64(z * Float64(t * -4.5)) / a);
	else
		tmp = t_1;
	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 / a) * (y / 2.0);
	tmp = 0.0;
	if ((x * y) <= -1e+82)
		tmp = t_1;
	elseif ((x * y) <= -2e-40)
		tmp = -4.5 * ((z * t) / a);
	elseif (~(((x * y) <= -5e-70)) && ((x * y) <= 1e-19))
		tmp = (z * (t * -4.5)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 / a), $MachinePrecision] * N[(y / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+82], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2e-40], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -5e-70]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 1e-19]], N[(N[(z * N[(t * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.9999999999999996e81 or -1.9999999999999999e-40 < (*.f64 x y) < -4.9999999999999998e-70 or 9.9999999999999998e-20 < (*.f64 x y)

   1. Initial program 83.6%

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

      1. fma-neg 84.4%

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

      2. distribute-lft-neg-in 84.4%

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

      3. distribute-rgt-neg-in 84.4%

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

      4. metadata-eval 84.4%

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

      5. associate-*r* 84.4%

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

      6. *-commutative 84.4%

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

      7. *-un-lft-identity 84.4%

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

      8. add-sqr-sqrt 40.7%

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

      9. times-frac 40.8%

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

      10. *-commutative 40.8%

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

      11. associate-*r* 40.8%

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

      12. metadata-eval 40.8%

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

      13. distribute-rgt-neg-in 40.8%

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

      14. *-commutative 40.8%

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

      15. distribute-rgt-neg-in 40.8%

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

      16. metadata-eval 40.8%

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

   4. Applied egg-rr 40.8%

      \[\leadsto \color{blue}{\frac{1}{\sqrt{a \cdot 2}} \cdot \frac{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}{\sqrt{a \cdot 2}}} \]
   5. Step-by-step derivation

      1. associate-*l/ 40.8%

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

      2. *-lft-identity 40.8%

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

      3. associate-*r* 40.8%

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

      4. *-commutative 40.8%

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

      5. metadata-eval 40.8%

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

      6. distribute-lft-neg-in 40.8%

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

      7. distribute-lft-neg-in 40.8%

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

      8. metadata-eval 40.8%

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

      9. associate-*r* 40.8%

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

      10. *-commutative 40.8%

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

      11. *-commutative 40.8%

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

   6. Simplified 40.8%

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

   7. Taylor expanded in x around inf 69.8%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot {\left(\sqrt{2}\right)}^{2}}} \]
   8. Step-by-step derivation

      1. times-frac 74.7%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{y}{{\left(\sqrt{2}\right)}^{2}}} \]

      2. unpow2 74.7%

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

      3. rem-square-sqrt 75.4%

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

   9. Simplified 75.4%

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

   if -9.9999999999999996e81 < (*.f64 x y) < -1.9999999999999999e-40

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 68.1%

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

   if -4.9999999999999998e-70 < (*.f64 x y) < 9.9999999999999998e-20

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0 81.9%

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

      1. associate-*r/ 81.9%

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

      2. associate-*r* 81.1%

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

      3. associate-*l/ 74.7%

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

      4. associate-*r/ 75.5%

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

      5. *-commutative 75.5%

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

      6. associate-*r/ 74.7%

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

   5. Simplified 74.7%

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

      1. associate-*r/ 81.1%

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

      2. *-commutative 81.1%

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

   7. Applied egg-rr 81.1%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-40}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;\neg \left(x \cdot y \leq -5 \cdot 10^{-70}\right) \land x \cdot y \leq 10^{-19}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+302} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+276}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \end{array} \]

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
 (if (or (<= (* x y) -1e+302) (not (<= (* x y) 5e+276)))
   (* x (/ (* y 0.5) a))
   (/ (- (* 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 tmp;
	if (((x * y) <= -1e+302) || !((x * y) <= 5e+276)) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 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+302)) .or. (.not. ((x * y) <= 5d+276))) then
        tmp = x * ((y * 0.5d0) / a)
    else
        tmp = ((x * y) - ((z * 9.0d0) * t)) / (a * 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+302) || !((x * y) <= 5e+276)) {
		tmp = x * ((y * 0.5) / a);
	} 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):
	tmp = 0
	if ((x * y) <= -1e+302) or not ((x * y) <= 5e+276):
		tmp = x * ((y * 0.5) / a)
	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)
	tmp = 0.0
	if ((Float64(x * y) <= -1e+302) || !(Float64(x * y) <= 5e+276))
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * 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)
	tmp = 0.0;
	if (((x * y) <= -1e+302) || ~(((x * y) <= 5e+276)))
		tmp = x * ((y * 0.5) / a);
	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_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+302], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+276]], $MachinePrecision]], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.0000000000000001e302 or 5.00000000000000001e276 < (*.f64 x y)

   1. Initial program 57.4%

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

   3. Taylor expanded in x around inf 62.6%

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

      1. *-commutative 62.6%

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

      2. associate-/l* 92.6%

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

      3. associate-*r* 92.6%

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

      4. *-commutative 92.6%

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

      5. associate-*r/ 92.6%

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

   5. Simplified 92.6%

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

   if -1.0000000000000001e302 < (*.f64 x y) < 5.00000000000000001e276

   1. Initial program 96.6%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+302} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+276}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-13} \lor \neg \left(y \leq 5.4 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

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 (or (<= y -2.25e-13) (not (<= y 5.4e-13)))
   (* x (/ (* y 0.5) a))
   (* -4.5 (/ z (/ 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 ((y <= -2.25e-13) || !(y <= 5.4e-13)) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = -4.5 * (z / (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 ((y <= (-2.25d-13)) .or. (.not. (y <= 5.4d-13))) then
        tmp = x * ((y * 0.5d0) / a)
    else
        tmp = (-4.5d0) * (z / (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 ((y <= -2.25e-13) || !(y <= 5.4e-13)) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = -4.5 * (z / (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 (y <= -2.25e-13) or not (y <= 5.4e-13):
		tmp = x * ((y * 0.5) / a)
	else:
		tmp = -4.5 * (z / (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 ((y <= -2.25e-13) || !(y <= 5.4e-13))
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = Float64(-4.5 * Float64(z / 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 ((y <= -2.25e-13) || ~((y <= 5.4e-13)))
		tmp = x * ((y * 0.5) / a);
	else
		tmp = -4.5 * (z / (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[Or[LessEqual[y, -2.25e-13], N[Not[LessEqual[y, 5.4e-13]], $MachinePrecision]], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.25e-13 or 5.40000000000000021e-13 < y

   1. Initial program 86.0%

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

   3. Taylor expanded in x around inf 60.3%

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

      1. *-commutative 60.3%

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

      2. associate-/l* 71.9%

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

      3. associate-*r* 71.9%

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

      4. *-commutative 71.9%

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

      5. associate-*r/ 71.9%

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

   5. Simplified 71.9%

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

   if -2.25e-13 < y < 5.40000000000000021e-13

   1. Initial program 96.4%

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

   3. Taylor expanded in x around 0 72.7%

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

      1. associate-*r/ 72.7%

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

      2. associate-*r* 71.9%

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

      3. associate-*l/ 66.8%

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

      4. associate-*r/ 67.5%

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

      5. *-commutative 67.5%

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

      6. associate-*r/ 66.8%

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

   5. Simplified 66.8%

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

      1. clear-num 66.4%

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

      2. un-div-inv 67.0%

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

      3. *-un-lft-identity 67.0%

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

      4. times-frac 67.8%

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

      5. metadata-eval 67.8%

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

   7. Applied egg-rr 67.8%

      \[\leadsto \color{blue}{\frac{z}{-0.2222222222222222 \cdot \frac{a}{t}}} \]
   8. Step-by-step derivation

      1. *-lft-identity 67.8%

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

      2. times-frac 67.8%

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

      3. metadata-eval 67.8%

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

   9. Simplified 67.8%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-13} \lor \neg \left(y \leq 5.4 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.6% 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 90.8%

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

3. Taylor expanded in x around 0 51.9%

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

   1. associate-/l* 52.6%

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

5. Simplified 52.6%

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

6. Final simplification 52.6%

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

Alternative 9: 51.7% accurate, 1.9× speedup

Math

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

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

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) * (z / (a / t))
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 * (z / (a / t));
}

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 * (z / (a / t))

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

Derivation

1. Initial program 90.8%

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

3. Taylor expanded in x around 0 51.9%

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

   1. associate-*r/ 51.9%

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

   2. associate-*r* 51.6%

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

   3. associate-*l/ 50.3%

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

   4. associate-*r/ 50.7%

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

   5. *-commutative 50.7%

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

   6. associate-*r/ 50.3%

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

5. Simplified 50.3%

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

   1. clear-num 50.1%

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

   2. un-div-inv 50.5%

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

   3. *-un-lft-identity 50.5%

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

   4. times-frac 50.8%

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

   5. metadata-eval 50.8%

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

7. Applied egg-rr 50.8%

   \[\leadsto \color{blue}{\frac{z}{-0.2222222222222222 \cdot \frac{a}{t}}} \]
8. Step-by-step derivation

   1. *-lft-identity 50.8%

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

   2. times-frac 50.8%

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

   3. metadata-eval 50.8%

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

9. Simplified 50.8%

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

10. Final simplification 50.8%

    \[\leadsto -4.5 \cdot \frac{z}{\frac{a}{t}} \]
11. 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 2024078 
(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)))