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

Percentage Accurate: 90.8% → 96.1%

Time: 8.9s

Alternatives: 13

Speedup: 0.5×

• 28.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.8% 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: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - t \cdot \left(z \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+195}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{z}{a} \cdot \frac{t \cdot 9}{2}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+267}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - \left(z \cdot 9\right) \cdot \frac{t}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* t (* z 9.0)))))
   (if (<= t_1 -5e+195)
     (- (* (/ x a) (/ y 2.0)) (* (/ z a) (/ (* t 9.0) 2.0)))
     (if (<= t_1 5e+267)
       (/ (- (* x y) (* z (* t 9.0))) (* a 2.0))
       (- (* x (/ y (* a 2.0))) (* (* z 9.0) (/ t (* a 2.0))))))))

C

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) - (t * (z * 9.0));
	double tmp;
	if (t_1 <= -5e+195) {
		tmp = ((x / a) * (y / 2.0)) - ((z / a) * ((t * 9.0) / 2.0));
	} else if (t_1 <= 5e+267) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = (x * (y / (a * 2.0))) - ((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.
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) - (t * (z * 9.0d0))
    if (t_1 <= (-5d+195)) then
        tmp = ((x / a) * (y / 2.0d0)) - ((z / a) * ((t * 9.0d0) / 2.0d0))
    else if (t_1 <= 5d+267) then
        tmp = ((x * y) - (z * (t * 9.0d0))) / (a * 2.0d0)
    else
        tmp = (x * (y / (a * 2.0d0))) - ((z * 9.0d0) * (t / (a * 2.0d0)))
    end if
    code = tmp
end function

Java

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) - (t * (z * 9.0));
	double tmp;
	if (t_1 <= -5e+195) {
		tmp = ((x / a) * (y / 2.0)) - ((z / a) * ((t * 9.0) / 2.0));
	} else if (t_1 <= 5e+267) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = (x * (y / (a * 2.0))) - ((z * 9.0) * (t / (a * 2.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (t * (z * 9.0))
	tmp = 0
	if t_1 <= -5e+195:
		tmp = ((x / a) * (y / 2.0)) - ((z / a) * ((t * 9.0) / 2.0))
	elif t_1 <= 5e+267:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	else:
		tmp = (x * (y / (a * 2.0))) - ((z * 9.0) * (t / (a * 2.0)))
	return tmp

Julia

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(t * Float64(z * 9.0)))
	tmp = 0.0
	if (t_1 <= -5e+195)
		tmp = Float64(Float64(Float64(x / a) * Float64(y / 2.0)) - Float64(Float64(z / a) * Float64(Float64(t * 9.0) / 2.0)));
	elseif (t_1 <= 5e+267)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(x * Float64(y / Float64(a * 2.0))) - Float64(Float64(z * 9.0) * Float64(t / Float64(a * 2.0))));
	end
	return tmp
end

MATLAB

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) - (t * (z * 9.0));
	tmp = 0.0;
	if (t_1 <= -5e+195)
		tmp = ((x / a) * (y / 2.0)) - ((z / a) * ((t * 9.0) / 2.0));
	elseif (t_1 <= 5e+267)
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	else
		tmp = (x * (y / (a * 2.0))) - ((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.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+195], N[(N[(N[(x / a), $MachinePrecision] * N[(y / 2.0), $MachinePrecision]), $MachinePrecision] - N[(N[(z / a), $MachinePrecision] * N[(N[(t * 9.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+267], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * N[(t / N[(a * 2.0), $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)) < -4.9999999999999998e195

   1. Initial program 83.3%

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

      1. div-sub 81.0%

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

      2. *-commutative 81.0%

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

      3. div-sub 83.3%

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

      4. cancel-sign-sub-inv 83.3%

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

      5. *-commutative 83.3%

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

      6. fma-define 83.3%

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

      7. distribute-rgt-neg-in 83.3%

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

      8. associate-*r* 83.3%

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

      9. distribute-lft-neg-in 83.3%

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

      10. *-commutative 83.3%

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

      11. distribute-rgt-neg-in 83.3%

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

      12. metadata-eval 83.3%

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

   3. Simplified 83.3%

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

      1. *-commutative 83.3%

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

      2. associate-*r* 83.3%

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

      3. metadata-eval 83.3%

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

      4. distribute-rgt-neg-in 83.3%

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

      5. distribute-lft-neg-in 83.3%

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

      6. fma-neg 83.3%

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

      7. associate-*l* 83.3%

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

   6. Applied egg-rr 83.3%

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

      1. div-sub 81.0%

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

      2. times-frac 91.6%

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

      3. times-frac 97.6%

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

   8. Applied egg-rr 97.6%

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

   if -4.9999999999999998e195 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 4.9999999999999999e267

   1. Initial program 98.5%

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

      1. div-sub 96.8%

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

      2. *-commutative 96.8%

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

      3. div-sub 98.5%

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

      4. cancel-sign-sub-inv 98.5%

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

      5. *-commutative 98.5%

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

      6. fma-define 98.5%

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

      7. distribute-rgt-neg-in 98.5%

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

      8. associate-*r* 98.5%

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

      9. distribute-lft-neg-in 98.5%

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

      10. *-commutative 98.5%

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

      11. distribute-rgt-neg-in 98.5%

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

      12. metadata-eval 98.5%

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

   3. Simplified 98.5%

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

      1. *-commutative 98.5%

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

      2. associate-*r* 98.5%

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

      3. metadata-eval 98.5%

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

      4. distribute-rgt-neg-in 98.5%

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

      5. distribute-lft-neg-in 98.5%

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

      6. fma-neg 98.5%

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

      7. associate-*l* 98.5%

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

   6. Applied egg-rr 98.5%

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

   if 4.9999999999999999e267 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 62.9%

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

      1. div-sub 60.4%

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

      2. associate-/l* 74.9%

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

      3. associate-/l* 87.0%

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

   4. Applied egg-rr 87.0%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - t \cdot \left(z \cdot 9\right) \leq -5 \cdot 10^{+195}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{z}{a} \cdot \frac{t \cdot 9}{2}\\ \mathbf{elif}\;x \cdot y - t \cdot \left(z \cdot 9\right) \leq 5 \cdot 10^{+267}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - \left(z \cdot 9\right) \cdot \frac{t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 2 \cdot 10^{+22}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{z}{a} \cdot \frac{t \cdot 9}{2}\\ \end{array} \end{array} \]

FPCore

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 (<= (* a 2.0) 2e+22)
   (/ (fma x y (* z (* t -9.0))) (* a 2.0))
   (- (* (/ x a) (/ y 2.0)) (* (/ z a) (/ (* t 9.0) 2.0)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 2e+22) {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = ((x / a) * (y / 2.0)) - ((z / a) * ((t * 9.0) / 2.0));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= 2e+22)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(x / a) * Float64(y / 2.0)) - Float64(Float64(z / a) * Float64(Float64(t * 9.0) / 2.0)));
	end
	return tmp
end

Wolfram

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[(a * 2.0), $MachinePrecision], 2e+22], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / a), $MachinePrecision] * N[(y / 2.0), $MachinePrecision]), $MachinePrecision] - N[(N[(z / a), $MachinePrecision] * N[(N[(t * 9.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 2e22

   1. Initial program 91.7%

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

      1. div-sub 89.1%

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

      2. *-commutative 89.1%

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

      3. div-sub 91.7%

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

      4. cancel-sign-sub-inv 91.7%

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

      5. *-commutative 91.7%

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

      6. fma-define 92.8%

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

      7. distribute-rgt-neg-in 92.8%

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

      8. associate-*r* 92.8%

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

      9. distribute-lft-neg-in 92.8%

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

      10. *-commutative 92.8%

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

      11. distribute-rgt-neg-in 92.8%

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

      12. metadata-eval 92.8%

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

   3. Simplified 92.8%

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

   if 2e22 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 86.5%

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

      1. div-sub 86.5%

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

      2. *-commutative 86.5%

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

      3. div-sub 86.5%

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

      4. cancel-sign-sub-inv 86.5%

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

      5. *-commutative 86.5%

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

      6. fma-define 88.1%

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

      7. distribute-rgt-neg-in 88.1%

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

      8. associate-*r* 88.0%

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

      9. distribute-lft-neg-in 88.0%

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

      10. *-commutative 88.0%

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

      11. distribute-rgt-neg-in 88.0%

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

      12. metadata-eval 88.0%

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

   3. Simplified 88.0%

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

      1. *-commutative 88.0%

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

      2. associate-*r* 88.1%

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

      3. metadata-eval 88.1%

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

      4. distribute-rgt-neg-in 88.1%

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

      5. distribute-lft-neg-in 88.1%

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

      6. fma-neg 86.5%

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

      7. associate-*l* 86.4%

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

   6. Applied egg-rr 86.4%

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

      1. div-sub 86.4%

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

      2. times-frac 89.5%

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

      3. times-frac 90.6%

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

   8. Applied egg-rr 90.6%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 2 \cdot 10^{+22}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{z}{a} \cdot \frac{t \cdot 9}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 2 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{z}{a} \cdot \frac{t \cdot 9}{2}\\ \end{array} \end{array} \]

FPCore

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 (<= (* a 2.0) 2e+37)
   (* (fma x y (* t (* z -9.0))) (/ 0.5 a))
   (- (* (/ x a) (/ y 2.0)) (* (/ z a) (/ (* t 9.0) 2.0)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 2e+37) {
		tmp = fma(x, y, (t * (z * -9.0))) * (0.5 / a);
	} else {
		tmp = ((x / a) * (y / 2.0)) - ((z / a) * ((t * 9.0) / 2.0));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= 2e+37)
		tmp = Float64(fma(x, y, Float64(t * Float64(z * -9.0))) * Float64(0.5 / a));
	else
		tmp = Float64(Float64(Float64(x / a) * Float64(y / 2.0)) - Float64(Float64(z / a) * Float64(Float64(t * 9.0) / 2.0)));
	end
	return tmp
end

Wolfram

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[(a * 2.0), $MachinePrecision], 2e+37], N[(N[(x * y + N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / a), $MachinePrecision] * N[(y / 2.0), $MachinePrecision]), $MachinePrecision] - N[(N[(z / a), $MachinePrecision] * N[(N[(t * 9.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 1.99999999999999991e37

   1. Initial program 91.8%

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

      1. div-inv 91.7%

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

      2. fma-neg 92.7%

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

      3. *-commutative 92.7%

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

      4. distribute-rgt-neg-in 92.7%

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

      5. distribute-rgt-neg-in 92.7%

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

      6. metadata-eval 92.7%

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

      7. *-commutative 92.7%

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

      8. associate-/r* 92.7%

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

      9. metadata-eval 92.7%

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

   4. Applied egg-rr 92.7%

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

   if 1.99999999999999991e37 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 86.3%

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

      1. div-sub 86.3%

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

      2. *-commutative 86.3%

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

      3. div-sub 86.3%

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

      4. cancel-sign-sub-inv 86.3%

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

      5. *-commutative 86.3%

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

      6. fma-define 87.9%

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

      7. distribute-rgt-neg-in 87.9%

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

      8. associate-*r* 87.8%

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

      9. distribute-lft-neg-in 87.8%

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

      10. *-commutative 87.8%

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

      11. distribute-rgt-neg-in 87.8%

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

      12. metadata-eval 87.8%

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

   3. Simplified 87.8%

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

      1. *-commutative 87.8%

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

      2. associate-*r* 87.9%

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

      3. metadata-eval 87.9%

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

      4. distribute-rgt-neg-in 87.9%

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

      5. distribute-lft-neg-in 87.9%

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

      6. fma-neg 86.3%

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

      7. associate-*l* 86.2%

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

   6. Applied egg-rr 86.2%

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

      1. div-sub 86.2%

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

      2. times-frac 89.4%

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

      3. times-frac 90.5%

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

   8. Applied egg-rr 90.5%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 2 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{z}{a} \cdot \frac{t \cdot 9}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - t \cdot \left(z \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+203} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+267}\right):\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - \left(z \cdot 9\right) \cdot \frac{t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* t (* z 9.0)))))
   (if (or (<= t_1 -4e+203) (not (<= t_1 5e+267)))
     (- (* x (/ y (* a 2.0))) (* (* z 9.0) (/ t (* a 2.0))))
     (/ (- (* x y) (* z (* t 9.0))) (* a 2.0)))))

C

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) - (t * (z * 9.0));
	double tmp;
	if ((t_1 <= -4e+203) || !(t_1 <= 5e+267)) {
		tmp = (x * (y / (a * 2.0))) - ((z * 9.0) * (t / (a * 2.0)));
	} else {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Fortran

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) - (t * (z * 9.0d0))
    if ((t_1 <= (-4d+203)) .or. (.not. (t_1 <= 5d+267))) then
        tmp = (x * (y / (a * 2.0d0))) - ((z * 9.0d0) * (t / (a * 2.0d0)))
    else
        tmp = ((x * y) - (z * (t * 9.0d0))) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

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) - (t * (z * 9.0));
	double tmp;
	if ((t_1 <= -4e+203) || !(t_1 <= 5e+267)) {
		tmp = (x * (y / (a * 2.0))) - ((z * 9.0) * (t / (a * 2.0)));
	} else {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (t * (z * 9.0))
	tmp = 0
	if (t_1 <= -4e+203) or not (t_1 <= 5e+267):
		tmp = (x * (y / (a * 2.0))) - ((z * 9.0) * (t / (a * 2.0)))
	else:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	return tmp

Julia

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(t * Float64(z * 9.0)))
	tmp = 0.0
	if ((t_1 <= -4e+203) || !(t_1 <= 5e+267))
		tmp = Float64(Float64(x * Float64(y / Float64(a * 2.0))) - Float64(Float64(z * 9.0) * Float64(t / Float64(a * 2.0))));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

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) - (t * (z * 9.0));
	tmp = 0.0;
	if ((t_1 <= -4e+203) || ~((t_1 <= 5e+267)))
		tmp = (x * (y / (a * 2.0))) - ((z * 9.0) * (t / (a * 2.0)));
	else
		tmp = ((x * y) - (z * (t * 9.0))) / (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.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+203], N[Not[LessEqual[t$95$1, 5e+267]], $MachinePrecision]], N[(N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * N[(t / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - 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)) < -4e203 or 4.9999999999999999e267 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 73.2%

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

      1. div-sub 70.8%

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

      2. associate-/l* 83.5%

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

      3. associate-/l* 92.5%

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

   4. Applied egg-rr 92.5%

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

   if -4e203 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 4.9999999999999999e267

   1. Initial program 98.5%

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

      1. div-sub 96.8%

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

      2. *-commutative 96.8%

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

      3. div-sub 98.5%

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

      4. cancel-sign-sub-inv 98.5%

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

      5. *-commutative 98.5%

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

      6. fma-define 98.5%

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

      7. distribute-rgt-neg-in 98.5%

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

      8. associate-*r* 98.5%

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

      9. distribute-lft-neg-in 98.5%

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

      10. *-commutative 98.5%

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

      11. distribute-rgt-neg-in 98.5%

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

      12. metadata-eval 98.5%

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

   3. Simplified 98.5%

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

      1. *-commutative 98.5%

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

      2. associate-*r* 98.5%

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

      3. metadata-eval 98.5%

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

      4. distribute-rgt-neg-in 98.5%

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

      5. distribute-lft-neg-in 98.5%

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

      6. fma-neg 98.5%

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

      7. associate-*l* 98.5%

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

   6. Applied egg-rr 98.5%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - t \cdot \left(z \cdot 9\right) \leq -4 \cdot 10^{+203} \lor \neg \left(x \cdot y - t \cdot \left(z \cdot 9\right) \leq 5 \cdot 10^{+267}\right):\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - \left(z \cdot 9\right) \cdot \frac{t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - t \cdot \left(z \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+262}\right):\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5 + \left(x \cdot 0.5\right) \cdot \frac{y}{a \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* t (* z 9.0)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+262)))
     (* t (+ (* (/ z a) -4.5) (* (* x 0.5) (/ y (* a t)))))
     (/ (- (* x y) (* z (* t 9.0))) (* a 2.0)))))

C

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) - (t * (z * 9.0));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+262)) {
		tmp = t * (((z / a) * -4.5) + ((x * 0.5) * (y / (a * t))));
	} else {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Java

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) - (t * (z * 9.0));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+262)) {
		tmp = t * (((z / a) * -4.5) + ((x * 0.5) * (y / (a * t))));
	} else {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (t * (z * 9.0))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+262):
		tmp = t * (((z / a) * -4.5) + ((x * 0.5) * (y / (a * t))))
	else:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	return tmp

Julia

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(t * Float64(z * 9.0)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+262))
		tmp = Float64(t * Float64(Float64(Float64(z / a) * -4.5) + Float64(Float64(x * 0.5) * Float64(y / Float64(a * t)))));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

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) - (t * (z * 9.0));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+262)))
		tmp = t * (((z / a) * -4.5) + ((x * 0.5) * (y / (a * t))));
	else
		tmp = ((x * y) - (z * (t * 9.0))) / (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.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+262]], $MachinePrecision]], N[(t * N[(N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision] + N[(N[(x * 0.5), $MachinePrecision] * N[(y / N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - 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)) < -inf.0 or 5.00000000000000008e262 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 67.3%

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

   3. Taylor expanded in t around inf 72.1%

      \[\leadsto \color{blue}{t \cdot \left(-4.5 \cdot \frac{z}{a} + 0.5 \cdot \frac{x \cdot y}{a \cdot t}\right)} \]
   4. Step-by-step derivation

      1. fma-define 72.1%

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

      2. associate-/l* 79.6%

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

      3. *-commutative 79.6%

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

   5. Simplified 79.6%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-4.5, \frac{z}{a}, 0.5 \cdot \left(x \cdot \frac{y}{t \cdot a}\right)\right)} \]
   6. Step-by-step derivation

      1. fma-undefine 79.6%

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

      2. associate-*r* 79.6%

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

   7. Applied egg-rr 79.6%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 5.00000000000000008e262

   1. Initial program 98.6%

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

      1. div-sub 97.0%

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

      2. *-commutative 97.0%

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

      3. div-sub 98.6%

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

      4. cancel-sign-sub-inv 98.6%

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

      5. *-commutative 98.6%

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

      6. fma-define 98.6%

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

      7. distribute-rgt-neg-in 98.6%

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

      8. associate-*r* 98.6%

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

      9. distribute-lft-neg-in 98.6%

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

      10. *-commutative 98.6%

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

      11. distribute-rgt-neg-in 98.6%

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

      12. metadata-eval 98.6%

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

   3. Simplified 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-*r* 98.6%

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

      3. metadata-eval 98.6%

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

      4. distribute-rgt-neg-in 98.6%

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

      5. distribute-lft-neg-in 98.6%

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

      6. fma-neg 98.6%

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

      7. associate-*l* 98.6%

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

   6. Applied egg-rr 98.6%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - t \cdot \left(z \cdot 9\right) \leq -\infty \lor \neg \left(x \cdot y - t \cdot \left(z \cdot 9\right) \leq 5 \cdot 10^{+262}\right):\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5 + \left(x \cdot 0.5\right) \cdot \frac{y}{a \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-155}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+111}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (* y 0.5) a))))
   (if (<= (* x y) -4e-14)
     t_1
     (if (<= (* x y) 4e-155)
       (* -4.5 (/ (* z t) a))
       (if (<= (* x y) 2e-71)
         t_1
         (if (<= (* x y) 2e-36)
           (* (/ t a) (* z -4.5))
           (if (<= (* x y) 4e+111) (/ (* x y) (* a 2.0)) t_1)))))))

C

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 * 0.5) / a);
	double tmp;
	if ((x * y) <= -4e-14) {
		tmp = t_1;
	} else if ((x * y) <= 4e-155) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 2e-71) {
		tmp = t_1;
	} else if ((x * y) <= 2e-36) {
		tmp = (t / a) * (z * -4.5);
	} else if ((x * y) <= 4e+111) {
		tmp = (x * y) / (a * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 * 0.5d0) / a)
    if ((x * y) <= (-4d-14)) then
        tmp = t_1
    else if ((x * y) <= 4d-155) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if ((x * y) <= 2d-71) then
        tmp = t_1
    else if ((x * y) <= 2d-36) then
        tmp = (t / a) * (z * (-4.5d0))
    else if ((x * y) <= 4d+111) then
        tmp = (x * y) / (a * 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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 * 0.5) / a);
	double tmp;
	if ((x * y) <= -4e-14) {
		tmp = t_1;
	} else if ((x * y) <= 4e-155) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 2e-71) {
		tmp = t_1;
	} else if ((x * y) <= 2e-36) {
		tmp = (t / a) * (z * -4.5);
	} else if ((x * y) <= 4e+111) {
		tmp = (x * y) / (a * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x * ((y * 0.5) / a)
	tmp = 0
	if (x * y) <= -4e-14:
		tmp = t_1
	elif (x * y) <= 4e-155:
		tmp = -4.5 * ((z * t) / a)
	elif (x * y) <= 2e-71:
		tmp = t_1
	elif (x * y) <= 2e-36:
		tmp = (t / a) * (z * -4.5)
	elif (x * y) <= 4e+111:
		tmp = (x * y) / (a * 2.0)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y * 0.5) / a))
	tmp = 0.0
	if (Float64(x * y) <= -4e-14)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e-155)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (Float64(x * y) <= 2e-71)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-36)
		tmp = Float64(Float64(t / a) * Float64(z * -4.5));
	elseif (Float64(x * y) <= 4e+111)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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 * 0.5) / a);
	tmp = 0.0;
	if ((x * y) <= -4e-14)
		tmp = t_1;
	elseif ((x * y) <= 4e-155)
		tmp = -4.5 * ((z * t) / a);
	elseif ((x * y) <= 2e-71)
		tmp = t_1;
	elseif ((x * y) <= 2e-36)
		tmp = (t / a) * (z * -4.5);
	elseif ((x * y) <= 4e+111)
		tmp = (x * y) / (a * 2.0);
	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.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e-14], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e-155], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-71], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-36], N[(N[(t / a), $MachinePrecision] * N[(z * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+111], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4e-14 or 4.00000000000000006e-155 < (*.f64 x y) < 1.9999999999999998e-71 or 3.99999999999999983e111 < (*.f64 x y)

   1. Initial program 85.1%

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

   3. Taylor expanded in x around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-/l* 81.0%

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

      3. associate-*r* 81.0%

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

      4. *-commutative 81.0%

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

      5. associate-*r/ 81.0%

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

   5. Simplified 81.0%

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

   if -4e-14 < (*.f64 x y) < 4.00000000000000006e-155

   1. Initial program 95.1%

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

   3. Taylor expanded in x around 0 81.9%

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

   if 1.9999999999999998e-71 < (*.f64 x y) < 1.9999999999999999e-36

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 67.5%

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

      1. associate-*r/ 67.9%

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

      2. associate-*r* 67.3%

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

      3. associate-*l/ 66.2%

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

      4. associate-*r/ 66.6%

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

      5. *-commutative 66.6%

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

      6. associate-*l* 66.4%

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

   5. Simplified 66.4%

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

   if 1.9999999999999999e-36 < (*.f64 x y) < 3.99999999999999983e111

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf 65.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-155}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+111}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-155}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+111}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (* y 0.5) a))))
   (if (<= (* x y) -4e-14)
     t_1
     (if (<= (* x y) 4e-155)
       (* -4.5 (/ (* z t) a))
       (if (<= (* x y) 2e-71)
         t_1
         (if (<= (* x y) 2e-36)
           (* (/ t a) (* z -4.5))
           (if (<= (* x y) 4e+111) (* (/ 0.5 a) (* x y)) t_1)))))))

C

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 * 0.5) / a);
	double tmp;
	if ((x * y) <= -4e-14) {
		tmp = t_1;
	} else if ((x * y) <= 4e-155) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 2e-71) {
		tmp = t_1;
	} else if ((x * y) <= 2e-36) {
		tmp = (t / a) * (z * -4.5);
	} else if ((x * y) <= 4e+111) {
		tmp = (0.5 / a) * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 * 0.5d0) / a)
    if ((x * y) <= (-4d-14)) then
        tmp = t_1
    else if ((x * y) <= 4d-155) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if ((x * y) <= 2d-71) then
        tmp = t_1
    else if ((x * y) <= 2d-36) then
        tmp = (t / a) * (z * (-4.5d0))
    else if ((x * y) <= 4d+111) then
        tmp = (0.5d0 / a) * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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 * 0.5) / a);
	double tmp;
	if ((x * y) <= -4e-14) {
		tmp = t_1;
	} else if ((x * y) <= 4e-155) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 2e-71) {
		tmp = t_1;
	} else if ((x * y) <= 2e-36) {
		tmp = (t / a) * (z * -4.5);
	} else if ((x * y) <= 4e+111) {
		tmp = (0.5 / a) * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x * ((y * 0.5) / a)
	tmp = 0
	if (x * y) <= -4e-14:
		tmp = t_1
	elif (x * y) <= 4e-155:
		tmp = -4.5 * ((z * t) / a)
	elif (x * y) <= 2e-71:
		tmp = t_1
	elif (x * y) <= 2e-36:
		tmp = (t / a) * (z * -4.5)
	elif (x * y) <= 4e+111:
		tmp = (0.5 / a) * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y * 0.5) / a))
	tmp = 0.0
	if (Float64(x * y) <= -4e-14)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e-155)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (Float64(x * y) <= 2e-71)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-36)
		tmp = Float64(Float64(t / a) * Float64(z * -4.5));
	elseif (Float64(x * y) <= 4e+111)
		tmp = Float64(Float64(0.5 / a) * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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 * 0.5) / a);
	tmp = 0.0;
	if ((x * y) <= -4e-14)
		tmp = t_1;
	elseif ((x * y) <= 4e-155)
		tmp = -4.5 * ((z * t) / a);
	elseif ((x * y) <= 2e-71)
		tmp = t_1;
	elseif ((x * y) <= 2e-36)
		tmp = (t / a) * (z * -4.5);
	elseif ((x * y) <= 4e+111)
		tmp = (0.5 / a) * (x * y);
	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.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e-14], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e-155], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-71], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-36], N[(N[(t / a), $MachinePrecision] * N[(z * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+111], N[(N[(0.5 / a), $MachinePrecision] * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4e-14 or 4.00000000000000006e-155 < (*.f64 x y) < 1.9999999999999998e-71 or 3.99999999999999983e111 < (*.f64 x y)

   1. Initial program 85.1%

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

   3. Taylor expanded in x around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-/l* 81.0%

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

      3. associate-*r* 81.0%

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

      4. *-commutative 81.0%

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

      5. associate-*r/ 81.0%

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

   5. Simplified 81.0%

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

   if -4e-14 < (*.f64 x y) < 4.00000000000000006e-155

   1. Initial program 95.1%

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

   3. Taylor expanded in x around 0 81.9%

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

   if 1.9999999999999998e-71 < (*.f64 x y) < 1.9999999999999999e-36

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 67.5%

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

      1. associate-*r/ 67.9%

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

      2. associate-*r* 67.3%

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

      3. associate-*l/ 66.2%

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

      4. associate-*r/ 66.6%

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

      5. *-commutative 66.6%

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

      6. associate-*l* 66.4%

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

   5. Simplified 66.4%

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

   if 1.9999999999999999e-36 < (*.f64 x y) < 3.99999999999999983e111

   1. Initial program 96.1%

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

      1. div-inv 96.2%

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

      2. fma-neg 96.2%

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

      3. *-commutative 96.2%

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

      4. distribute-rgt-neg-in 96.2%

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

      5. distribute-rgt-neg-in 96.2%

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

      6. metadata-eval 96.2%

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

      7. *-commutative 96.2%

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

      8. associate-/r* 96.2%

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

      9. metadata-eval 96.2%

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

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in x around inf 65.8%

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot \frac{0.5}{a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-155}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+111}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-155}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+111}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (* y 0.5) a))))
   (if (<= (* x y) -4e-14)
     t_1
     (if (<= (* x y) 4e-155)
       (* -4.5 (/ (* z t) a))
       (if (<= (* x y) 2e-71)
         t_1
         (if (<= (* x y) 2e-36)
           (* z (/ (* t -4.5) a))
           (if (<= (* x y) 4e+111) (* (/ 0.5 a) (* x y)) t_1)))))))

C

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 * 0.5) / a);
	double tmp;
	if ((x * y) <= -4e-14) {
		tmp = t_1;
	} else if ((x * y) <= 4e-155) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 2e-71) {
		tmp = t_1;
	} else if ((x * y) <= 2e-36) {
		tmp = z * ((t * -4.5) / a);
	} else if ((x * y) <= 4e+111) {
		tmp = (0.5 / a) * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 * 0.5d0) / a)
    if ((x * y) <= (-4d-14)) then
        tmp = t_1
    else if ((x * y) <= 4d-155) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if ((x * y) <= 2d-71) then
        tmp = t_1
    else if ((x * y) <= 2d-36) then
        tmp = z * ((t * (-4.5d0)) / a)
    else if ((x * y) <= 4d+111) then
        tmp = (0.5d0 / a) * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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 * 0.5) / a);
	double tmp;
	if ((x * y) <= -4e-14) {
		tmp = t_1;
	} else if ((x * y) <= 4e-155) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 2e-71) {
		tmp = t_1;
	} else if ((x * y) <= 2e-36) {
		tmp = z * ((t * -4.5) / a);
	} else if ((x * y) <= 4e+111) {
		tmp = (0.5 / a) * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x * ((y * 0.5) / a)
	tmp = 0
	if (x * y) <= -4e-14:
		tmp = t_1
	elif (x * y) <= 4e-155:
		tmp = -4.5 * ((z * t) / a)
	elif (x * y) <= 2e-71:
		tmp = t_1
	elif (x * y) <= 2e-36:
		tmp = z * ((t * -4.5) / a)
	elif (x * y) <= 4e+111:
		tmp = (0.5 / a) * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y * 0.5) / a))
	tmp = 0.0
	if (Float64(x * y) <= -4e-14)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e-155)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (Float64(x * y) <= 2e-71)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-36)
		tmp = Float64(z * Float64(Float64(t * -4.5) / a));
	elseif (Float64(x * y) <= 4e+111)
		tmp = Float64(Float64(0.5 / a) * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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 * 0.5) / a);
	tmp = 0.0;
	if ((x * y) <= -4e-14)
		tmp = t_1;
	elseif ((x * y) <= 4e-155)
		tmp = -4.5 * ((z * t) / a);
	elseif ((x * y) <= 2e-71)
		tmp = t_1;
	elseif ((x * y) <= 2e-36)
		tmp = z * ((t * -4.5) / a);
	elseif ((x * y) <= 4e+111)
		tmp = (0.5 / a) * (x * y);
	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.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e-14], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e-155], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-71], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-36], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+111], N[(N[(0.5 / a), $MachinePrecision] * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4e-14 or 4.00000000000000006e-155 < (*.f64 x y) < 1.9999999999999998e-71 or 3.99999999999999983e111 < (*.f64 x y)

   1. Initial program 85.1%

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

   3. Taylor expanded in x around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-/l* 81.0%

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

      3. associate-*r* 81.0%

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

      4. *-commutative 81.0%

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

      5. associate-*r/ 81.0%

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

   5. Simplified 81.0%

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

   if -4e-14 < (*.f64 x y) < 4.00000000000000006e-155

   1. Initial program 95.1%

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

   3. Taylor expanded in x around 0 81.9%

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

   if 1.9999999999999998e-71 < (*.f64 x y) < 1.9999999999999999e-36

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 67.5%

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

      1. associate-*r/ 67.9%

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

      2. associate-*r* 67.3%

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

      3. associate-*l/ 66.2%

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

      4. associate-*r/ 66.6%

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

      5. *-commutative 66.6%

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

      6. associate-*r/ 66.2%

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

   5. Simplified 66.2%

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

   if 1.9999999999999999e-36 < (*.f64 x y) < 3.99999999999999983e111

   1. Initial program 96.1%

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

      1. div-inv 96.2%

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

      2. fma-neg 96.2%

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

      3. *-commutative 96.2%

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

      4. distribute-rgt-neg-in 96.2%

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

      5. distribute-rgt-neg-in 96.2%

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

      6. metadata-eval 96.2%

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

      7. *-commutative 96.2%

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

      8. associate-/r* 96.2%

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

      9. metadata-eval 96.2%

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

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in x around inf 65.8%

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot \frac{0.5}{a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-155}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+111}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+234}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+164}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+234)
   (* x (* y (/ 0.5 a)))
   (if (<= (* x y) 1e+164)
     (/ (- (* x y) (* z (* t 9.0))) (* a 2.0))
     (* x (/ (* y 0.5) a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+234) {
		tmp = x * (y * (0.5 / a));
	} else if ((x * y) <= 1e+164) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-5d+234)) then
        tmp = x * (y * (0.5d0 / a))
    else if ((x * y) <= 1d+164) then
        tmp = ((x * y) - (z * (t * 9.0d0))) / (a * 2.0d0)
    else
        tmp = x * ((y * 0.5d0) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+234) {
		tmp = x * (y * (0.5 / a));
	} else if ((x * y) <= 1e+164) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+234:
		tmp = x * (y * (0.5 / a))
	elif (x * y) <= 1e+164:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+234)
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	elseif (Float64(x * y) <= 1e+164)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+234)
		tmp = x * (y * (0.5 / a));
	elseif ((x * y) <= 1e+164)
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+234], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+164], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.0000000000000003e234

   1. Initial program 71.3%

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

   3. Taylor expanded in x around inf 71.3%

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

      1. associate-/l* 88.8%

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

      2. *-commutative 88.8%

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

      3. div-inv 88.9%

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

      4. *-commutative 88.9%

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

      5. associate-/r* 88.9%

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

      6. metadata-eval 88.9%

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

   5. Applied egg-rr 88.9%

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

   if -5.0000000000000003e234 < (*.f64 x y) < 1e164

   1. Initial program 95.4%

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

      1. div-sub 94.4%

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

      2. *-commutative 94.4%

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

      3. div-sub 95.4%

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

      4. cancel-sign-sub-inv 95.4%

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

      5. *-commutative 95.4%

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

      6. fma-define 95.4%

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

      7. distribute-rgt-neg-in 95.4%

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

      8. associate-*r* 95.4%

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

      9. distribute-lft-neg-in 95.4%

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

      10. *-commutative 95.4%

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

      11. distribute-rgt-neg-in 95.4%

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

      12. metadata-eval 95.4%

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

   3. Simplified 95.4%

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

      1. *-commutative 95.4%

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

      2. associate-*r* 95.4%

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

      3. metadata-eval 95.4%

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

      4. distribute-rgt-neg-in 95.4%

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

      5. distribute-lft-neg-in 95.4%

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

      6. fma-neg 95.4%

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

      7. associate-*l* 95.4%

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

   6. Applied egg-rr 95.4%

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

   if 1e164 < (*.f64 x y)

   1. Initial program 76.6%

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

   3. Taylor expanded in x around inf 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-/l* 91.4%

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

      3. associate-*r* 91.4%

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

      4. *-commutative 91.4%

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

      5. associate-*r/ 91.4%

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

   5. Simplified 91.4%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+234}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+164}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+24} \lor \neg \left(x \leq 4.5 \cdot 10^{-43}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1e+24) (not (<= x 4.5e-43)))
   (* x (/ (* y 0.5) a))
   (* -4.5 (/ (* z t) a))))

C

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 <= -1e+24) || !(x <= 4.5e-43)) {
		tmp = x * ((y * 0.5) / a);
	} 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.
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 <= (-1d+24)) .or. (.not. (x <= 4.5d-43))) then
        tmp = x * ((y * 0.5d0) / a)
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

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 <= -1e+24) || !(x <= 4.5e-43)) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1e+24) or not (x <= 4.5e-43):
		tmp = x * ((y * 0.5) / a)
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1e+24) || !(x <= 4.5e-43))
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	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])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1e+24) || ~((x <= 4.5e-43)))
		tmp = x * ((y * 0.5) / a);
	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.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1e+24], N[Not[LessEqual[x, 4.5e-43]], $MachinePrecision]], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.9999999999999998e23 or 4.50000000000000025e-43 < x

   1. Initial program 85.3%

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

   3. Taylor expanded in x around inf 65.8%

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

      1. *-commutative 65.8%

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

      2. associate-/l* 70.6%

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

      3. associate-*r* 70.6%

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

      4. *-commutative 70.6%

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

      5. associate-*r/ 70.6%

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

   5. Simplified 70.6%

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

   if -9.9999999999999998e23 < x < 4.50000000000000025e-43

   1. Initial program 95.4%

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

   3. Taylor expanded in x around 0 63.1%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+24} \lor \neg \left(x \leq 4.5 \cdot 10^{-43}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -9e+75) (* t (* (/ z a) -4.5)) (* -4.5 (/ (* z t) a))))

C

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 <= -9e+75) {
		tmp = t * ((z / a) * -4.5);
	} 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.
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 <= (-9d+75)) then
        tmp = t * ((z / a) * (-4.5d0))
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

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 <= -9e+75) {
		tmp = t * ((z / a) * -4.5);
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -9e+75:
		tmp = t * ((z / a) * -4.5)
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -9e+75)
		tmp = Float64(t * Float64(Float64(z / a) * -4.5));
	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])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -9e+75)
		tmp = t * ((z / a) * -4.5);
	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.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -9e+75], N[(t * N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.0000000000000007e75

   1. Initial program 78.6%

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

   3. Taylor expanded in t around inf 65.1%

      \[\leadsto \color{blue}{t \cdot \left(-4.5 \cdot \frac{z}{a} + 0.5 \cdot \frac{x \cdot y}{a \cdot t}\right)} \]
   4. Step-by-step derivation

      1. fma-define 65.1%

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

      2. associate-/l* 65.4%

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

      3. *-commutative 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in z around inf 24.1%

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

   if -9.0000000000000007e75 < x

   1. Initial program 92.9%

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

   3. Taylor expanded in x around 0 52.5%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+74}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -8.2e+74) (* -4.5 (* t (/ z a))) (* -4.5 (/ (* z t) a))))

C

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 <= -8.2e+74) {
		tmp = -4.5 * (t * (z / a));
	} 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.
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 <= (-8.2d+74)) then
        tmp = (-4.5d0) * (t * (z / a))
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

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 <= -8.2e+74) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -8.2e+74:
		tmp = -4.5 * (t * (z / a))
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -8.2e+74)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	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])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -8.2e+74)
		tmp = -4.5 * (t * (z / a));
	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.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -8.2e+74], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.2000000000000001e74

   1. Initial program 78.6%

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

   3. Taylor expanded in x around 0 17.9%

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

      1. associate-/l* 24.1%

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

   5. Simplified 24.1%

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

   if -8.2000000000000001e74 < x

   1. Initial program 92.9%

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

   3. Taylor expanded in x around 0 52.5%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+74}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.0% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Derivation

1. Initial program 90.4%

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

3. Taylor expanded in x around 0 46.4%

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

   1. associate-/l* 45.2%

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

5. Simplified 45.2%

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

Developer target: 93.0% 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 2024089 
(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)))