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

Percentage Accurate: 91.1% → 96.8%

Time: 12.0s

Alternatives: 10

Speedup: 0.6×

• 29.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{y}{a}}{2} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ t_2 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+302}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 1.5 \cdot 10^{+291}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 a)) 2.0) (* t (* (/ z a) 4.5))))
        (t_2 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_2 -5e+302)
     t_1
     (if (<= t_2 1.5e+291) (/ (+ (* x y) (* z (* t -9.0))) (* 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 / a)) / 2.0) - (t * ((z / a) * 4.5));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -5e+302) {
		tmp = t_1;
	} else if (t_2 <= 1.5e+291) {
		tmp = ((x * y) + (z * (t * -9.0))) / (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) :: t_2
    real(8) :: tmp
    t_1 = ((x * (y / a)) / 2.0d0) - (t * ((z / a) * 4.5d0))
    t_2 = (x * y) - ((z * 9.0d0) * t)
    if (t_2 <= (-5d+302)) then
        tmp = t_1
    else if (t_2 <= 1.5d+291) then
        tmp = ((x * y) + (z * (t * (-9.0d0)))) / (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 / a)) / 2.0) - (t * ((z / a) * 4.5));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -5e+302) {
		tmp = t_1;
	} else if (t_2 <= 1.5e+291) {
		tmp = ((x * y) + (z * (t * -9.0))) / (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 / a)) / 2.0) - (t * ((z / a) * 4.5))
	t_2 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_2 <= -5e+302:
		tmp = t_1
	elif t_2 <= 1.5e+291:
		tmp = ((x * y) + (z * (t * -9.0))) / (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(Float64(Float64(x * Float64(y / a)) / 2.0) - Float64(t * Float64(Float64(z / a) * 4.5)))
	t_2 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_2 <= -5e+302)
		tmp = t_1;
	elseif (t_2 <= 1.5e+291)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t * -9.0))) / 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 / a)) / 2.0) - (t * ((z / a) * 4.5));
	t_2 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_2 <= -5e+302)
		tmp = t_1;
	elseif (t_2 <= 1.5e+291)
		tmp = ((x * y) + (z * (t * -9.0))) / (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[(N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision] - N[(t * N[(N[(z / a), $MachinePrecision] * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+302], t$95$1, If[LessEqual[t$95$2, 1.5e+291], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -5e302 or 1.50000000000000008e291 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 67.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 67.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 67.1%

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

      1. frac-2neg N/A

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

      2. distribute-neg-in N/A

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

      3. unsub-neg N/A

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

      4. sub-div N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. metadata-eval N/A

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

      9. distribute-rgt-neg-in N/A

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

      10. distribute-lft-neg-in N/A

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

      11. frac-2neg N/A

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

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{a \cdot 2}\right), \color{blue}{\left(\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right)}\right) \]

      13. associate-/r* N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(\frac{\frac{x \cdot y}{a}}{2}\right), \left(\frac{\color{blue}{\left(z \cdot 9\right) \cdot t}}{a \cdot 2}\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot y}{a}\right), 2\right), \left(\frac{\color{blue}{\left(z \cdot 9\right) \cdot t}}{a \cdot 2}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), a\right), 2\right), \left(\frac{\color{blue}{\left(z \cdot 9\right)} \cdot t}{a \cdot 2}\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right), 2\right), \left(\frac{\left(\color{blue}{z} \cdot 9\right) \cdot t}{a \cdot 2}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right), 2\right), \left(\frac{t \cdot \left(z \cdot 9\right)}{\color{blue}{a} \cdot 2}\right)\right) \]

      18. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right), 2\right), \left(t \cdot \color{blue}{\frac{z \cdot 9}{a \cdot 2}}\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right), 2\right), \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{z \cdot 9}{a \cdot 2}\right)}\right)\right) \]

   6. Applied egg-rr 77.5%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{a}}{2} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)} \]
   7. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \frac{y}{a}\right), 2\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), \frac{9}{2}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\frac{y}{a} \cdot x\right), 2\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), \frac{9}{2}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\frac{y}{a}\right), x\right), 2\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), \frac{9}{2}\right)\right)\right) \]

      4. /-lowering-/.f64 93.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), x\right), 2\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), \frac{9}{2}\right)\right)\right) \]

   8. Applied egg-rr 93.2%

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

   if -5e302 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 1.50000000000000008e291

   1. Initial program 99.5%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 99.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 99.5%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x \cdot \frac{y}{a}}{2} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 1.5 \cdot 10^{+291}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{a}}{2} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot \frac{0.5}{a}\right) - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ t_2 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+302}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+291}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (- (* y (* x (/ 0.5 a))) (* t (* (/ z a) 4.5))))
        (t_2 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_2 -5e+302)
     t_1
     (if (<= t_2 2e+291) (/ (+ (* x y) (* z (* t -9.0))) (* 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 = (y * (x * (0.5 / a))) - (t * ((z / a) * 4.5));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -5e+302) {
		tmp = t_1;
	} else if (t_2 <= 2e+291) {
		tmp = ((x * y) + (z * (t * -9.0))) / (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) :: t_2
    real(8) :: tmp
    t_1 = (y * (x * (0.5d0 / a))) - (t * ((z / a) * 4.5d0))
    t_2 = (x * y) - ((z * 9.0d0) * t)
    if (t_2 <= (-5d+302)) then
        tmp = t_1
    else if (t_2 <= 2d+291) then
        tmp = ((x * y) + (z * (t * (-9.0d0)))) / (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 = (y * (x * (0.5 / a))) - (t * ((z / a) * 4.5));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -5e+302) {
		tmp = t_1;
	} else if (t_2 <= 2e+291) {
		tmp = ((x * y) + (z * (t * -9.0))) / (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 = (y * (x * (0.5 / a))) - (t * ((z / a) * 4.5))
	t_2 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_2 <= -5e+302:
		tmp = t_1
	elif t_2 <= 2e+291:
		tmp = ((x * y) + (z * (t * -9.0))) / (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(Float64(y * Float64(x * Float64(0.5 / a))) - Float64(t * Float64(Float64(z / a) * 4.5)))
	t_2 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_2 <= -5e+302)
		tmp = t_1;
	elseif (t_2 <= 2e+291)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t * -9.0))) / 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 = (y * (x * (0.5 / a))) - (t * ((z / a) * 4.5));
	t_2 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_2 <= -5e+302)
		tmp = t_1;
	elseif (t_2 <= 2e+291)
		tmp = ((x * y) + (z * (t * -9.0))) / (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[(N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z / a), $MachinePrecision] * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+302], t$95$1, If[LessEqual[t$95$2, 2e+291], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -5e302 or 1.9999999999999999e291 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 66.6%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 66.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 66.6%

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

      1. frac-2neg N/A

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

      2. distribute-neg-in N/A

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

      3. unsub-neg N/A

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

      4. sub-div N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. metadata-eval N/A

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

      9. distribute-rgt-neg-in N/A

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

      10. distribute-lft-neg-in N/A

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

      11. frac-2neg N/A

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

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{a \cdot 2}\right), \color{blue}{\left(\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right)}\right) \]

      13. associate-/r* N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(\frac{\frac{x \cdot y}{a}}{2}\right), \left(\frac{\color{blue}{\left(z \cdot 9\right) \cdot t}}{a \cdot 2}\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot y}{a}\right), 2\right), \left(\frac{\color{blue}{\left(z \cdot 9\right) \cdot t}}{a \cdot 2}\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), a\right), 2\right), \left(\frac{\color{blue}{\left(z \cdot 9\right)} \cdot t}{a \cdot 2}\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right), 2\right), \left(\frac{\left(\color{blue}{z} \cdot 9\right) \cdot t}{a \cdot 2}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right), 2\right), \left(\frac{t \cdot \left(z \cdot 9\right)}{\color{blue}{a} \cdot 2}\right)\right) \]

      18. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right), 2\right), \left(t \cdot \color{blue}{\frac{z \cdot 9}{a \cdot 2}}\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right), 2\right), \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{z \cdot 9}{a \cdot 2}\right)}\right)\right) \]

   6. Applied egg-rr 77.1%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{a}}{2} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)} \]
   7. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{a} \cdot \frac{1}{2}\right), \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), \frac{9}{2}\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{a} \cdot \frac{1}{2}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), \frac{9}{2}\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{\left(x \cdot y\right) \cdot \frac{1}{2}}{a}\right), \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), \frac{9}{2}\right)\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot y\right) \cdot \frac{\frac{1}{2}}{a}\right), \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), \frac{9}{2}\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{\frac{1}{2}}{a} \cdot \left(x \cdot y\right)\right), \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), \frac{9}{2}\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\frac{\frac{1}{2}}{a} \cdot x\right) \cdot y\right), \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), \frac{9}{2}\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{a} \cdot x\right), y\right), \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), \frac{9}{2}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{a}\right), x\right), y\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), \frac{9}{2}\right)\right)\right) \]

      9. /-lowering-/.f64 92.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), x\right), y\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), \frac{9}{2}\right)\right)\right) \]

   8. Applied egg-rr 92.9%

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

   if -5e302 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 1.9999999999999999e291

   1. Initial program 99.5%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 99.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 99.5%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+302}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right) - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+291}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right) - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+299}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-4.5 \cdot \left(t \cdot \frac{z}{y}\right) + x \cdot 0.5\right)\\ \end{array} \end{array} \]

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) (* (* z 9.0) t)) 2e+299)
   (/ (+ (* x y) (* z (* t -9.0))) (* a 2.0))
   (* (/ y a) (+ (* -4.5 (* t (/ z y))) (* x 0.5)))))

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) - ((z * 9.0) * t)) <= 2e+299) {
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = (y / a) * ((-4.5 * (t * (z / y))) + (x * 0.5));
	}
	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) - ((z * 9.0d0) * t)) <= 2d+299) then
        tmp = ((x * y) + (z * (t * (-9.0d0)))) / (a * 2.0d0)
    else
        tmp = (y / a) * (((-4.5d0) * (t * (z / y))) + (x * 0.5d0))
    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) - ((z * 9.0) * t)) <= 2e+299) {
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = (y / a) * ((-4.5 * (t * (z / y))) + (x * 0.5));
	}
	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) - ((z * 9.0) * t)) <= 2e+299:
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0)
	else:
		tmp = (y / a) * ((-4.5 * (t * (z / y))) + (x * 0.5))
	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(Float64(x * y) - Float64(Float64(z * 9.0) * t)) <= 2e+299)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(y / a) * Float64(Float64(-4.5 * Float64(t * Float64(z / y))) + Float64(x * 0.5)));
	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) - ((z * 9.0) * t)) <= 2e+299)
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	else
		tmp = (y / a) * ((-4.5 * (t * (z / y))) + (x * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], 2e+299], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(N[(-4.5 * N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 2.0000000000000001e299

   1. Initial program 96.3%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 96.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 96.3%

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

   if 2.0000000000000001e299 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 52.7%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 52.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 52.7%

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

   5. Taylor expanded in x around inf

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

      1. distribute-lft-in N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. fma-define N/A

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

      9. associate-*l/ N/A

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

      10. times-frac N/A

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

      11. *-inverses N/A

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

      12. *-inverses N/A

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

      13. times-frac N/A

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

      14. associate-*l/ N/A

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

      15. fma-define N/A

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

      16. associate-*l* N/A

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

   7. Simplified 84.8%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-4.5 \cdot \left(t \cdot \frac{z}{y}\right) + 0.5 \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+299}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-4.5 \cdot \left(t \cdot \frac{z}{y}\right) + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}}\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+116}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -1e+89)
   (* x (/ y (/ a 0.5)))
   (if (<= (* x y) 6e+116) (* z (/ (* t -4.5) a)) (* 0.5 (* y (/ x 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) <= -1e+89) {
		tmp = x * (y / (a / 0.5));
	} else if ((x * y) <= 6e+116) {
		tmp = z * ((t * -4.5) / a);
	} else {
		tmp = 0.5 * (y * (x / 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) <= (-1d+89)) then
        tmp = x * (y / (a / 0.5d0))
    else if ((x * y) <= 6d+116) then
        tmp = z * ((t * (-4.5d0)) / a)
    else
        tmp = 0.5d0 * (y * (x / 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) <= -1e+89) {
		tmp = x * (y / (a / 0.5));
	} else if ((x * y) <= 6e+116) {
		tmp = z * ((t * -4.5) / a);
	} else {
		tmp = 0.5 * (y * (x / 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) <= -1e+89:
		tmp = x * (y / (a / 0.5))
	elif (x * y) <= 6e+116:
		tmp = z * ((t * -4.5) / a)
	else:
		tmp = 0.5 * (y * (x / 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) <= -1e+89)
		tmp = Float64(x * Float64(y / Float64(a / 0.5)));
	elseif (Float64(x * y) <= 6e+116)
		tmp = Float64(z * Float64(Float64(t * -4.5) / a));
	else
		tmp = Float64(0.5 * Float64(y * Float64(x / 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) <= -1e+89)
		tmp = x * (y / (a / 0.5));
	elseif ((x * y) <= 6e+116)
		tmp = z * ((t * -4.5) / a);
	else
		tmp = 0.5 * (y * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+89], N[(x * N[(y / N[(a / 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6e+116], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999995e88

   1. Initial program 92.9%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 92.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 92.9%

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

      1. frac-2neg N/A

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

      2. distribute-neg-in N/A

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

      3. unsub-neg N/A

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

      4. sub-div N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. metadata-eval N/A

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

      9. distribute-rgt-neg-in N/A

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

      10. distribute-lft-neg-in N/A

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

      11. frac-2neg N/A

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

      12. div-sub N/A

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

      13. div-inv N/A

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

      14. *-commutative N/A

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

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{a \cdot 2}\right), \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{2 \cdot a}\right), \left(x \cdot \color{blue}{y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{a}\right), \left(\color{blue}{x \cdot y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2}\right), a\right), \left(\color{blue}{x \cdot y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \left(\color{blue}{x} \cdot y - \left(z \cdot 9\right) \cdot t\right)\right) \]

      20. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(z \cdot 9\right)\right) \cdot t}\right)\right) \]

   6. Applied egg-rr 92.9%

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

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \color{blue}{\left(x \cdot y\right)}\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 85.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   9. Simplified 85.6%

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

       1. *-commutative N/A

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

       2. associate-*l* N/A

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

       3. metadata-eval N/A

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

       4. associate-/r* N/A

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

       5. *-commutative N/A

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

       6. div-inv N/A

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

       7. *-commutative N/A

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

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a \cdot 2}\right), \color{blue}{x}\right) \]

       9. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a \cdot 2\right)\right), x\right) \]

       10. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a \cdot \frac{1}{\frac{1}{2}}\right)\right), x\right) \]

       11. div-inv N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{a}{\frac{1}{2}}\right)\right), x\right) \]

       12. /-lowering-/.f64 88.0%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \frac{1}{2}\right)\right), x\right) \]

   11. Applied egg-rr 88.0%

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

   if -9.99999999999999995e88 < (*.f64 x y) < 5.9999999999999997e116

   1. Initial program 93.7%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 93.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 93.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 72.7%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 72.7%

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

      1. *-commutative N/A

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

      2. metadata-eval N/A

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

      3. times-frac N/A

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

      4. associate-*r* N/A

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

      5. times-frac N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{a}\right), \color{blue}{\left(\frac{z \cdot -9}{2}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, a\right), \left(\frac{\color{blue}{z \cdot -9}}{2}\right)\right) \]

      8. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, a\right), \left(z \cdot \color{blue}{\frac{-9}{2}}\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, a\right), \left(z \cdot \frac{-9}{2}\right)\right) \]

      10. *-lowering-*.f64 71.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, a\right), \mathsf{*.f64}\left(z, \color{blue}{\frac{-9}{2}}\right)\right) \]

   9. Applied egg-rr 71.2%

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

       1. *-commutative N/A

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

       2. associate-*r/ N/A

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

       5. associate-/l* N/A

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

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{t \cdot \frac{-9}{2}}{a}\right)}\right) \]

       7. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(t \cdot \frac{-9}{2}\right), \color{blue}{a}\right)\right) \]

       8. *-lowering-*.f64 71.2%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{-9}{2}\right), a\right)\right) \]

   11. Applied egg-rr 71.2%

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

   if 5.9999999999999997e116 < (*.f64 x y)

   1. Initial program 85.4%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 85.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 85.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{x \cdot y}{a}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\frac{y \cdot x}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\frac{x}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{a}\right)}\right)\right) \]

      5. /-lowering-/.f64 90.3%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 90.3%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}}\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+116}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+116}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (* y (/ x a)))))
   (if (<= (* x y) -1e+89)
     t_1
     (if (<= (* x y) 6e+116) (* z (/ (* t -4.5) a)) 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 = 0.5 * (y * (x / a));
	double tmp;
	if ((x * y) <= -1e+89) {
		tmp = t_1;
	} else if ((x * y) <= 6e+116) {
		tmp = z * ((t * -4.5) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 * (y * (x / a))
    if ((x * y) <= (-1d+89)) then
        tmp = t_1
    else if ((x * y) <= 6d+116) then
        tmp = z * ((t * (-4.5d0)) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (y * (x / a));
	double tmp;
	if ((x * y) <= -1e+89) {
		tmp = t_1;
	} else if ((x * y) <= 6e+116) {
		tmp = z * ((t * -4.5) / a);
	} 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 = 0.5 * (y * (x / a))
	tmp = 0
	if (x * y) <= -1e+89:
		tmp = t_1
	elif (x * y) <= 6e+116:
		tmp = z * ((t * -4.5) / a)
	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(0.5 * Float64(y * Float64(x / a)))
	tmp = 0.0
	if (Float64(x * y) <= -1e+89)
		tmp = t_1;
	elseif (Float64(x * y) <= 6e+116)
		tmp = Float64(z * Float64(Float64(t * -4.5) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (y * (x / a));
	tmp = 0.0;
	if ((x * y) <= -1e+89)
		tmp = t_1;
	elseif ((x * y) <= 6e+116)
		tmp = z * ((t * -4.5) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+89], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 6e+116], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.99999999999999995e88 or 5.9999999999999997e116 < (*.f64 x y)

   1. Initial program 88.7%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 88.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 88.6%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{x \cdot y}{a}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\frac{y \cdot x}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\frac{x}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{a}\right)}\right)\right) \]

      5. /-lowering-/.f64 90.3%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 90.3%

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

   if -9.99999999999999995e88 < (*.f64 x y) < 5.9999999999999997e116

   1. Initial program 93.7%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 93.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 93.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 72.7%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 72.7%

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

      1. *-commutative N/A

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

      2. metadata-eval N/A

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

      3. times-frac N/A

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

      4. associate-*r* N/A

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

      5. times-frac N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{a}\right), \color{blue}{\left(\frac{z \cdot -9}{2}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, a\right), \left(\frac{\color{blue}{z \cdot -9}}{2}\right)\right) \]

      8. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, a\right), \left(z \cdot \color{blue}{\frac{-9}{2}}\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, a\right), \left(z \cdot \frac{-9}{2}\right)\right) \]

      10. *-lowering-*.f64 71.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, a\right), \mathsf{*.f64}\left(z, \color{blue}{\frac{-9}{2}}\right)\right) \]

   9. Applied egg-rr 71.2%

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

       1. *-commutative N/A

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

       2. associate-*r/ N/A

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

       5. associate-/l* N/A

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

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{t \cdot \frac{-9}{2}}{a}\right)}\right) \]

       7. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(t \cdot \frac{-9}{2}\right), \color{blue}{a}\right)\right) \]

       8. *-lowering-*.f64 71.2%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{-9}{2}\right), a\right)\right) \]

   11. Applied egg-rr 71.2%

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

Alternative 6: 92.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 10^{+255}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}}\\ \end{array} \end{array} \]

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) 1e+255)
   (/ (+ (* x y) (* z (* t -9.0))) (* a 2.0))
   (* x (/ y (/ a 0.5)))))

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) <= 1e+255) {
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = x * (y / (a / 0.5));
	}
	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) <= 1d+255) then
        tmp = ((x * y) + (z * (t * (-9.0d0)))) / (a * 2.0d0)
    else
        tmp = x * (y / (a / 0.5d0))
    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) <= 1e+255) {
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = x * (y / (a / 0.5));
	}
	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) <= 1e+255:
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0)
	else:
		tmp = x * (y / (a / 0.5))
	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) <= 1e+255)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(x * Float64(y / Float64(a / 0.5)));
	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) <= 1e+255)
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	else
		tmp = x * (y / (a / 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], 1e+255], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(a / 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 9.99999999999999988e254

   1. Initial program 94.4%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 94.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 94.4%

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

   if 9.99999999999999988e254 < (*.f64 x y)

   1. Initial program 65.5%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 65.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 65.5%

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

      1. frac-2neg N/A

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

      2. distribute-neg-in N/A

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

      3. unsub-neg N/A

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

      4. sub-div N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. metadata-eval N/A

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

      9. distribute-rgt-neg-in N/A

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

      10. distribute-lft-neg-in N/A

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

      11. frac-2neg N/A

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

      12. div-sub N/A

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

      13. div-inv N/A

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

      14. *-commutative N/A

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

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{a \cdot 2}\right), \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{2 \cdot a}\right), \left(x \cdot \color{blue}{y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{a}\right), \left(\color{blue}{x \cdot y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2}\right), a\right), \left(\color{blue}{x \cdot y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \left(\color{blue}{x} \cdot y - \left(z \cdot 9\right) \cdot t\right)\right) \]

      20. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(z \cdot 9\right)\right) \cdot t}\right)\right) \]

   6. Applied egg-rr 65.5%

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

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \color{blue}{\left(x \cdot y\right)}\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 65.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   9. Simplified 65.5%

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

       1. *-commutative N/A

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

       2. associate-*l* N/A

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

       3. metadata-eval N/A

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

       4. associate-/r* N/A

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

       5. *-commutative N/A

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

       6. div-inv N/A

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

       7. *-commutative N/A

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

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a \cdot 2}\right), \color{blue}{x}\right) \]

       9. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a \cdot 2\right)\right), x\right) \]

       10. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a \cdot \frac{1}{\frac{1}{2}}\right)\right), x\right) \]

       11. div-inv N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{a}{\frac{1}{2}}\right)\right), x\right) \]

       12. /-lowering-/.f64 100.0%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \frac{1}{2}\right)\right), x\right) \]

   11. Applied egg-rr 100.0%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 10^{+255}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 10^{+255}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + -9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}}\\ \end{array} \end{array} \]

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) 1e+255)
   (* (/ 0.5 a) (+ (* x y) (* -9.0 (* z t))))
   (* x (/ y (/ a 0.5)))))

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) <= 1e+255) {
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)));
	} else {
		tmp = x * (y / (a / 0.5));
	}
	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) <= 1d+255) then
        tmp = (0.5d0 / a) * ((x * y) + ((-9.0d0) * (z * t)))
    else
        tmp = x * (y / (a / 0.5d0))
    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) <= 1e+255) {
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)));
	} else {
		tmp = x * (y / (a / 0.5));
	}
	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) <= 1e+255:
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)))
	else:
		tmp = x * (y / (a / 0.5))
	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) <= 1e+255)
		tmp = Float64(Float64(0.5 / a) * Float64(Float64(x * y) + Float64(-9.0 * Float64(z * t))));
	else
		tmp = Float64(x * Float64(y / Float64(a / 0.5)));
	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) <= 1e+255)
		tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)));
	else
		tmp = x * (y / (a / 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], 1e+255], N[(N[(0.5 / a), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] + N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(a / 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 9.99999999999999988e254

   1. Initial program 94.4%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 94.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 94.4%

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

      1. frac-2neg N/A

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

      2. distribute-neg-in N/A

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

      3. unsub-neg N/A

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

      4. sub-div N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. metadata-eval N/A

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

      9. distribute-rgt-neg-in N/A

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

      10. distribute-lft-neg-in N/A

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

      11. frac-2neg N/A

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

      12. div-sub N/A

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

      13. div-inv N/A

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

      14. *-commutative N/A

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

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{a \cdot 2}\right), \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{2 \cdot a}\right), \left(x \cdot \color{blue}{y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{a}\right), \left(\color{blue}{x \cdot y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2}\right), a\right), \left(\color{blue}{x \cdot y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \left(\color{blue}{x} \cdot y - \left(z \cdot 9\right) \cdot t\right)\right) \]

      20. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(z \cdot 9\right)\right) \cdot t}\right)\right) \]

   6. Applied egg-rr 94.3%

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

   if 9.99999999999999988e254 < (*.f64 x y)

   1. Initial program 65.5%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 65.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 65.5%

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

      1. frac-2neg N/A

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

      2. distribute-neg-in N/A

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

      3. unsub-neg N/A

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

      4. sub-div N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. metadata-eval N/A

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

      9. distribute-rgt-neg-in N/A

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

      10. distribute-lft-neg-in N/A

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

      11. frac-2neg N/A

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

      12. div-sub N/A

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

      13. div-inv N/A

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

      14. *-commutative N/A

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

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{a \cdot 2}\right), \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{2 \cdot a}\right), \left(x \cdot \color{blue}{y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{a}\right), \left(\color{blue}{x \cdot y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2}\right), a\right), \left(\color{blue}{x \cdot y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \left(\color{blue}{x} \cdot y - \left(z \cdot 9\right) \cdot t\right)\right) \]

      20. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(z \cdot 9\right)\right) \cdot t}\right)\right) \]

   6. Applied egg-rr 65.5%

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

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \color{blue}{\left(x \cdot y\right)}\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 65.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   9. Simplified 65.5%

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

       1. *-commutative N/A

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

       2. associate-*l* N/A

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

       3. metadata-eval N/A

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

       4. associate-/r* N/A

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

       5. *-commutative N/A

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

       6. div-inv N/A

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

       7. *-commutative N/A

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

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a \cdot 2}\right), \color{blue}{x}\right) \]

       9. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a \cdot 2\right)\right), x\right) \]

       10. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a \cdot \frac{1}{\frac{1}{2}}\right)\right), x\right) \]

       11. div-inv N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{a}{\frac{1}{2}}\right)\right), x\right) \]

       12. /-lowering-/.f64 100.0%

           \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \frac{1}{2}\right)\right), x\right) \]

   11. Applied egg-rr 100.0%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 10^{+255}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + -9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-75}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* 0.5 (* y (/ x a)))))
   (if (<= x -9e-42) t_1 (if (<= x 1.35e-75) (* -4.5 (* t (/ z a))) 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 = 0.5 * (y * (x / a));
	double tmp;
	if (x <= -9e-42) {
		tmp = t_1;
	} else if (x <= 1.35e-75) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 * (y * (x / a))
    if (x <= (-9d-42)) then
        tmp = t_1
    else if (x <= 1.35d-75) then
        tmp = (-4.5d0) * (t * (z / a))
    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 = 0.5 * (y * (x / a));
	double tmp;
	if (x <= -9e-42) {
		tmp = t_1;
	} else if (x <= 1.35e-75) {
		tmp = -4.5 * (t * (z / a));
	} 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 = 0.5 * (y * (x / a))
	tmp = 0
	if x <= -9e-42:
		tmp = t_1
	elif x <= 1.35e-75:
		tmp = -4.5 * (t * (z / a))
	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(0.5 * Float64(y * Float64(x / a)))
	tmp = 0.0
	if (x <= -9e-42)
		tmp = t_1;
	elseif (x <= 1.35e-75)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	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 = 0.5 * (y * (x / a));
	tmp = 0.0;
	if (x <= -9e-42)
		tmp = t_1;
	elseif (x <= 1.35e-75)
		tmp = -4.5 * (t * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e-42], t$95$1, If[LessEqual[x, 1.35e-75], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9e-42 or 1.3499999999999999e-75 < x

   1. Initial program 91.8%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 91.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 91.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{x \cdot y}{a}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(\frac{y \cdot x}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\frac{x}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{a}\right)}\right)\right) \]

      5. /-lowering-/.f64 65.6%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 65.6%

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

   if -9e-42 < x < 1.3499999999999999e-75

   1. Initial program 92.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 92.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 92.1%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 70.4%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 70.4%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(t \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(\frac{z}{a} \cdot \color{blue}{t}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(\left(\frac{z}{a}\right), \color{blue}{t}\right)\right) \]

      4. /-lowering-/.f64 72.3%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), t\right)\right) \]

   9. Applied egg-rr 72.3%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-42}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-75}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-96}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

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 -3.9e-96) (* -4.5 (/ (* z t) a)) (* -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) {
	double tmp;
	if (x <= -3.9e-96) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = -4.5 * (t * (z / 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 <= (-3.9d-96)) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = (-4.5d0) * (t * (z / 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 <= -3.9e-96) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = -4.5 * (t * (z / 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 <= -3.9e-96:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = -4.5 * (t * (z / 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 <= -3.9e-96)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(-4.5 * Float64(t * Float64(z / 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 <= -3.9e-96)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = -4.5 * (t * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.9e-96], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.8999999999999998e-96

   1. Initial program 91.5%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 91.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 91.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 40.6%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 40.6%

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

   if -3.8999999999999998e-96 < x

   1. Initial program 92.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      9. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

      12. *-lowering-*.f64 92.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

   3. Simplified 92.1%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 59.7%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

   7. Simplified 59.7%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(t \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(\frac{z}{a} \cdot \color{blue}{t}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(\left(\frac{z}{a}\right), \color{blue}{t}\right)\right) \]

      4. /-lowering-/.f64 61.9%

         \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), t\right)\right) \]

   9. Applied egg-rr 61.9%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-96}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.7% 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 91.9%

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

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right), \color{blue}{\left(a \cdot 2\right)}\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(\color{blue}{a} \cdot 2\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)\right), \left(a \cdot 2\right)\right) \]

   5. associate-*l* N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

   6. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9 \cdot t\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

   8. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

   9. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

   10. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(9\right)\right)\right)\right)\right), \left(a \cdot 2\right)\right) \]

   11. metadata-eval N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \left(a \cdot 2\right)\right) \]

   12. *-lowering-*.f64 91.9%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right), \mathsf{*.f64}\left(a, \color{blue}{2}\right)\right) \]

3. Simplified 91.9%

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

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{a}\right)\right) \]

   3. *-lowering-*.f64 52.9%

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), a\right)\right) \]

7. Simplified 52.9%

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

   1. associate-/l* N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(t \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \left(\frac{z}{a} \cdot \color{blue}{t}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(\left(\frac{z}{a}\right), \color{blue}{t}\right)\right) \]

   4. /-lowering-/.f64 54.8%

      \[\leadsto \mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, a\right), t\right)\right) \]

9. Applied egg-rr 54.8%

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

10. Final simplification 54.8%

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

Developer Target 1: 93.2% 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 2024152 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< a -209046455797670900000000000000000000000000000000000000000000000000000000000000000000000) (- (* 1/2 (/ (* y x) a)) (* 9/2 (/ t (/ a z)))) (if (< a 2144030707833976000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z (* 9 t))) (* a 2)) (- (* (/ y a) (* x 1/2)) (* (/ t a) (* z 9/2))))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))