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

Percentage Accurate: 91.4% → 96.2%

Time: 12.0s

Alternatives: 12

Speedup: 0.5×

• 28.6% 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: 91.4% 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: 96.2% accurate, 0.3× speedup

Math

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

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
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 (- INFINITY))
     (* y (/ (+ (* t (* (/ z y) -4.5)) (* x 0.5)) a))
     (if (<= t_1 5e+262)
       (/ (- (* x y) (* 9.0 (* z t))) (* a 2.0))
       (* (/ y a) (+ (* x 0.5) (* -4.5 (* t (/ z y)))))))))

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

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (((t * ((z / y) * -4.5)) + (x * 0.5)) / a);
	} else if (t_1 <= 5e+262) {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = (y / a) * ((x * 0.5) + (-4.5 * (t * (z / y))));
	}
	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) - ((z * 9.0) * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (((t * ((z / y) * -4.5)) + (x * 0.5)) / a)
	elif t_1 <= 5e+262:
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0)
	else:
		tmp = (y / a) * ((x * 0.5) + (-4.5 * (t * (z / y))))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(Float64(t * Float64(Float64(z / y) * -4.5)) + Float64(x * 0.5)) / a));
	elseif (t_1 <= 5e+262)
		tmp = Float64(Float64(Float64(x * y) - Float64(9.0 * Float64(z * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(y / a) * Float64(Float64(x * 0.5) + Float64(-4.5 * Float64(t * Float64(z / y)))));
	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) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (((t * ((z / y) * -4.5)) + (x * 0.5)) / a);
	elseif (t_1 <= 5e+262)
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	else
		tmp = (y / a) * ((x * 0.5) + (-4.5 * (t * (z / y))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(N[(N[(t * N[(N[(z / y), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+262], N[(N[(N[(x * y), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(N[(x * 0.5), $MachinePrecision] + N[(-4.5 * N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 55.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 55.2%

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

   3. Simplified 55.2%

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

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

      7. associate-/r* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. metadata-eval N/A

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

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

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

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

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

      13. frac-2neg N/A

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

      14. *-commutative N/A

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

      15. associate-/r* N/A

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

      16. frac-sub N/A

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

   6. Applied egg-rr 51.2%

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

   7. Taylor expanded in y around inf

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

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

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

      8. distribute-lft-out N/A

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

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

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

      10. associate-*l/ N/A

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

      11. *-commutative N/A

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

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

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

      13. associate-/l* N/A

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

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

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

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

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

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

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

      17. *-lowering-*.f64 51.5%

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

   9. Simplified 51.5%

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

       1. associate-/l* N/A

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

       2. *-commutative N/A

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

       3. times-frac N/A

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

       4. *-inverses N/A

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

       5. *-lft-identity N/A

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

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

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

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

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

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

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

       9. associate-*r/ N/A

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

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

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

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

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

       12. *-commutative N/A

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

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

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

       14. *-lowering-*.f64 76.6%

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

   11. Applied egg-rr 76.6%

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

       1. associate-/l* N/A

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

       2. *-commutative N/A

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

       3. *-commutative N/A

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

       4. associate-/l* N/A

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

       5. associate-*l* N/A

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

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

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

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

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

       8. /-lowering-/.f64 89.4%

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

   13. Applied egg-rr 89.4%

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

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

   1. Initial program 99.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

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

   1. Initial program 72.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 72.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot x} + \frac{1}{2} \cdot \frac{y}{a}\right)} \]
   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 90.2%

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

4. Final simplification 96.5%

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

Alternative 2: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(x \cdot 0.5 + -4.5 \cdot \left(t \cdot \frac{z}{y}\right)\right)\\ t_2 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+262}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 a) (+ (* x 0.5) (* -4.5 (* t (/ z y))))))
        (t_2 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 5e+262) (/ (- (* x y) (* 9.0 (* z t))) (* 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 / a) * ((x * 0.5) + (-4.5 * (t * (z / y))));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 5e+262) {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * ((x * 0.5) + (-4.5 * (t * (z / y))));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 5e+262) {
		tmp = ((x * y) - (9.0 * (z * t))) / (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 / a) * ((x * 0.5) + (-4.5 * (t * (z / y))))
	t_2 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 5e+262:
		tmp = ((x * y) - (9.0 * (z * t))) / (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 / a) * Float64(Float64(x * 0.5) + Float64(-4.5 * Float64(t * Float64(z / y)))))
	t_2 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 5e+262)
		tmp = Float64(Float64(Float64(x * y) - Float64(9.0 * Float64(z * t))) / 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 / a) * ((x * 0.5) + (-4.5 * (t * (z / y))));
	t_2 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 5e+262)
		tmp = ((x * y) - (9.0 * (z * t))) / (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 / a), $MachinePrecision] * N[(N[(x * 0.5), $MachinePrecision] + N[(-4.5 * N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $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, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 5e+262], N[(N[(N[(x * y), $MachinePrecision] - N[(9.0 * N[(z * t), $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)) < -inf.0 or 5.00000000000000008e262 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 63.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 63.2%

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

   3. Simplified 63.2%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 89.6%

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

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

   1. Initial program 99.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

4. Final simplification 96.5%

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

Alternative 3: 94.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ t_2 := t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+228}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)) (t_2 (* t (* z (/ -4.5 a)))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 1e+228) (/ (- (* x y) (* 9.0 (* z t))) (* a 2.0)) t_2))))

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 = (z * 9.0) * t;
	double t_2 = t * (z * (-4.5 / a));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 1e+228) {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double t_2 = t * (z * (-4.5 / a));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 1e+228) {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	t_2 = t * (z * (-4.5 / a))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 1e+228:
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0)
	else:
		tmp = t_2
	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(z * 9.0) * t)
	t_2 = Float64(t * Float64(z * Float64(-4.5 / a)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 1e+228)
		tmp = Float64(Float64(Float64(x * y) - Float64(9.0 * Float64(z * t))) / Float64(a * 2.0));
	else
		tmp = t_2;
	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 = (z * 9.0) * t;
	t_2 = t * (z * (-4.5 / a));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 1e+228)
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	else
		tmp = t_2;
	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[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 1e+228], N[(N[(N[(x * y), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -inf.0 or 9.9999999999999992e227 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 66.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 66.7%

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

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 68.7%

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

   7. Simplified 68.7%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

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

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

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

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

      13. *-lowering-*.f64 97.8%

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

   9. Applied egg-rr 97.8%

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

       1. *-commutative N/A

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

       2. associate-*l* N/A

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

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

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

       4. clear-num N/A

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

       5. un-div-inv N/A

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

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

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

       7. /-lowering-/.f64 98.2%

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

   11. Applied egg-rr 98.2%

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

       1. associate-*r/ N/A

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

       2. associate-*l/ N/A

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

       3. associate-/r/ N/A

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

       4. associate-*l* N/A

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

       5. *-commutative N/A

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

       6. associate-*r* N/A

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

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

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

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

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

       9. /-lowering-/.f64 98.3%

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

   13. Applied egg-rr 98.3%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 9.9999999999999992e227

   1. Initial program 92.9%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 93.0%

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

   4. Applied egg-rr 93.0%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 10^{+228}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ t_2 := t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+228}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)) (t_2 (* t (* z (/ -4.5 a)))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 1e+228) (/ (+ (* x y) (* z (* t -9.0))) (* a 2.0)) t_2))))

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 = (z * 9.0) * t;
	double t_2 = t * (z * (-4.5 / a));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 1e+228) {
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double t_2 = t * (z * (-4.5 / a));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 1e+228) {
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	t_2 = t * (z * (-4.5 / a))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 1e+228:
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0)
	else:
		tmp = t_2
	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(z * 9.0) * t)
	t_2 = Float64(t * Float64(z * Float64(-4.5 / a)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 1e+228)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = t_2;
	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 = (z * 9.0) * t;
	t_2 = t * (z * (-4.5 / a));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 1e+228)
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	else
		tmp = t_2;
	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[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 1e+228], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -inf.0 or 9.9999999999999992e227 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 66.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 66.7%

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

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 68.7%

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

   7. Simplified 68.7%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

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

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

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

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

      13. *-lowering-*.f64 97.8%

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

   9. Applied egg-rr 97.8%

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

       1. *-commutative N/A

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

       2. associate-*l* N/A

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

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

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

       4. clear-num N/A

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

       5. un-div-inv N/A

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

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

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

       7. /-lowering-/.f64 98.2%

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

   11. Applied egg-rr 98.2%

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

       1. associate-*r/ N/A

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

       2. associate-*l/ N/A

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

       3. associate-/r/ N/A

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

       4. associate-*l* N/A

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

       5. *-commutative N/A

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

       6. associate-*r* N/A

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

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

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

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

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

       9. /-lowering-/.f64 98.3%

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

   13. Applied egg-rr 98.3%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 9.9999999999999992e227

   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
3. Recombined 2 regimes into one program.

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 10^{+228}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+234}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y + z \cdot \left(t \cdot -9\right)}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* (* x 0.5) (/ y a))
   (if (<= (* x y) 4e+234)
     (/ 0.5 (/ a (+ (* x y) (* z (* t -9.0)))))
     (* x (/ (* y 0.5) a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = (x * 0.5) * (y / a);
	} else if ((x * y) <= 4e+234) {
		tmp = 0.5 / (a / ((x * y) + (z * (t * -9.0))));
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = (x * 0.5) * (y / a);
	} else if ((x * y) <= 4e+234) {
		tmp = 0.5 / (a / ((x * y) + (z * (t * -9.0))));
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = (x * 0.5) * (y / a)
	elif (x * y) <= 4e+234:
		tmp = 0.5 / (a / ((x * y) + (z * (t * -9.0))))
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(Float64(x * 0.5) * Float64(y / a));
	elseif (Float64(x * y) <= 4e+234)
		tmp = Float64(0.5 / Float64(a / Float64(Float64(x * y) + Float64(z * Float64(t * -9.0)))));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = (x * 0.5) * (y / a);
	elseif ((x * y) <= 4e+234)
		tmp = 0.5 / (a / ((x * y) + (z * (t * -9.0))));
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(N[(x * 0.5), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+234], N[(0.5 / N[(a / N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -inf.0

   1. Initial program 56.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 56.5%

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

   3. Simplified 56.5%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 95.8%

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

   7. Simplified 95.8%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. associate-/l* N/A

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

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

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

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

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

      8. /-lowering-/.f64 95.7%

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

   9. Applied egg-rr 95.7%

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

   if -inf.0 < (*.f64 x y) < 4.00000000000000007e234

   1. Initial program 93.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 93.1%

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

   3. Simplified 93.1%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. flip3-+ N/A

         \[\leadsto \frac{\frac{1}{2}}{a} \cdot \frac{{\left(x \cdot y\right)}^{3} + {\left(z \cdot \left(t \cdot -9\right)\right)}^{3}}{\color{blue}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(z \cdot \left(t \cdot -9\right)\right) \cdot \left(z \cdot \left(t \cdot -9\right)\right) - \left(x \cdot y\right) \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)}} \]

      6. clear-num N/A

         \[\leadsto \frac{\frac{1}{2}}{a} \cdot \frac{1}{\color{blue}{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(z \cdot \left(t \cdot -9\right)\right) \cdot \left(z \cdot \left(t \cdot -9\right)\right) - \left(x \cdot y\right) \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)}{{\left(x \cdot y\right)}^{3} + {\left(z \cdot \left(t \cdot -9\right)\right)}^{3}}}} \]

      7. frac-times N/A

         \[\leadsto \frac{\frac{1}{2} \cdot 1}{\color{blue}{a \cdot \frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(z \cdot \left(t \cdot -9\right)\right) \cdot \left(z \cdot \left(t \cdot -9\right)\right) - \left(x \cdot y\right) \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)}{{\left(x \cdot y\right)}^{3} + {\left(z \cdot \left(t \cdot -9\right)\right)}^{3}}}} \]

      8. metadata-eval N/A

         \[\leadsto \frac{\frac{1}{2} \cdot 1}{a \cdot \frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(z \cdot \left(t \cdot -9\right)\right) \cdot \left(z \cdot \left(t \cdot -9\right)\right) - \left(x \cdot y\right) \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)}{{\left(x \cdot y\right)}^{3} + {\left(z \cdot \left(t \cdot -9\right)\right)}^{3}}} \]

      9. metadata-eval N/A

         \[\leadsto \frac{\frac{1}{2}}{\color{blue}{a} \cdot \frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(z \cdot \left(t \cdot -9\right)\right) \cdot \left(z \cdot \left(t \cdot -9\right)\right) - \left(x \cdot y\right) \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)}{{\left(x \cdot y\right)}^{3} + {\left(z \cdot \left(t \cdot -9\right)\right)}^{3}}} \]

      10. metadata-eval N/A

          \[\leadsto \frac{\frac{1}{2}}{\color{blue}{a} \cdot \frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(z \cdot \left(t \cdot -9\right)\right) \cdot \left(z \cdot \left(t \cdot -9\right)\right) - \left(x \cdot y\right) \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)}{{\left(x \cdot y\right)}^{3} + {\left(z \cdot \left(t \cdot -9\right)\right)}^{3}}} \]

      11. clear-num N/A

          \[\leadsto \frac{\frac{1}{2}}{a \cdot \frac{1}{\color{blue}{\frac{{\left(x \cdot y\right)}^{3} + {\left(z \cdot \left(t \cdot -9\right)\right)}^{3}}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(z \cdot \left(t \cdot -9\right)\right) \cdot \left(z \cdot \left(t \cdot -9\right)\right) - \left(x \cdot y\right) \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)}}}} \]

   6. Applied egg-rr 93.0%

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

   if 4.00000000000000007e234 < (*.f64 x y)

   1. Initial program 72.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 72.8%

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

   3. Simplified 72.8%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 95.9%

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

   7. Simplified 95.9%

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

      1. associate-*r* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. /-lowering-/.f64 95.9%

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

   9. Applied egg-rr 95.9%

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

       1. associate-/r/ N/A

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

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

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

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

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

       4. *-commutative N/A

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

       5. *-lowering-*.f64 95.9%

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

   11. Applied egg-rr 95.9%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+234}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y + z \cdot \left(t \cdot -9\right)}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+234}:\\ \;\;\;\;\left(x \cdot y + z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* (* x 0.5) (/ y a))
   (if (<= (* x y) 4e+234)
     (* (+ (* x y) (* z (* t -9.0))) (/ 0.5 a))
     (* x (/ (* y 0.5) a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = (x * 0.5) * (y / a);
	} else if ((x * y) <= 4e+234) {
		tmp = ((x * y) + (z * (t * -9.0))) * (0.5 / a);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = (x * 0.5) * (y / a);
	} else if ((x * y) <= 4e+234) {
		tmp = ((x * y) + (z * (t * -9.0))) * (0.5 / a);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = (x * 0.5) * (y / a)
	elif (x * y) <= 4e+234:
		tmp = ((x * y) + (z * (t * -9.0))) * (0.5 / a)
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(Float64(x * 0.5) * Float64(y / a));
	elseif (Float64(x * y) <= 4e+234)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t * -9.0))) * Float64(0.5 / a));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = (x * 0.5) * (y / a);
	elseif ((x * y) <= 4e+234)
		tmp = ((x * y) + (z * (t * -9.0))) * (0.5 / a);
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(N[(x * 0.5), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+234], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -inf.0

   1. Initial program 56.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 56.5%

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

   3. Simplified 56.5%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 95.8%

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

   7. Simplified 95.8%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. associate-/l* N/A

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

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

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

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

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

      8. /-lowering-/.f64 95.7%

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

   9. Applied egg-rr 95.7%

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

   if -inf.0 < (*.f64 x y) < 4.00000000000000007e234

   1. Initial program 93.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 93.1%

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

   3. Simplified 93.1%

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

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

   6. Applied egg-rr 92.9%

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

   if 4.00000000000000007e234 < (*.f64 x y)

   1. Initial program 72.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 72.8%

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

   3. Simplified 72.8%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 95.9%

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

   7. Simplified 95.9%

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

      1. associate-*r* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. /-lowering-/.f64 95.9%

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

   9. Applied egg-rr 95.9%

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

       1. associate-/r/ N/A

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

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

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

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

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

       4. *-commutative N/A

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

       5. *-lowering-*.f64 95.9%

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

   11. Applied egg-rr 95.9%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+234}:\\ \;\;\;\;\left(x \cdot y + z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\frac{x \cdot 0.5}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+38}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

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+90)
   (/ (* x 0.5) (/ a y))
   (if (<= (* x y) 1e+38) (* (/ t a) (* z -4.5)) (* 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+90) {
		tmp = (x * 0.5) / (a / y);
	} else if ((x * y) <= 1e+38) {
		tmp = (t / a) * (z * -4.5);
	} 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+90)) then
        tmp = (x * 0.5d0) / (a / y)
    else if ((x * y) <= 1d+38) then
        tmp = (t / a) * (z * (-4.5d0))
    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+90) {
		tmp = (x * 0.5) / (a / y);
	} else if ((x * y) <= 1e+38) {
		tmp = (t / a) * (z * -4.5);
	} 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+90:
		tmp = (x * 0.5) / (a / y)
	elif (x * y) <= 1e+38:
		tmp = (t / a) * (z * -4.5)
	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+90)
		tmp = Float64(Float64(x * 0.5) / Float64(a / y));
	elseif (Float64(x * y) <= 1e+38)
		tmp = Float64(Float64(t / a) * Float64(z * -4.5));
	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+90)
		tmp = (x * 0.5) / (a / y);
	elseif ((x * y) <= 1e+38)
		tmp = (t / a) * (z * -4.5);
	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+90], N[(N[(x * 0.5), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+38], N[(N[(t / a), $MachinePrecision] * N[(z * -4.5), $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) < -9.99999999999999966e89

   1. Initial program 79.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 79.5%

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

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 77.4%

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

   7. Simplified 77.4%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. associate-/l* N/A

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

      6. clear-num N/A

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

      7. un-div-inv N/A

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

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

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

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

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

      10. /-lowering-/.f64 74.6%

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

   9. Applied egg-rr 74.6%

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

   if -9.99999999999999966e89 < (*.f64 x y) < 9.99999999999999977e37

   1. Initial program 92.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in x around 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 75.1%

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

   7. Simplified 75.1%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

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

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

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

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

      13. *-lowering-*.f64 79.1%

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

   9. Applied egg-rr 79.1%

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

   if 9.99999999999999977e37 < (*.f64 x y)

   1. Initial program 85.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 85.7%

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

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 79.1%

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

   7. Simplified 79.1%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\frac{x \cdot 0.5}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+38}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+38}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

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+90)
   (* (* x 0.5) (/ y a))
   (if (<= (* x y) 1e+38) (* (/ t a) (* z -4.5)) (* 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+90) {
		tmp = (x * 0.5) * (y / a);
	} else if ((x * y) <= 1e+38) {
		tmp = (t / a) * (z * -4.5);
	} 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+90)) then
        tmp = (x * 0.5d0) * (y / a)
    else if ((x * y) <= 1d+38) then
        tmp = (t / a) * (z * (-4.5d0))
    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+90) {
		tmp = (x * 0.5) * (y / a);
	} else if ((x * y) <= 1e+38) {
		tmp = (t / a) * (z * -4.5);
	} 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+90:
		tmp = (x * 0.5) * (y / a)
	elif (x * y) <= 1e+38:
		tmp = (t / a) * (z * -4.5)
	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+90)
		tmp = Float64(Float64(x * 0.5) * Float64(y / a));
	elseif (Float64(x * y) <= 1e+38)
		tmp = Float64(Float64(t / a) * Float64(z * -4.5));
	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+90)
		tmp = (x * 0.5) * (y / a);
	elseif ((x * y) <= 1e+38)
		tmp = (t / a) * (z * -4.5);
	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+90], N[(N[(x * 0.5), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+38], N[(N[(t / a), $MachinePrecision] * N[(z * -4.5), $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) < -9.99999999999999966e89

   1. Initial program 79.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 79.5%

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

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 77.4%

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

   7. Simplified 77.4%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. associate-/l* N/A

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

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

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

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

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

      8. /-lowering-/.f64 74.5%

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

   9. Applied egg-rr 74.5%

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

   if -9.99999999999999966e89 < (*.f64 x y) < 9.99999999999999977e37

   1. Initial program 92.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in x around 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 75.1%

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

   7. Simplified 75.1%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

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

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

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

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

      13. *-lowering-*.f64 79.1%

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

   9. Applied egg-rr 79.1%

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

   if 9.99999999999999977e37 < (*.f64 x y)

   1. Initial program 85.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 85.7%

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

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 79.1%

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

   7. Simplified 79.1%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+38}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

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+90)
   (* (* x 0.5) (/ y a))
   (if (<= (* x y) 2e+117) (* t (* z (/ -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+90) {
		tmp = (x * 0.5) * (y / a);
	} else if ((x * y) <= 2e+117) {
		tmp = t * (z * (-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+90)) then
        tmp = (x * 0.5d0) * (y / a)
    else if ((x * y) <= 2d+117) then
        tmp = t * (z * ((-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+90) {
		tmp = (x * 0.5) * (y / a);
	} else if ((x * y) <= 2e+117) {
		tmp = t * (z * (-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+90:
		tmp = (x * 0.5) * (y / a)
	elif (x * y) <= 2e+117:
		tmp = t * (z * (-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+90)
		tmp = Float64(Float64(x * 0.5) * Float64(y / a));
	elseif (Float64(x * y) <= 2e+117)
		tmp = Float64(t * Float64(z * Float64(-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+90)
		tmp = (x * 0.5) * (y / a);
	elseif ((x * y) <= 2e+117)
		tmp = t * (z * (-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+90], N[(N[(x * 0.5), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+117], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $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) < -9.99999999999999966e89

   1. Initial program 79.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 79.5%

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

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 77.4%

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

   7. Simplified 77.4%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r* N/A

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

      5. associate-/l* N/A

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

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

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

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

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

      8. /-lowering-/.f64 74.5%

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

   9. Applied egg-rr 74.5%

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

   if -9.99999999999999966e89 < (*.f64 x y) < 2.0000000000000001e117

   1. Initial program 92.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 92.5%

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

   3. Simplified 92.5%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 72.1%

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

   7. Simplified 72.1%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

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

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

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

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

      13. *-lowering-*.f64 76.4%

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

   9. Applied egg-rr 76.4%

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

       1. *-commutative N/A

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

       2. associate-*l* N/A

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

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

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

       4. clear-num N/A

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

       5. un-div-inv N/A

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

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

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

       7. /-lowering-/.f64 75.2%

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

   11. Applied egg-rr 75.2%

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

       1. associate-*r/ N/A

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

       2. associate-*l/ N/A

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

       3. associate-/r/ N/A

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

       4. associate-*l* N/A

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

       5. *-commutative N/A

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

       6. associate-*r* N/A

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

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

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

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

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

       9. /-lowering-/.f64 74.0%

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

   13. Applied egg-rr 74.0%

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

   if 2.0000000000000001e117 < (*.f64 x y)

   1. Initial program 83.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 83.5%

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

   3. Simplified 83.5%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 89.5%

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

   7. Simplified 89.5%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := -4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* -4.5 (/ z (/ a t)))))
   (if (<= t -1.4e-81) t_1 (if (<= t 5.5e-5) (* 0.5 (* y (/ x 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 = -4.5 * (z / (a / t));
	double tmp;
	if (t <= -1.4e-81) {
		tmp = t_1;
	} else if (t <= 5.5e-5) {
		tmp = 0.5 * (y * (x / 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 = (-4.5d0) * (z / (a / t))
    if (t <= (-1.4d-81)) then
        tmp = t_1
    else if (t <= 5.5d-5) then
        tmp = 0.5d0 * (y * (x / 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 = -4.5 * (z / (a / t));
	double tmp;
	if (t <= -1.4e-81) {
		tmp = t_1;
	} else if (t <= 5.5e-5) {
		tmp = 0.5 * (y * (x / 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 = -4.5 * (z / (a / t))
	tmp = 0
	if t <= -1.4e-81:
		tmp = t_1
	elif t <= 5.5e-5:
		tmp = 0.5 * (y * (x / 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(-4.5 * Float64(z / Float64(a / t)))
	tmp = 0.0
	if (t <= -1.4e-81)
		tmp = t_1;
	elseif (t <= 5.5e-5)
		tmp = Float64(0.5 * Float64(y * Float64(x / 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 = -4.5 * (z / (a / t));
	tmp = 0.0;
	if (t <= -1.4e-81)
		tmp = t_1;
	elseif (t <= 5.5e-5)
		tmp = 0.5 * (y * (x / 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[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e-81], t$95$1, If[LessEqual[t, 5.5e-5], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3999999999999999e-81 or 5.5000000000000002e-5 < t

   1. Initial program 84.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 84.8%

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

   3. Simplified 84.8%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 57.5%

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

   7. Simplified 57.5%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

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

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

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

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

      13. *-lowering-*.f64 68.9%

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

   9. Applied egg-rr 68.9%

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

       1. *-commutative N/A

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

       2. associate-*l* N/A

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

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

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

       4. clear-num N/A

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

       5. un-div-inv N/A

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

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

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

       7. /-lowering-/.f64 68.2%

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

   11. Applied egg-rr 68.2%

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

   if -1.3999999999999999e-81 < t < 5.5000000000000002e-5

   1. Initial program 92.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 92.5%

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

   3. Simplified 92.5%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 68.4%

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

   7. Simplified 68.4%

      \[\leadsto \color{blue}{0.5 \cdot \left(y \cdot \frac{x}{a}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 51.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{-255}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x 2.1e-255) (* -4.5 (/ z (/ a t))) (* -4.5 (/ (* z t) a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 2.1e-255) {
		tmp = -4.5 * (z / (a / t));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= 2.1d-255) then
        tmp = (-4.5d0) * (z / (a / t))
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 2.1e-255) {
		tmp = -4.5 * (z / (a / t));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= 2.1e-255:
		tmp = -4.5 * (z / (a / t))
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 2.1e-255)
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 2.1e-255)
		tmp = -4.5 * (z / (a / t));
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, 2.1e-255], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.1e-255

   1. Initial program 86.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 86.7%

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

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 51.3%

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

   7. Simplified 51.3%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

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

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. associate-*l* N/A

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

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

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

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

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

      13. *-lowering-*.f64 58.2%

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

   9. Applied egg-rr 58.2%

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

       1. *-commutative N/A

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

       2. associate-*l* N/A

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

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

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

       4. clear-num N/A

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

       5. un-div-inv N/A

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

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

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

       7. /-lowering-/.f64 57.1%

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

   11. Applied egg-rr 57.1%

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

   if 2.1e-255 < x

   1. Initial program 89.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 89.5%

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

   3. Simplified 89.5%

      \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
   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 48.8%

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

   7. Simplified 48.8%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{-255}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.5% accurate, 1.9× speedup

Math

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

FPCore

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

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

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.0%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
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 88.0%

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

3. Simplified 88.0%

   \[\leadsto \color{blue}{\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}} \]
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 50.2%

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

7. Simplified 50.2%

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

   1. *-commutative N/A

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

   2. *-commutative N/A

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

   3. associate-/l* N/A

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

   4. associate-*r* N/A

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

   5. metadata-eval N/A

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

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

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

   7. *-commutative N/A

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

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

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

   9. metadata-eval N/A

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

   10. associate-*l* N/A

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

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

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

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

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

   13. *-lowering-*.f64 55.7%

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

9. Applied egg-rr 55.7%

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

    1. *-commutative N/A

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

    2. associate-*l* N/A

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

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

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

    4. clear-num N/A

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

    5. un-div-inv N/A

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

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

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

    7. /-lowering-/.f64 54.7%

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

11. Applied egg-rr 54.7%

    \[\leadsto \color{blue}{-4.5 \cdot \frac{z}{\frac{a}{t}}} \]
12. Add Preprocessing

Developer Target 1: 93.6% 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 2024138 
(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)))