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

Percentage Accurate: 91.6% → 94.7%

Time: 7.9s

Alternatives: 10

Speedup: 0.4×

• 28.8% 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: 91.6% 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: 94.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \mathsf{fma}\left(-4.5, \frac{\frac{z}{\frac{a}{t}}}{y}, x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+296}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a} + 0.5 \cdot \frac{x \cdot y}{t \cdot a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 (- INFINITY))
     (* y (fma -4.5 (/ (/ z (/ a t)) y) (* x (/ 0.5 a))))
     (if (<= t_1 4e+296)
       (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
       (* t (+ (* -4.5 (/ z a)) (* 0.5 (/ (* x y) (* t a)))))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * fma(-4.5, ((z / (a / t)) / y), (x * (0.5 / a)));
	} else if (t_1 <= 4e+296) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = t * ((-4.5 * (z / a)) + (0.5 * ((x * y) / (t * a))));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * fma(-4.5, Float64(Float64(z / Float64(a / t)) / y), Float64(x * Float64(0.5 / a))));
	elseif (t_1 <= 4e+296)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(t * Float64(Float64(-4.5 * Float64(z / a)) + Float64(0.5 * Float64(Float64(x * y) / Float64(t * a)))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := 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[(-4.5 * N[(N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+296], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(-4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[(x * y), $MachinePrecision] / N[(t * a), $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 67.6%

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

      1. div-inv 67.6%

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

      2. fma-neg 67.6%

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

      3. *-commutative 67.6%

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

      4. distribute-rgt-neg-in 67.6%

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

      5. distribute-rgt-neg-in 67.6%

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

      6. metadata-eval 67.6%

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

      7. *-commutative 67.6%

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

      8. associate-/r* 67.6%

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

      9. metadata-eval 67.6%

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

   4. Applied egg-rr 67.6%

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

   5. Taylor expanded in y around inf 83.3%

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

      1. fma-define 83.3%

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

      2. associate-/r* 83.4%

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

      3. *-commutative 83.4%

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

      4. associate-*l/ 86.7%

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

      5. associate-/r/ 83.2%

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

      6. associate-*r/ 83.2%

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

      7. associate-*l/ 83.1%

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

      8. *-commutative 83.1%

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

   7. Simplified 83.1%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 3.99999999999999993e296

   1. Initial program 99.2%

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

      1. div-sub 96.7%

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

      2. *-commutative 96.7%

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

      3. div-sub 99.2%

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

      4. cancel-sign-sub-inv 99.2%

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

      5. *-commutative 99.2%

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

      6. fma-define 99.2%

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

      7. distribute-rgt-neg-in 99.2%

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

      8. associate-*r* 99.2%

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

      9. distribute-lft-neg-in 99.2%

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

      10. *-commutative 99.2%

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

      11. distribute-rgt-neg-in 99.2%

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

      12. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

      1. *-commutative 99.2%

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

      2. associate-*r* 99.2%

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

      3. metadata-eval 99.2%

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

      4. distribute-rgt-neg-in 99.2%

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

      5. distribute-lft-neg-in 99.2%

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

      6. fma-neg 99.2%

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

      7. associate-*l* 99.2%

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

   6. Applied egg-rr 99.2%

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

   if 3.99999999999999993e296 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 53.4%

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

   3. Taylor expanded in t around inf 82.6%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;y \cdot \mathsf{fma}\left(-4.5, \frac{\frac{z}{\frac{a}{t}}}{y}, x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 4 \cdot 10^{+296}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a} + 0.5 \cdot \frac{x \cdot y}{t \cdot a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a \cdot 2}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+29)
   (* y (/ x (* a 2.0)))
   (if (<= (* x y) 2e-126)
     (/ (* t -4.5) (/ a z))
     (if (<= (* x y) 1e-97)
       (* (* x y) (/ 0.5 a))
       (if (<= (* x y) 5e-8) (* z (/ (* t -4.5) a)) (/ x (/ (* a 2.0) y)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = y * (x / (a * 2.0));
	} else if ((x * y) <= 2e-126) {
		tmp = (t * -4.5) / (a / z);
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e-8) {
		tmp = z * ((t * -4.5) / a);
	} else {
		tmp = x / ((a * 2.0) / y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-5d+29)) then
        tmp = y * (x / (a * 2.0d0))
    else if ((x * y) <= 2d-126) then
        tmp = (t * (-4.5d0)) / (a / z)
    else if ((x * y) <= 1d-97) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 5d-8) then
        tmp = z * ((t * (-4.5d0)) / a)
    else
        tmp = x / ((a * 2.0d0) / y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = y * (x / (a * 2.0));
	} else if ((x * y) <= 2e-126) {
		tmp = (t * -4.5) / (a / z);
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e-8) {
		tmp = z * ((t * -4.5) / a);
	} else {
		tmp = x / ((a * 2.0) / y);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+29:
		tmp = y * (x / (a * 2.0))
	elif (x * y) <= 2e-126:
		tmp = (t * -4.5) / (a / z)
	elif (x * y) <= 1e-97:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 5e-8:
		tmp = z * ((t * -4.5) / a)
	else:
		tmp = x / ((a * 2.0) / y)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+29)
		tmp = Float64(y * Float64(x / Float64(a * 2.0)));
	elseif (Float64(x * y) <= 2e-126)
		tmp = Float64(Float64(t * -4.5) / Float64(a / z));
	elseif (Float64(x * y) <= 1e-97)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 5e-8)
		tmp = Float64(z * Float64(Float64(t * -4.5) / a));
	else
		tmp = Float64(x / Float64(Float64(a * 2.0) / y));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+29)
		tmp = y * (x / (a * 2.0));
	elseif ((x * y) <= 2e-126)
		tmp = (t * -4.5) / (a / z);
	elseif ((x * y) <= 1e-97)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 5e-8)
		tmp = z * ((t * -4.5) / a);
	else
		tmp = x / ((a * 2.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+29], N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-126], N[(N[(t * -4.5), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-97], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-8], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(a * 2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -5.0000000000000001e29

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-/l* 79.9%

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

      3. associate-*r* 79.9%

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

      4. *-commutative 79.9%

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

      5. associate-*r/ 79.9%

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

   5. Simplified 79.9%

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

      1. clear-num 79.8%

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

      2. un-div-inv 79.9%

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

      3. associate-/r* 79.9%

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

      4. div-inv 79.9%

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

      5. metadata-eval 79.9%

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

   7. Applied egg-rr 79.9%

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

      1. associate-/r/ 81.9%

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

   9. Simplified 81.9%

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

   if -5.0000000000000001e29 < (*.f64 x y) < 1.9999999999999999e-126

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 82.4%

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

      1. associate-/l* 83.9%

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

   5. Simplified 83.9%

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

      1. associate-*r* 83.8%

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

      2. clear-num 83.8%

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

      3. un-div-inv 84.2%

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

      4. *-commutative 84.2%

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

   7. Applied egg-rr 84.2%

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

   if 1.9999999999999999e-126 < (*.f64 x y) < 1.00000000000000004e-97

   1. Initial program 99.0%

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

      1. div-inv 99.2%

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

      2. fma-neg 99.2%

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

      3. *-commutative 99.2%

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

      4. distribute-rgt-neg-in 99.2%

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

      5. distribute-rgt-neg-in 99.2%

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

      6. metadata-eval 99.2%

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

      7. *-commutative 99.2%

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

      8. associate-/r* 99.2%

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

      9. metadata-eval 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in x around inf 99.2%

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

   if 1.00000000000000004e-97 < (*.f64 x y) < 4.9999999999999998e-8

   1. Initial program 84.5%

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

   3. Taylor expanded in x around 0 58.5%

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

      1. associate-*r/ 58.4%

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

      2. associate-*r* 58.6%

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

      3. associate-*l/ 68.5%

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

      4. associate-*r/ 68.4%

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

      5. *-commutative 68.4%

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

      6. associate-*r/ 68.5%

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

   5. Simplified 68.5%

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

   if 4.9999999999999998e-8 < (*.f64 x y)

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 76.1%

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

      1. *-commutative 76.1%

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

      2. associate-/l* 74.3%

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

      3. associate-*r* 74.3%

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

      4. *-commutative 74.3%

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

      5. associate-*r/ 74.3%

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

   5. Simplified 74.3%

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

      1. clear-num 74.2%

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

      2. un-div-inv 74.2%

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

      3. associate-/r* 74.2%

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

      4. div-inv 74.2%

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

      5. metadata-eval 74.2%

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

   7. Applied egg-rr 74.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{a \cdot 2}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a \cdot 2}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a \cdot 2}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+29)
   (* y (/ x (* a 2.0)))
   (if (<= (* x y) 2e-126)
     (* (/ z a) (* t -4.5))
     (if (<= (* x y) 1e-97)
       (* (* x y) (/ 0.5 a))
       (if (<= (* x y) 5e-8) (* z (/ (* t -4.5) a)) (/ x (/ (* a 2.0) y)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = y * (x / (a * 2.0));
	} else if ((x * y) <= 2e-126) {
		tmp = (z / a) * (t * -4.5);
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e-8) {
		tmp = z * ((t * -4.5) / a);
	} else {
		tmp = x / ((a * 2.0) / y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-5d+29)) then
        tmp = y * (x / (a * 2.0d0))
    else if ((x * y) <= 2d-126) then
        tmp = (z / a) * (t * (-4.5d0))
    else if ((x * y) <= 1d-97) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 5d-8) then
        tmp = z * ((t * (-4.5d0)) / a)
    else
        tmp = x / ((a * 2.0d0) / y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = y * (x / (a * 2.0));
	} else if ((x * y) <= 2e-126) {
		tmp = (z / a) * (t * -4.5);
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e-8) {
		tmp = z * ((t * -4.5) / a);
	} else {
		tmp = x / ((a * 2.0) / y);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+29:
		tmp = y * (x / (a * 2.0))
	elif (x * y) <= 2e-126:
		tmp = (z / a) * (t * -4.5)
	elif (x * y) <= 1e-97:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 5e-8:
		tmp = z * ((t * -4.5) / a)
	else:
		tmp = x / ((a * 2.0) / y)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+29)
		tmp = Float64(y * Float64(x / Float64(a * 2.0)));
	elseif (Float64(x * y) <= 2e-126)
		tmp = Float64(Float64(z / a) * Float64(t * -4.5));
	elseif (Float64(x * y) <= 1e-97)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 5e-8)
		tmp = Float64(z * Float64(Float64(t * -4.5) / a));
	else
		tmp = Float64(x / Float64(Float64(a * 2.0) / y));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+29)
		tmp = y * (x / (a * 2.0));
	elseif ((x * y) <= 2e-126)
		tmp = (z / a) * (t * -4.5);
	elseif ((x * y) <= 1e-97)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 5e-8)
		tmp = z * ((t * -4.5) / a);
	else
		tmp = x / ((a * 2.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+29], N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-126], N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-97], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-8], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(a * 2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -5.0000000000000001e29

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-/l* 79.9%

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

      3. associate-*r* 79.9%

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

      4. *-commutative 79.9%

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

      5. associate-*r/ 79.9%

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

   5. Simplified 79.9%

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

      1. clear-num 79.8%

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

      2. un-div-inv 79.9%

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

      3. associate-/r* 79.9%

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

      4. div-inv 79.9%

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

      5. metadata-eval 79.9%

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

   7. Applied egg-rr 79.9%

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

      1. associate-/r/ 81.9%

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

   9. Simplified 81.9%

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

   if -5.0000000000000001e29 < (*.f64 x y) < 1.9999999999999999e-126

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 82.3%

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

      1. *-commutative 82.3%

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

      2. associate-*r* 82.3%

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

   5. Simplified 82.3%

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

      1. associate-*r* 82.3%

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

      2. times-frac 82.4%

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

      3. associate-*r/ 83.9%

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

      4. metadata-eval 83.9%

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

      5. *-commutative 83.9%

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

      6. associate-*l* 83.8%

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

   7. Applied egg-rr 83.8%

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

   if 1.9999999999999999e-126 < (*.f64 x y) < 1.00000000000000004e-97

   1. Initial program 99.0%

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

      1. div-inv 99.2%

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

      2. fma-neg 99.2%

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

      3. *-commutative 99.2%

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

      4. distribute-rgt-neg-in 99.2%

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

      5. distribute-rgt-neg-in 99.2%

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

      6. metadata-eval 99.2%

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

      7. *-commutative 99.2%

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

      8. associate-/r* 99.2%

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

      9. metadata-eval 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in x around inf 99.2%

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

   if 1.00000000000000004e-97 < (*.f64 x y) < 4.9999999999999998e-8

   1. Initial program 84.5%

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

   3. Taylor expanded in x around 0 58.5%

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

      1. associate-*r/ 58.4%

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

      2. associate-*r* 58.6%

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

      3. associate-*l/ 68.5%

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

      4. associate-*r/ 68.4%

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

      5. *-commutative 68.4%

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

      6. associate-*r/ 68.5%

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

   5. Simplified 68.5%

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

   if 4.9999999999999998e-8 < (*.f64 x y)

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 76.1%

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

      1. *-commutative 76.1%

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

      2. associate-/l* 74.3%

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

      3. associate-*r* 74.3%

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

      4. *-commutative 74.3%

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

      5. associate-*r/ 74.3%

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

   5. Simplified 74.3%

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

      1. clear-num 74.2%

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

      2. un-div-inv 74.2%

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

      3. associate-/r* 74.2%

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

      4. div-inv 74.2%

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

      5. metadata-eval 74.2%

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

   7. Applied egg-rr 74.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{a \cdot 2}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a \cdot 2}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+29)
   (* y (/ x (* a 2.0)))
   (if (<= (* x y) 2e-126)
     (* (/ z a) (* t -4.5))
     (if (<= (* x y) 1e-97)
       (* (* x y) (/ 0.5 a))
       (if (<= (* x y) 5e-8) (* z (/ (* t -4.5) a)) (* x (/ (* y 0.5) a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = y * (x / (a * 2.0));
	} else if ((x * y) <= 2e-126) {
		tmp = (z / a) * (t * -4.5);
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e-8) {
		tmp = z * ((t * -4.5) / a);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-5d+29)) then
        tmp = y * (x / (a * 2.0d0))
    else if ((x * y) <= 2d-126) then
        tmp = (z / a) * (t * (-4.5d0))
    else if ((x * y) <= 1d-97) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 5d-8) then
        tmp = z * ((t * (-4.5d0)) / a)
    else
        tmp = x * ((y * 0.5d0) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = y * (x / (a * 2.0));
	} else if ((x * y) <= 2e-126) {
		tmp = (z / a) * (t * -4.5);
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e-8) {
		tmp = z * ((t * -4.5) / a);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+29:
		tmp = y * (x / (a * 2.0))
	elif (x * y) <= 2e-126:
		tmp = (z / a) * (t * -4.5)
	elif (x * y) <= 1e-97:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 5e-8:
		tmp = z * ((t * -4.5) / a)
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+29)
		tmp = Float64(y * Float64(x / Float64(a * 2.0)));
	elseif (Float64(x * y) <= 2e-126)
		tmp = Float64(Float64(z / a) * Float64(t * -4.5));
	elseif (Float64(x * y) <= 1e-97)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 5e-8)
		tmp = Float64(z * Float64(Float64(t * -4.5) / 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])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+29)
		tmp = y * (x / (a * 2.0));
	elseif ((x * y) <= 2e-126)
		tmp = (z / a) * (t * -4.5);
	elseif ((x * y) <= 1e-97)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 5e-8)
		tmp = z * ((t * -4.5) / 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.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+29], N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-126], N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-97], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-8], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -5.0000000000000001e29

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-/l* 79.9%

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

      3. associate-*r* 79.9%

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

      4. *-commutative 79.9%

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

      5. associate-*r/ 79.9%

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

   5. Simplified 79.9%

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

      1. clear-num 79.8%

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

      2. un-div-inv 79.9%

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

      3. associate-/r* 79.9%

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

      4. div-inv 79.9%

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

      5. metadata-eval 79.9%

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

   7. Applied egg-rr 79.9%

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

      1. associate-/r/ 81.9%

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

   9. Simplified 81.9%

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

   if -5.0000000000000001e29 < (*.f64 x y) < 1.9999999999999999e-126

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 82.3%

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

      1. *-commutative 82.3%

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

      2. associate-*r* 82.3%

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

   5. Simplified 82.3%

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

      1. associate-*r* 82.3%

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

      2. times-frac 82.4%

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

      3. associate-*r/ 83.9%

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

      4. metadata-eval 83.9%

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

      5. *-commutative 83.9%

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

      6. associate-*l* 83.8%

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

   7. Applied egg-rr 83.8%

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

   if 1.9999999999999999e-126 < (*.f64 x y) < 1.00000000000000004e-97

   1. Initial program 99.0%

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

      1. div-inv 99.2%

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

      2. fma-neg 99.2%

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

      3. *-commutative 99.2%

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

      4. distribute-rgt-neg-in 99.2%

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

      5. distribute-rgt-neg-in 99.2%

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

      6. metadata-eval 99.2%

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

      7. *-commutative 99.2%

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

      8. associate-/r* 99.2%

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

      9. metadata-eval 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in x around inf 99.2%

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

   if 1.00000000000000004e-97 < (*.f64 x y) < 4.9999999999999998e-8

   1. Initial program 84.5%

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

   3. Taylor expanded in x around 0 58.5%

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

      1. associate-*r/ 58.4%

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

      2. associate-*r* 58.6%

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

      3. associate-*l/ 68.5%

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

      4. associate-*r/ 68.4%

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

      5. *-commutative 68.4%

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

      6. associate-*r/ 68.5%

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

   5. Simplified 68.5%

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

   if 4.9999999999999998e-8 < (*.f64 x y)

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 76.1%

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

      1. *-commutative 76.1%

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

      2. associate-/l* 74.3%

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

      3. associate-*r* 74.3%

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

      4. *-commutative 74.3%

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

      5. associate-*r/ 74.3%

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

   5. Simplified 74.3%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+29)
   (* y (/ x (* a 2.0)))
   (if (<= (* x y) 2e-126)
     (* -4.5 (* t (/ z a)))
     (if (<= (* x y) 1e-97)
       (* (* x y) (/ 0.5 a))
       (if (<= (* x y) 5e-8) (* z (/ (* t -4.5) a)) (* x (/ (* y 0.5) a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = y * (x / (a * 2.0));
	} else if ((x * y) <= 2e-126) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e-8) {
		tmp = z * ((t * -4.5) / a);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-5d+29)) then
        tmp = y * (x / (a * 2.0d0))
    else if ((x * y) <= 2d-126) then
        tmp = (-4.5d0) * (t * (z / a))
    else if ((x * y) <= 1d-97) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 5d-8) then
        tmp = z * ((t * (-4.5d0)) / a)
    else
        tmp = x * ((y * 0.5d0) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = y * (x / (a * 2.0));
	} else if ((x * y) <= 2e-126) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e-8) {
		tmp = z * ((t * -4.5) / a);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+29:
		tmp = y * (x / (a * 2.0))
	elif (x * y) <= 2e-126:
		tmp = -4.5 * (t * (z / a))
	elif (x * y) <= 1e-97:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 5e-8:
		tmp = z * ((t * -4.5) / a)
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+29)
		tmp = Float64(y * Float64(x / Float64(a * 2.0)));
	elseif (Float64(x * y) <= 2e-126)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (Float64(x * y) <= 1e-97)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 5e-8)
		tmp = Float64(z * Float64(Float64(t * -4.5) / 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])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+29)
		tmp = y * (x / (a * 2.0));
	elseif ((x * y) <= 2e-126)
		tmp = -4.5 * (t * (z / a));
	elseif ((x * y) <= 1e-97)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 5e-8)
		tmp = z * ((t * -4.5) / 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.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+29], N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-126], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-97], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-8], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -5.0000000000000001e29

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-/l* 79.9%

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

      3. associate-*r* 79.9%

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

      4. *-commutative 79.9%

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

      5. associate-*r/ 79.9%

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

   5. Simplified 79.9%

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

      1. clear-num 79.8%

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

      2. un-div-inv 79.9%

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

      3. associate-/r* 79.9%

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

      4. div-inv 79.9%

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

      5. metadata-eval 79.9%

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

   7. Applied egg-rr 79.9%

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

      1. associate-/r/ 81.9%

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

   9. Simplified 81.9%

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

   if -5.0000000000000001e29 < (*.f64 x y) < 1.9999999999999999e-126

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 82.4%

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

      1. associate-/l* 83.9%

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

   5. Simplified 83.9%

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

   if 1.9999999999999999e-126 < (*.f64 x y) < 1.00000000000000004e-97

   1. Initial program 99.0%

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

      1. div-inv 99.2%

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

      2. fma-neg 99.2%

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

      3. *-commutative 99.2%

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

      4. distribute-rgt-neg-in 99.2%

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

      5. distribute-rgt-neg-in 99.2%

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

      6. metadata-eval 99.2%

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

      7. *-commutative 99.2%

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

      8. associate-/r* 99.2%

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

      9. metadata-eval 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in x around inf 99.2%

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

   if 1.00000000000000004e-97 < (*.f64 x y) < 4.9999999999999998e-8

   1. Initial program 84.5%

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

   3. Taylor expanded in x around 0 58.5%

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

      1. associate-*r/ 58.4%

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

      2. associate-*r* 58.6%

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

      3. associate-*l/ 68.5%

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

      4. associate-*r/ 68.4%

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

      5. *-commutative 68.4%

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

      6. associate-*r/ 68.5%

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

   5. Simplified 68.5%

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

   if 4.9999999999999998e-8 < (*.f64 x y)

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 76.1%

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

      1. *-commutative 76.1%

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

      2. associate-/l* 74.3%

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

      3. associate-*r* 74.3%

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

      4. *-commutative 74.3%

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

      5. associate-*r/ 74.3%

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

   5. Simplified 74.3%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+29)
   (* y (* x (/ 0.5 a)))
   (if (<= (* x y) 2e-126)
     (* -4.5 (* t (/ z a)))
     (if (<= (* x y) 1e-97)
       (* (* x y) (/ 0.5 a))
       (if (<= (* x y) 5e-8) (* z (/ (* t -4.5) a)) (* x (/ (* y 0.5) a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = y * (x * (0.5 / a));
	} else if ((x * y) <= 2e-126) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e-8) {
		tmp = z * ((t * -4.5) / a);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-5d+29)) then
        tmp = y * (x * (0.5d0 / a))
    else if ((x * y) <= 2d-126) then
        tmp = (-4.5d0) * (t * (z / a))
    else if ((x * y) <= 1d-97) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 5d-8) then
        tmp = z * ((t * (-4.5d0)) / a)
    else
        tmp = x * ((y * 0.5d0) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = y * (x * (0.5 / a));
	} else if ((x * y) <= 2e-126) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e-8) {
		tmp = z * ((t * -4.5) / a);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+29:
		tmp = y * (x * (0.5 / a))
	elif (x * y) <= 2e-126:
		tmp = -4.5 * (t * (z / a))
	elif (x * y) <= 1e-97:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 5e-8:
		tmp = z * ((t * -4.5) / a)
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+29)
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	elseif (Float64(x * y) <= 2e-126)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (Float64(x * y) <= 1e-97)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 5e-8)
		tmp = Float64(z * Float64(Float64(t * -4.5) / 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])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+29)
		tmp = y * (x * (0.5 / a));
	elseif ((x * y) <= 2e-126)
		tmp = -4.5 * (t * (z / a));
	elseif ((x * y) <= 1e-97)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 5e-8)
		tmp = z * ((t * -4.5) / 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.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+29], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-126], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-97], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-8], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -5.0000000000000001e29

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-/l* 79.9%

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

      3. associate-*r* 79.9%

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

      4. *-commutative 79.9%

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

      5. associate-*r/ 79.9%

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

   5. Simplified 79.9%

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

      1. associate-*r/ 75.7%

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

      2. *-commutative 75.7%

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

   7. Applied egg-rr 75.7%

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

      1. associate-*r* 75.7%

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

      2. associate-*r/ 75.5%

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

      3. *-commutative 75.5%

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

      4. associate-*r* 81.8%

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

   9. Applied egg-rr 81.8%

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

   if -5.0000000000000001e29 < (*.f64 x y) < 1.9999999999999999e-126

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 82.4%

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

      1. associate-/l* 83.9%

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

   5. Simplified 83.9%

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

   if 1.9999999999999999e-126 < (*.f64 x y) < 1.00000000000000004e-97

   1. Initial program 99.0%

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

      1. div-inv 99.2%

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

      2. fma-neg 99.2%

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

      3. *-commutative 99.2%

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

      4. distribute-rgt-neg-in 99.2%

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

      5. distribute-rgt-neg-in 99.2%

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

      6. metadata-eval 99.2%

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

      7. *-commutative 99.2%

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

      8. associate-/r* 99.2%

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

      9. metadata-eval 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in x around inf 99.2%

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

   if 1.00000000000000004e-97 < (*.f64 x y) < 4.9999999999999998e-8

   1. Initial program 84.5%

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

   3. Taylor expanded in x around 0 58.5%

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

      1. associate-*r/ 58.4%

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

      2. associate-*r* 58.6%

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

      3. associate-*l/ 68.5%

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

      4. associate-*r/ 68.4%

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

      5. *-commutative 68.4%

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

      6. associate-*r/ 68.5%

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

   5. Simplified 68.5%

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

   if 4.9999999999999998e-8 < (*.f64 x y)

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 76.1%

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

      1. *-commutative 76.1%

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

      2. associate-/l* 74.3%

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

      3. associate-*r* 74.3%

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

      4. *-commutative 74.3%

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

      5. associate-*r/ 74.3%

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

   5. Simplified 74.3%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (* y 0.5) a))))
   (if (<= (* x y) -5e+29)
     t_1
     (if (<= (* x y) 2e-126)
       (* -4.5 (* t (/ z a)))
       (if (<= (* x y) 1e-97)
         (* (* x y) (/ 0.5 a))
         (if (<= (* x y) 5e-8) (* z (/ (* t -4.5) a)) t_1))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y * 0.5) / a);
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = t_1;
	} else if ((x * y) <= 2e-126) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e-8) {
		tmp = z * ((t * -4.5) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * 0.5d0) / a)
    if ((x * y) <= (-5d+29)) then
        tmp = t_1
    else if ((x * y) <= 2d-126) then
        tmp = (-4.5d0) * (t * (z / a))
    else if ((x * y) <= 1d-97) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 5d-8) then
        tmp = z * ((t * (-4.5d0)) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y * 0.5) / a);
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = t_1;
	} else if ((x * y) <= 2e-126) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e-8) {
		tmp = z * ((t * -4.5) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x * ((y * 0.5) / a)
	tmp = 0
	if (x * y) <= -5e+29:
		tmp = t_1
	elif (x * y) <= 2e-126:
		tmp = -4.5 * (t * (z / a))
	elif (x * y) <= 1e-97:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 5e-8:
		tmp = z * ((t * -4.5) / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y * 0.5) / a))
	tmp = 0.0
	if (Float64(x * y) <= -5e+29)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-126)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (Float64(x * y) <= 1e-97)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 5e-8)
		tmp = Float64(z * Float64(Float64(t * -4.5) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y * 0.5) / a);
	tmp = 0.0;
	if ((x * y) <= -5e+29)
		tmp = t_1;
	elseif ((x * y) <= 2e-126)
		tmp = -4.5 * (t * (z / a));
	elseif ((x * y) <= 1e-97)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 5e-8)
		tmp = z * ((t * -4.5) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+29], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-126], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-97], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-8], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -5.0000000000000001e29 or 4.9999999999999998e-8 < (*.f64 x y)

   1. Initial program 89.4%

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

   3. Taylor expanded in x around inf 75.9%

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

      1. *-commutative 75.9%

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

      2. associate-/l* 77.0%

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

      3. associate-*r* 77.0%

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

      4. *-commutative 77.0%

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

      5. associate-*r/ 77.0%

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

   5. Simplified 77.0%

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

   if -5.0000000000000001e29 < (*.f64 x y) < 1.9999999999999999e-126

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 82.4%

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

      1. associate-/l* 83.9%

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

   5. Simplified 83.9%

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

   if 1.9999999999999999e-126 < (*.f64 x y) < 1.00000000000000004e-97

   1. Initial program 99.0%

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

      1. div-inv 99.2%

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

      2. fma-neg 99.2%

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

      3. *-commutative 99.2%

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

      4. distribute-rgt-neg-in 99.2%

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

      5. distribute-rgt-neg-in 99.2%

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

      6. metadata-eval 99.2%

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

      7. *-commutative 99.2%

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

      8. associate-/r* 99.2%

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

      9. metadata-eval 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in x around inf 99.2%

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

   if 1.00000000000000004e-97 < (*.f64 x y) < 4.9999999999999998e-8

   1. Initial program 84.5%

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

   3. Taylor expanded in x around 0 58.5%

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

      1. associate-*r/ 58.4%

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

      2. associate-*r* 58.6%

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

      3. associate-*l/ 68.5%

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

      4. associate-*r/ 68.4%

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

      5. *-commutative 68.4%

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

      6. associate-*r/ 68.5%

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

   5. Simplified 68.5%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+266}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+219}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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)))
   (if (<= t_1 -5e+266)
     (* z (/ (* t -4.5) a))
     (if (<= t_1 2e+219)
       (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
       (* -4.5 (* t (/ z a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -5e+266) {
		tmp = z * ((t * -4.5) / a);
	} else if (t_1 <= 2e+219) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = (z * 9.0d0) * t
    if (t_1 <= (-5d+266)) then
        tmp = z * ((t * (-4.5d0)) / a)
    else if (t_1 <= 2d+219) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = (-4.5d0) * (t * (z / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -5e+266) {
		tmp = z * ((t * -4.5) / a);
	} else if (t_1 <= 2e+219) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -5e+266:
		tmp = z * ((t * -4.5) / a)
	elif t_1 <= 2e+219:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = -4.5 * (t * (z / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -5e+266)
		tmp = Float64(z * Float64(Float64(t * -4.5) / a));
	elseif (t_1 <= 2e+219)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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;
	tmp = 0.0;
	if (t_1 <= -5e+266)
		tmp = z * ((t * -4.5) / a);
	elseif (t_1 <= 2e+219)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = -4.5 * (t * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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]}, If[LessEqual[t$95$1, -5e+266], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+219], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -4.9999999999999999e266

   1. Initial program 65.8%

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

   3. Taylor expanded in x around 0 65.9%

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

      1. associate-*r/ 65.8%

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

      2. associate-*r* 65.7%

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

      3. associate-*l/ 96.0%

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

      4. associate-*r/ 96.0%

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

      5. *-commutative 96.0%

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

      6. associate-*r/ 96.0%

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

   5. Simplified 96.0%

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

   if -4.9999999999999999e266 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.99999999999999993e219

   1. Initial program 96.1%

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

      1. div-sub 93.7%

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

      2. *-commutative 93.7%

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

      3. div-sub 96.1%

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

      4. cancel-sign-sub-inv 96.1%

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

      5. *-commutative 96.1%

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

      6. fma-define 96.1%

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

      7. distribute-rgt-neg-in 96.1%

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

      8. associate-*r* 96.2%

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

      9. distribute-lft-neg-in 96.2%

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

      10. *-commutative 96.2%

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

      11. distribute-rgt-neg-in 96.2%

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

      12. metadata-eval 96.2%

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

   3. Simplified 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-*r* 96.1%

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

      3. metadata-eval 96.1%

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

      4. distribute-rgt-neg-in 96.1%

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

      5. distribute-lft-neg-in 96.1%

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

      6. fma-neg 96.1%

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

      7. associate-*l* 96.2%

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

   6. Applied egg-rr 96.2%

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

   if 1.99999999999999993e219 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 70.6%

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

   3. Taylor expanded in x around 0 74.9%

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

      1. associate-/l* 95.7%

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

   5. Simplified 95.7%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+266}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+219}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-165} \lor \neg \left(y \leq 2.8 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.2e-165) (not (<= y 2.8e+34)))
   (* x (/ (* y 0.5) a))
   (* -4.5 (* t (/ z a)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.2e-165) || !(y <= 2.8e+34)) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.2d-165)) .or. (.not. (y <= 2.8d+34))) then
        tmp = x * ((y * 0.5d0) / a)
    else
        tmp = (-4.5d0) * (t * (z / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.2e-165) || !(y <= 2.8e+34)) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.2e-165) or not (y <= 2.8e+34):
		tmp = x * ((y * 0.5) / a)
	else:
		tmp = -4.5 * (t * (z / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.2e-165) || !(y <= 2.8e+34))
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.2e-165) || ~((y <= 2.8e+34)))
		tmp = x * ((y * 0.5) / a);
	else
		tmp = -4.5 * (t * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.2e-165], N[Not[LessEqual[y, 2.8e+34]], $MachinePrecision]], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2000000000000001e-165 or 2.80000000000000008e34 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-/l* 59.0%

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

      3. associate-*r* 59.0%

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

      4. *-commutative 59.0%

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

      5. associate-*r/ 59.0%

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

   5. Simplified 59.0%

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

   if -1.2000000000000001e-165 < y < 2.80000000000000008e34

   1. Initial program 90.5%

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

   3. Taylor expanded in x around 0 64.3%

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

      1. associate-/l* 66.9%

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

   5. Simplified 66.9%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-165} \lor \neg \left(y \leq 2.8 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.3% accurate, 1.9× speedup

Math

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

FPCore

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

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t * (z / a));
}

Fortran

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

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t * (z / a));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

3. Taylor expanded in x around 0 51.6%

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

   1. associate-/l* 54.2%

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

5. Simplified 54.2%

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

Developer target: 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 2024108 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :alt
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))