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

Percentage Accurate: 91.2% → 94.5%

Time: 12.0s

Alternatives: 13

Speedup: 1.0×

• 27.9% 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: 91.2% 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: 94.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (- (* x y) (* (* z 9.0) t)) (- INFINITY))
   (- (* (/ x a) (/ y 2.0)) (/ t (* (/ a z) 0.2222222222222222)))
   (/ (fma x y (* z (* t -9.0))) (* a 2.0))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) - ((z * 9.0) * t)) <= -((double) INFINITY)) {
		tmp = ((x / a) * (y / 2.0)) - (t / ((a / z) * 0.2222222222222222));
	} else {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) <= Float64(-Inf))
		tmp = Float64(Float64(Float64(x / a) * Float64(y / 2.0)) - Float64(t / Float64(Float64(a / z) * 0.2222222222222222)));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], (-Infinity)], N[(N[(N[(x / a), $MachinePrecision] * N[(y / 2.0), $MachinePrecision]), $MachinePrecision] - N[(t / N[(N[(a / z), $MachinePrecision] * 0.2222222222222222), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 80.3%

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

      1. div-sub 80.3%

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

      2. sub-neg 80.3%

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

      3. times-frac 90.1%

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

      4. *-commutative 90.1%

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

      5. associate-/l* 96.4%

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

   4. Applied egg-rr 96.4%

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

      1. sub-neg 96.4%

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

      2. times-frac 96.4%

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

      3. metadata-eval 96.4%

         \[\leadsto \frac{x}{a} \cdot \frac{y}{2} - \frac{t}{\frac{a}{z} \cdot \color{blue}{0.2222222222222222}} \]

   6. Simplified 96.4%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{y}{2} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}} \]

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 95.1%

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

      1. fma-neg 95.5%

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

      2. associate-*l* 95.5%

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

      3. distribute-rgt-neg-in 95.5%

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

      4. *-commutative 95.5%

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

      5. distribute-rgt-neg-in 95.5%

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

      6. metadata-eval 95.5%

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

   3. Simplified 95.5%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -1 \cdot 10^{+255}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (- (* x y) (* (* z 9.0) t)) -1e+255)
   (- (* (/ x a) (/ y 2.0)) (/ t (* (/ a z) 0.2222222222222222)))
   (* (fma x y (* t (* z -9.0))) (/ 0.5 a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) - ((z * 9.0) * t)) <= -1e+255) {
		tmp = ((x / a) * (y / 2.0)) - (t / ((a / z) * 0.2222222222222222));
	} else {
		tmp = fma(x, y, (t * (z * -9.0))) * (0.5 / a);
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) <= -1e+255)
		tmp = Float64(Float64(Float64(x / a) * Float64(y / 2.0)) - Float64(t / Float64(Float64(a / z) * 0.2222222222222222)));
	else
		tmp = Float64(fma(x, y, Float64(t * Float64(z * -9.0))) * Float64(0.5 / a));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], -1e+255], N[(N[(N[(x / a), $MachinePrecision] * N[(y / 2.0), $MachinePrecision]), $MachinePrecision] - N[(t / N[(N[(a / z), $MachinePrecision] * 0.2222222222222222), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -9.99999999999999988e254

   1. Initial program 84.0%

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

      1. div-sub 84.0%

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

      2. sub-neg 84.0%

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

      3. times-frac 92.0%

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

      4. *-commutative 92.0%

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

      5. associate-/l* 97.0%

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

   4. Applied egg-rr 97.0%

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

      1. sub-neg 97.0%

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

      2. times-frac 97.1%

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

      3. metadata-eval 97.1%

         \[\leadsto \frac{x}{a} \cdot \frac{y}{2} - \frac{t}{\frac{a}{z} \cdot \color{blue}{0.2222222222222222}} \]

   6. Simplified 97.1%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{y}{2} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}} \]

   if -9.99999999999999988e254 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 94.9%

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

      1. div-inv 94.9%

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

      2. fma-neg 95.3%

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

      3. *-commutative 95.3%

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

      4. distribute-rgt-neg-in 95.3%

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

      5. distribute-rgt-neg-in 95.3%

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

      6. metadata-eval 95.3%

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

      7. *-commutative 95.3%

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

      8. associate-/r* 95.3%

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

      9. metadata-eval 95.3%

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

   4. Applied egg-rr 95.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -1 \cdot 10^{+255}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot 0.5}{\frac{a}{y}}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-22}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot \left(y \cdot 0.5\right)}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x 0.5) (/ a y))))
   (if (<= (* x y) -1e+109)
     t_1
     (if (<= (* x y) -5e+38)
       (* t (* (/ z a) -4.5))
       (if (<= (* x y) -4e-84)
         (/ (* x y) (* a 2.0))
         (if (<= (* x y) 5e-53)
           (* -4.5 (/ t (/ a z)))
           (if (<= (* x y) 1e-22)
             (/ 1.0 (/ a (* x (* y 0.5))))
             (if (<= (* x y) 2e+31) (/ (* t (* z -9.0)) (* a 2.0)) t_1))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * 0.5) / (a / y);
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = t_1;
	} else if ((x * y) <= -5e+38) {
		tmp = t * ((z / a) * -4.5);
	} else if ((x * y) <= -4e-84) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 5e-53) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x * y) <= 1e-22) {
		tmp = 1.0 / (a / (x * (y * 0.5)));
	} else if ((x * y) <= 2e+31) {
		tmp = (t * (z * -9.0)) / (a * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 0.5d0) / (a / y)
    if ((x * y) <= (-1d+109)) then
        tmp = t_1
    else if ((x * y) <= (-5d+38)) then
        tmp = t * ((z / a) * (-4.5d0))
    else if ((x * y) <= (-4d-84)) then
        tmp = (x * y) / (a * 2.0d0)
    else if ((x * y) <= 5d-53) then
        tmp = (-4.5d0) * (t / (a / z))
    else if ((x * y) <= 1d-22) then
        tmp = 1.0d0 / (a / (x * (y * 0.5d0)))
    else if ((x * y) <= 2d+31) then
        tmp = (t * (z * (-9.0d0))) / (a * 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * 0.5) / (a / y);
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = t_1;
	} else if ((x * y) <= -5e+38) {
		tmp = t * ((z / a) * -4.5);
	} else if ((x * y) <= -4e-84) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 5e-53) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x * y) <= 1e-22) {
		tmp = 1.0 / (a / (x * (y * 0.5)));
	} else if ((x * y) <= 2e+31) {
		tmp = (t * (z * -9.0)) / (a * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * 0.5) / (a / y)
	tmp = 0
	if (x * y) <= -1e+109:
		tmp = t_1
	elif (x * y) <= -5e+38:
		tmp = t * ((z / a) * -4.5)
	elif (x * y) <= -4e-84:
		tmp = (x * y) / (a * 2.0)
	elif (x * y) <= 5e-53:
		tmp = -4.5 * (t / (a / z))
	elif (x * y) <= 1e-22:
		tmp = 1.0 / (a / (x * (y * 0.5)))
	elif (x * y) <= 2e+31:
		tmp = (t * (z * -9.0)) / (a * 2.0)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * 0.5) / Float64(a / y))
	tmp = 0.0
	if (Float64(x * y) <= -1e+109)
		tmp = t_1;
	elseif (Float64(x * y) <= -5e+38)
		tmp = Float64(t * Float64(Float64(z / a) * -4.5));
	elseif (Float64(x * y) <= -4e-84)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (Float64(x * y) <= 5e-53)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (Float64(x * y) <= 1e-22)
		tmp = Float64(1.0 / Float64(a / Float64(x * Float64(y * 0.5))));
	elseif (Float64(x * y) <= 2e+31)
		tmp = Float64(Float64(t * Float64(z * -9.0)) / Float64(a * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * 0.5) / (a / y);
	tmp = 0.0;
	if ((x * y) <= -1e+109)
		tmp = t_1;
	elseif ((x * y) <= -5e+38)
		tmp = t * ((z / a) * -4.5);
	elseif ((x * y) <= -4e-84)
		tmp = (x * y) / (a * 2.0);
	elseif ((x * y) <= 5e-53)
		tmp = -4.5 * (t / (a / z));
	elseif ((x * y) <= 1e-22)
		tmp = 1.0 / (a / (x * (y * 0.5)));
	elseif ((x * y) <= 2e+31)
		tmp = (t * (z * -9.0)) / (a * 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * 0.5), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+109], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5e+38], N[(t * N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-84], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-53], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-22], N[(1.0 / N[(a / N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+31], N[(N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 x y) < -9.99999999999999982e108 or 1.9999999999999999e31 < (*.f64 x y)

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf 83.2%

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

      1. associate-/l* 86.6%

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

      2. associate-*r/ 86.6%

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

   5. Simplified 86.6%

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

   if -9.99999999999999982e108 < (*.f64 x y) < -4.9999999999999997e38

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0 65.2%

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

      1. associate-/l* 74.0%

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

      2. associate-/r/ 65.7%

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

   5. Simplified 65.7%

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

      1. *-commutative 65.7%

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

      2. associate-*l/ 65.2%

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

      3. metadata-eval 65.2%

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

      4. times-frac 65.2%

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

      5. associate-*r* 65.4%

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

   7. Applied egg-rr 65.4%

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

      1. associate-*r/ 74.0%

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

      2. times-frac 74.0%

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

      3. metadata-eval 74.0%

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

   9. Simplified 74.0%

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

   if -4.9999999999999997e38 < (*.f64 x y) < -4.0000000000000001e-84

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 70.0%

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

   if -4.0000000000000001e-84 < (*.f64 x y) < 5e-53

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 80.2%

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

      1. associate-/l* 79.9%

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

   5. Simplified 79.9%

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

   if 5e-53 < (*.f64 x y) < 1e-22

   1. Initial program 99.2%

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

      1. div-inv 99.5%

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

      2. fma-neg 99.5%

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

      3. *-commutative 99.5%

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

      4. distribute-rgt-neg-in 99.5%

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

      5. distribute-rgt-neg-in 99.5%

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

      6. metadata-eval 99.5%

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

      7. *-commutative 99.5%

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

      8. associate-/r* 99.5%

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

      9. metadata-eval 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in x around inf 79.2%

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

      1. associate-*r/ 79.2%

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

      2. clear-num 79.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\left(x \cdot y\right) \cdot 0.5}}} \]

      3. associate-*l* 79.2%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{x \cdot \left(y \cdot 0.5\right)}}} \]

   7. Applied egg-rr 79.2%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{x \cdot \left(y \cdot 0.5\right)}}} \]

   if 1e-22 < (*.f64 x y) < 1.9999999999999999e31

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-*r* 82.4%

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

      3. *-commutative 82.4%

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

      4. *-commutative 82.4%

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

   5. Simplified 82.4%

      \[\leadsto \frac{\color{blue}{t \cdot \left(z \cdot -9\right)}}{a \cdot 2} \]
3. Recombined 6 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\frac{x \cdot 0.5}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-22}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot \left(y \cdot 0.5\right)}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.5}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ t_2 := \left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* x 0.5) (/ y a))) (t_2 (* (* x y) (/ 0.5 a))))
   (if (<= (* x y) -1e+109)
     t_1
     (if (<= (* x y) -5e+38)
       (* t (* (/ z a) -4.5))
       (if (<= (* x y) -4e-84)
         t_2
         (if (<= (* x y) 5e-53)
           (* -4.5 (/ t (/ a z)))
           (if (<= (* x y) 1e-22)
             t_2
             (if (<= (* x y) 2e+31) (* -4.5 (/ (* z t) a)) t_1))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * 0.5) * (y / a);
	double t_2 = (x * y) * (0.5 / a);
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = t_1;
	} else if ((x * y) <= -5e+38) {
		tmp = t * ((z / a) * -4.5);
	} else if ((x * y) <= -4e-84) {
		tmp = t_2;
	} else if ((x * y) <= 5e-53) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x * y) <= 1e-22) {
		tmp = t_2;
	} else if ((x * y) <= 2e+31) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * 0.5d0) * (y / a)
    t_2 = (x * y) * (0.5d0 / a)
    if ((x * y) <= (-1d+109)) then
        tmp = t_1
    else if ((x * y) <= (-5d+38)) then
        tmp = t * ((z / a) * (-4.5d0))
    else if ((x * y) <= (-4d-84)) then
        tmp = t_2
    else if ((x * y) <= 5d-53) then
        tmp = (-4.5d0) * (t / (a / z))
    else if ((x * y) <= 1d-22) then
        tmp = t_2
    else if ((x * y) <= 2d+31) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * 0.5) * (y / a);
	double t_2 = (x * y) * (0.5 / a);
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = t_1;
	} else if ((x * y) <= -5e+38) {
		tmp = t * ((z / a) * -4.5);
	} else if ((x * y) <= -4e-84) {
		tmp = t_2;
	} else if ((x * y) <= 5e-53) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x * y) <= 1e-22) {
		tmp = t_2;
	} else if ((x * y) <= 2e+31) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * 0.5) * (y / a)
	t_2 = (x * y) * (0.5 / a)
	tmp = 0
	if (x * y) <= -1e+109:
		tmp = t_1
	elif (x * y) <= -5e+38:
		tmp = t * ((z / a) * -4.5)
	elif (x * y) <= -4e-84:
		tmp = t_2
	elif (x * y) <= 5e-53:
		tmp = -4.5 * (t / (a / z))
	elif (x * y) <= 1e-22:
		tmp = t_2
	elif (x * y) <= 2e+31:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * 0.5) * Float64(y / a))
	t_2 = Float64(Float64(x * y) * Float64(0.5 / a))
	tmp = 0.0
	if (Float64(x * y) <= -1e+109)
		tmp = t_1;
	elseif (Float64(x * y) <= -5e+38)
		tmp = Float64(t * Float64(Float64(z / a) * -4.5));
	elseif (Float64(x * y) <= -4e-84)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e-53)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (Float64(x * y) <= 1e-22)
		tmp = t_2;
	elseif (Float64(x * y) <= 2e+31)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * 0.5) * (y / a);
	t_2 = (x * y) * (0.5 / a);
	tmp = 0.0;
	if ((x * y) <= -1e+109)
		tmp = t_1;
	elseif ((x * y) <= -5e+38)
		tmp = t * ((z / a) * -4.5);
	elseif ((x * y) <= -4e-84)
		tmp = t_2;
	elseif ((x * y) <= 5e-53)
		tmp = -4.5 * (t / (a / z));
	elseif ((x * y) <= 1e-22)
		tmp = t_2;
	elseif ((x * y) <= 2e+31)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * 0.5), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+109], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5e+38], N[(t * N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-84], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e-53], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-22], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2e+31], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -9.99999999999999982e108 or 1.9999999999999999e31 < (*.f64 x y)

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf 83.2%

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

      1. associate-/l* 86.6%

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

      2. associate-*r/ 86.6%

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

   5. Simplified 86.6%

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

      1. div-inv 86.0%

         \[\leadsto \color{blue}{\left(0.5 \cdot x\right) \cdot \frac{1}{\frac{a}{y}}} \]

      2. *-commutative 86.0%

         \[\leadsto \color{blue}{\left(x \cdot 0.5\right)} \cdot \frac{1}{\frac{a}{y}} \]

      3. clear-num 86.1%

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

   7. Applied egg-rr 86.1%

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

   if -9.99999999999999982e108 < (*.f64 x y) < -4.9999999999999997e38

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0 65.2%

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

      1. associate-/l* 74.0%

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

      2. associate-/r/ 65.7%

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

   5. Simplified 65.7%

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

      1. *-commutative 65.7%

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

      2. associate-*l/ 65.2%

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

      3. metadata-eval 65.2%

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

      4. times-frac 65.2%

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

      5. associate-*r* 65.4%

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

   7. Applied egg-rr 65.4%

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

      1. associate-*r/ 74.0%

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

      2. times-frac 74.0%

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

      3. metadata-eval 74.0%

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

   9. Simplified 74.0%

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

   if -4.9999999999999997e38 < (*.f64 x y) < -4.0000000000000001e-84 or 5e-53 < (*.f64 x y) < 1e-22

   1. Initial program 96.3%

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

      1. div-inv 96.3%

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

      2. fma-neg 96.3%

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

      3. *-commutative 96.3%

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

      4. distribute-rgt-neg-in 96.3%

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

      5. distribute-rgt-neg-in 96.3%

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

      6. metadata-eval 96.3%

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

      7. *-commutative 96.3%

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

      8. associate-/r* 96.3%

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

      9. metadata-eval 96.3%

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in x around inf 71.7%

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

   if -4.0000000000000001e-84 < (*.f64 x y) < 5e-53

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 80.2%

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

      1. associate-/l* 79.9%

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

   5. Simplified 79.9%

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

   if 1e-22 < (*.f64 x y) < 1.9999999999999999e31

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 82.4%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-22}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot 0.5}{\frac{a}{y}}\\ t_2 := \left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x 0.5) (/ a y))) (t_2 (* (* x y) (/ 0.5 a))))
   (if (<= (* x y) -1e+109)
     t_1
     (if (<= (* x y) -5e+38)
       (* t (* (/ z a) -4.5))
       (if (<= (* x y) -4e-84)
         t_2
         (if (<= (* x y) 5e-53)
           (* -4.5 (/ t (/ a z)))
           (if (<= (* x y) 1e-22)
             t_2
             (if (<= (* x y) 2e+31) (* -4.5 (/ (* z t) a)) t_1))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * 0.5) / (a / y);
	double t_2 = (x * y) * (0.5 / a);
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = t_1;
	} else if ((x * y) <= -5e+38) {
		tmp = t * ((z / a) * -4.5);
	} else if ((x * y) <= -4e-84) {
		tmp = t_2;
	} else if ((x * y) <= 5e-53) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x * y) <= 1e-22) {
		tmp = t_2;
	} else if ((x * y) <= 2e+31) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * 0.5d0) / (a / y)
    t_2 = (x * y) * (0.5d0 / a)
    if ((x * y) <= (-1d+109)) then
        tmp = t_1
    else if ((x * y) <= (-5d+38)) then
        tmp = t * ((z / a) * (-4.5d0))
    else if ((x * y) <= (-4d-84)) then
        tmp = t_2
    else if ((x * y) <= 5d-53) then
        tmp = (-4.5d0) * (t / (a / z))
    else if ((x * y) <= 1d-22) then
        tmp = t_2
    else if ((x * y) <= 2d+31) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * 0.5) / (a / y);
	double t_2 = (x * y) * (0.5 / a);
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = t_1;
	} else if ((x * y) <= -5e+38) {
		tmp = t * ((z / a) * -4.5);
	} else if ((x * y) <= -4e-84) {
		tmp = t_2;
	} else if ((x * y) <= 5e-53) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x * y) <= 1e-22) {
		tmp = t_2;
	} else if ((x * y) <= 2e+31) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * 0.5) / (a / y)
	t_2 = (x * y) * (0.5 / a)
	tmp = 0
	if (x * y) <= -1e+109:
		tmp = t_1
	elif (x * y) <= -5e+38:
		tmp = t * ((z / a) * -4.5)
	elif (x * y) <= -4e-84:
		tmp = t_2
	elif (x * y) <= 5e-53:
		tmp = -4.5 * (t / (a / z))
	elif (x * y) <= 1e-22:
		tmp = t_2
	elif (x * y) <= 2e+31:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * 0.5) / Float64(a / y))
	t_2 = Float64(Float64(x * y) * Float64(0.5 / a))
	tmp = 0.0
	if (Float64(x * y) <= -1e+109)
		tmp = t_1;
	elseif (Float64(x * y) <= -5e+38)
		tmp = Float64(t * Float64(Float64(z / a) * -4.5));
	elseif (Float64(x * y) <= -4e-84)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e-53)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (Float64(x * y) <= 1e-22)
		tmp = t_2;
	elseif (Float64(x * y) <= 2e+31)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * 0.5) / (a / y);
	t_2 = (x * y) * (0.5 / a);
	tmp = 0.0;
	if ((x * y) <= -1e+109)
		tmp = t_1;
	elseif ((x * y) <= -5e+38)
		tmp = t * ((z / a) * -4.5);
	elseif ((x * y) <= -4e-84)
		tmp = t_2;
	elseif ((x * y) <= 5e-53)
		tmp = -4.5 * (t / (a / z));
	elseif ((x * y) <= 1e-22)
		tmp = t_2;
	elseif ((x * y) <= 2e+31)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * 0.5), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+109], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5e+38], N[(t * N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-84], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e-53], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-22], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2e+31], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -9.99999999999999982e108 or 1.9999999999999999e31 < (*.f64 x y)

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf 83.2%

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

      1. associate-/l* 86.6%

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

      2. associate-*r/ 86.6%

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

   5. Simplified 86.6%

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

   if -9.99999999999999982e108 < (*.f64 x y) < -4.9999999999999997e38

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0 65.2%

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

      1. associate-/l* 74.0%

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

      2. associate-/r/ 65.7%

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

   5. Simplified 65.7%

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

      1. *-commutative 65.7%

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

      2. associate-*l/ 65.2%

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

      3. metadata-eval 65.2%

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

      4. times-frac 65.2%

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

      5. associate-*r* 65.4%

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

   7. Applied egg-rr 65.4%

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

      1. associate-*r/ 74.0%

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

      2. times-frac 74.0%

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

      3. metadata-eval 74.0%

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

   9. Simplified 74.0%

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

   if -4.9999999999999997e38 < (*.f64 x y) < -4.0000000000000001e-84 or 5e-53 < (*.f64 x y) < 1e-22

   1. Initial program 96.3%

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

      1. div-inv 96.3%

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

      2. fma-neg 96.3%

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

      3. *-commutative 96.3%

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

      4. distribute-rgt-neg-in 96.3%

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

      5. distribute-rgt-neg-in 96.3%

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

      6. metadata-eval 96.3%

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

      7. *-commutative 96.3%

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

      8. associate-/r* 96.3%

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

      9. metadata-eval 96.3%

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in x around inf 71.7%

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

   if -4.0000000000000001e-84 < (*.f64 x y) < 5e-53

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 80.2%

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

      1. associate-/l* 79.9%

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

   5. Simplified 79.9%

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

   if 1e-22 < (*.f64 x y) < 1.9999999999999999e31

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 82.4%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\frac{x \cdot 0.5}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-22}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.5}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot 0.5}{\frac{a}{y}}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-22}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x 0.5) (/ a y))))
   (if (<= (* x y) -1e+109)
     t_1
     (if (<= (* x y) -5e+38)
       (* t (* (/ z a) -4.5))
       (if (<= (* x y) -4e-84)
         (/ (* x y) (* a 2.0))
         (if (<= (* x y) 5e-53)
           (* -4.5 (/ t (/ a z)))
           (if (<= (* x y) 1e-22)
             (* (* x y) (/ 0.5 a))
             (if (<= (* x y) 2e+31) (* -4.5 (/ (* z t) a)) t_1))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * 0.5) / (a / y);
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = t_1;
	} else if ((x * y) <= -5e+38) {
		tmp = t * ((z / a) * -4.5);
	} else if ((x * y) <= -4e-84) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 5e-53) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x * y) <= 1e-22) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 2e+31) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 0.5d0) / (a / y)
    if ((x * y) <= (-1d+109)) then
        tmp = t_1
    else if ((x * y) <= (-5d+38)) then
        tmp = t * ((z / a) * (-4.5d0))
    else if ((x * y) <= (-4d-84)) then
        tmp = (x * y) / (a * 2.0d0)
    else if ((x * y) <= 5d-53) then
        tmp = (-4.5d0) * (t / (a / z))
    else if ((x * y) <= 1d-22) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 2d+31) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * 0.5) / (a / y);
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = t_1;
	} else if ((x * y) <= -5e+38) {
		tmp = t * ((z / a) * -4.5);
	} else if ((x * y) <= -4e-84) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 5e-53) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x * y) <= 1e-22) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 2e+31) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * 0.5) / (a / y)
	tmp = 0
	if (x * y) <= -1e+109:
		tmp = t_1
	elif (x * y) <= -5e+38:
		tmp = t * ((z / a) * -4.5)
	elif (x * y) <= -4e-84:
		tmp = (x * y) / (a * 2.0)
	elif (x * y) <= 5e-53:
		tmp = -4.5 * (t / (a / z))
	elif (x * y) <= 1e-22:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 2e+31:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * 0.5) / Float64(a / y))
	tmp = 0.0
	if (Float64(x * y) <= -1e+109)
		tmp = t_1;
	elseif (Float64(x * y) <= -5e+38)
		tmp = Float64(t * Float64(Float64(z / a) * -4.5));
	elseif (Float64(x * y) <= -4e-84)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (Float64(x * y) <= 5e-53)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (Float64(x * y) <= 1e-22)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 2e+31)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * 0.5) / (a / y);
	tmp = 0.0;
	if ((x * y) <= -1e+109)
		tmp = t_1;
	elseif ((x * y) <= -5e+38)
		tmp = t * ((z / a) * -4.5);
	elseif ((x * y) <= -4e-84)
		tmp = (x * y) / (a * 2.0);
	elseif ((x * y) <= 5e-53)
		tmp = -4.5 * (t / (a / z));
	elseif ((x * y) <= 1e-22)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 2e+31)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * 0.5), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+109], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5e+38], N[(t * N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-84], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-53], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-22], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+31], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 x y) < -9.99999999999999982e108 or 1.9999999999999999e31 < (*.f64 x y)

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf 83.2%

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

      1. associate-/l* 86.6%

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

      2. associate-*r/ 86.6%

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

   5. Simplified 86.6%

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

   if -9.99999999999999982e108 < (*.f64 x y) < -4.9999999999999997e38

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0 65.2%

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

      1. associate-/l* 74.0%

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

      2. associate-/r/ 65.7%

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

   5. Simplified 65.7%

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

      1. *-commutative 65.7%

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

      2. associate-*l/ 65.2%

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

      3. metadata-eval 65.2%

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

      4. times-frac 65.2%

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

      5. associate-*r* 65.4%

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

   7. Applied egg-rr 65.4%

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

      1. associate-*r/ 74.0%

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

      2. times-frac 74.0%

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

      3. metadata-eval 74.0%

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

   9. Simplified 74.0%

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

   if -4.9999999999999997e38 < (*.f64 x y) < -4.0000000000000001e-84

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 70.0%

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

   if -4.0000000000000001e-84 < (*.f64 x y) < 5e-53

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 80.2%

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

      1. associate-/l* 79.9%

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

   5. Simplified 79.9%

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

   if 5e-53 < (*.f64 x y) < 1e-22

   1. Initial program 99.2%

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

      1. div-inv 99.5%

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

      2. fma-neg 99.5%

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

      3. *-commutative 99.5%

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

      4. distribute-rgt-neg-in 99.5%

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

      5. distribute-rgt-neg-in 99.5%

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

      6. metadata-eval 99.5%

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

      7. *-commutative 99.5%

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

      8. associate-/r* 99.5%

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

      9. metadata-eval 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in x around inf 79.2%

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

   if 1e-22 < (*.f64 x y) < 1.9999999999999999e31

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 82.4%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\frac{x \cdot 0.5}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-22}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.5}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot 0.5}{\frac{a}{y}}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-22}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot \left(y \cdot 0.5\right)}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x 0.5) (/ a y))))
   (if (<= (* x y) -1e+109)
     t_1
     (if (<= (* x y) -5e+38)
       (* t (* (/ z a) -4.5))
       (if (<= (* x y) -4e-84)
         (/ (* x y) (* a 2.0))
         (if (<= (* x y) 5e-53)
           (* -4.5 (/ t (/ a z)))
           (if (<= (* x y) 1e-22)
             (/ 1.0 (/ a (* x (* y 0.5))))
             (if (<= (* x y) 2e+31) (* -4.5 (/ (* z t) a)) t_1))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * 0.5) / (a / y);
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = t_1;
	} else if ((x * y) <= -5e+38) {
		tmp = t * ((z / a) * -4.5);
	} else if ((x * y) <= -4e-84) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 5e-53) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x * y) <= 1e-22) {
		tmp = 1.0 / (a / (x * (y * 0.5)));
	} else if ((x * y) <= 2e+31) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 0.5d0) / (a / y)
    if ((x * y) <= (-1d+109)) then
        tmp = t_1
    else if ((x * y) <= (-5d+38)) then
        tmp = t * ((z / a) * (-4.5d0))
    else if ((x * y) <= (-4d-84)) then
        tmp = (x * y) / (a * 2.0d0)
    else if ((x * y) <= 5d-53) then
        tmp = (-4.5d0) * (t / (a / z))
    else if ((x * y) <= 1d-22) then
        tmp = 1.0d0 / (a / (x * (y * 0.5d0)))
    else if ((x * y) <= 2d+31) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * 0.5) / (a / y);
	double tmp;
	if ((x * y) <= -1e+109) {
		tmp = t_1;
	} else if ((x * y) <= -5e+38) {
		tmp = t * ((z / a) * -4.5);
	} else if ((x * y) <= -4e-84) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 5e-53) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x * y) <= 1e-22) {
		tmp = 1.0 / (a / (x * (y * 0.5)));
	} else if ((x * y) <= 2e+31) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * 0.5) / (a / y)
	tmp = 0
	if (x * y) <= -1e+109:
		tmp = t_1
	elif (x * y) <= -5e+38:
		tmp = t * ((z / a) * -4.5)
	elif (x * y) <= -4e-84:
		tmp = (x * y) / (a * 2.0)
	elif (x * y) <= 5e-53:
		tmp = -4.5 * (t / (a / z))
	elif (x * y) <= 1e-22:
		tmp = 1.0 / (a / (x * (y * 0.5)))
	elif (x * y) <= 2e+31:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * 0.5) / Float64(a / y))
	tmp = 0.0
	if (Float64(x * y) <= -1e+109)
		tmp = t_1;
	elseif (Float64(x * y) <= -5e+38)
		tmp = Float64(t * Float64(Float64(z / a) * -4.5));
	elseif (Float64(x * y) <= -4e-84)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (Float64(x * y) <= 5e-53)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (Float64(x * y) <= 1e-22)
		tmp = Float64(1.0 / Float64(a / Float64(x * Float64(y * 0.5))));
	elseif (Float64(x * y) <= 2e+31)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * 0.5) / (a / y);
	tmp = 0.0;
	if ((x * y) <= -1e+109)
		tmp = t_1;
	elseif ((x * y) <= -5e+38)
		tmp = t * ((z / a) * -4.5);
	elseif ((x * y) <= -4e-84)
		tmp = (x * y) / (a * 2.0);
	elseif ((x * y) <= 5e-53)
		tmp = -4.5 * (t / (a / z));
	elseif ((x * y) <= 1e-22)
		tmp = 1.0 / (a / (x * (y * 0.5)));
	elseif ((x * y) <= 2e+31)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * 0.5), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+109], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5e+38], N[(t * N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-84], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-53], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-22], N[(1.0 / N[(a / N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+31], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 x y) < -9.99999999999999982e108 or 1.9999999999999999e31 < (*.f64 x y)

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf 83.2%

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

      1. associate-/l* 86.6%

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

      2. associate-*r/ 86.6%

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

   5. Simplified 86.6%

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

   if -9.99999999999999982e108 < (*.f64 x y) < -4.9999999999999997e38

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0 65.2%

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

      1. associate-/l* 74.0%

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

      2. associate-/r/ 65.7%

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

   5. Simplified 65.7%

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

      1. *-commutative 65.7%

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

      2. associate-*l/ 65.2%

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

      3. metadata-eval 65.2%

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

      4. times-frac 65.2%

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

      5. associate-*r* 65.4%

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

   7. Applied egg-rr 65.4%

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

      1. associate-*r/ 74.0%

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

      2. times-frac 74.0%

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

      3. metadata-eval 74.0%

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

   9. Simplified 74.0%

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

   if -4.9999999999999997e38 < (*.f64 x y) < -4.0000000000000001e-84

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 70.0%

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

   if -4.0000000000000001e-84 < (*.f64 x y) < 5e-53

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 80.2%

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

      1. associate-/l* 79.9%

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

   5. Simplified 79.9%

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

   if 5e-53 < (*.f64 x y) < 1e-22

   1. Initial program 99.2%

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

      1. div-inv 99.5%

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

      2. fma-neg 99.5%

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

      3. *-commutative 99.5%

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

      4. distribute-rgt-neg-in 99.5%

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

      5. distribute-rgt-neg-in 99.5%

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

      6. metadata-eval 99.5%

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

      7. *-commutative 99.5%

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

      8. associate-/r* 99.5%

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

      9. metadata-eval 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in x around inf 79.2%

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

      1. associate-*r/ 79.2%

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

      2. clear-num 79.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{\left(x \cdot y\right) \cdot 0.5}}} \]

      3. associate-*l* 79.2%

         \[\leadsto \frac{1}{\frac{a}{\color{blue}{x \cdot \left(y \cdot 0.5\right)}}} \]

   7. Applied egg-rr 79.2%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{x \cdot \left(y \cdot 0.5\right)}}} \]

   if 1e-22 < (*.f64 x y) < 1.9999999999999999e31

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 82.4%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\frac{x \cdot 0.5}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-84}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-53}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-22}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot \left(y \cdot 0.5\right)}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+31}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.5}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -1 \cdot 10^{+234}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (- (* x y) (* (* z 9.0) t)) -1e+234)
   (- (* (/ x a) (/ y 2.0)) (/ t (* (/ a z) 0.2222222222222222)))
   (/ (- (* x y) (* 9.0 (* z t))) (* a 2.0))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) - ((z * 9.0) * t)) <= -1e+234) {
		tmp = ((x / a) * (y / 2.0)) - (t / ((a / z) * 0.2222222222222222));
	} else {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((x * y) - ((z * 9.0d0) * t)) <= (-1d+234)) then
        tmp = ((x / a) * (y / 2.0d0)) - (t / ((a / z) * 0.2222222222222222d0))
    else
        tmp = ((x * y) - (9.0d0 * (z * t))) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) - ((z * 9.0) * t)) <= -1e+234) {
		tmp = ((x / a) * (y / 2.0)) - (t / ((a / z) * 0.2222222222222222));
	} else {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) - ((z * 9.0) * t)) <= -1e+234:
		tmp = ((x / a) * (y / 2.0)) - (t / ((a / z) * 0.2222222222222222))
	else:
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) <= -1e+234)
		tmp = Float64(Float64(Float64(x / a) * Float64(y / 2.0)) - Float64(t / Float64(Float64(a / z) * 0.2222222222222222)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(9.0 * Float64(z * t))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) - ((z * 9.0) * t)) <= -1e+234)
		tmp = ((x / a) * (y / 2.0)) - (t / ((a / z) * 0.2222222222222222));
	else
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], -1e+234], N[(N[(N[(x / a), $MachinePrecision] * N[(y / 2.0), $MachinePrecision]), $MachinePrecision] - N[(t / N[(N[(a / z), $MachinePrecision] * 0.2222222222222222), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -1.00000000000000002e234

   1. Initial program 85.6%

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

      1. div-sub 85.6%

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

      2. sub-neg 85.6%

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

      3. times-frac 92.8%

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

      4. *-commutative 92.8%

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

      5. associate-/l* 97.3%

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

   4. Applied egg-rr 97.3%

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

      1. sub-neg 97.3%

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

      2. times-frac 97.3%

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

      3. metadata-eval 97.3%

         \[\leadsto \frac{x}{a} \cdot \frac{y}{2} - \frac{t}{\frac{a}{z} \cdot \color{blue}{0.2222222222222222}} \]

   6. Simplified 97.3%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{y}{2} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}} \]

   if -1.00000000000000002e234 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 94.8%

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

      1. fma-neg 95.3%

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

      2. associate-*l* 95.3%

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

      3. distribute-rgt-neg-in 95.3%

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

      4. *-commutative 95.3%

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

      5. distribute-rgt-neg-in 95.3%

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

      6. metadata-eval 95.3%

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

   3. Simplified 95.3%

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

      1. *-commutative 95.3%

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

      2. associate-*r* 95.3%

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

      3. metadata-eval 95.3%

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

      4. distribute-rgt-neg-in 95.3%

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

      5. distribute-lft-neg-in 95.3%

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

      6. fma-neg 94.8%

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

      7. *-commutative 94.8%

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

      8. associate-*l* 94.8%

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

   6. Applied egg-rr 94.8%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -1 \cdot 10^{+234}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2} - \frac{t}{\frac{a}{z} \cdot 0.2222222222222222}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+14} \lor \neg \left(x \leq 5 \cdot 10^{-104}\right):\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.02e+14) (not (<= x 5e-104)))
   (* (* x 0.5) (/ y a))
   (* -4.5 (/ t (/ a z)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.02e+14) || !(x <= 5e-104)) {
		tmp = (x * 0.5) * (y / a);
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.02d+14)) .or. (.not. (x <= 5d-104))) then
        tmp = (x * 0.5d0) * (y / a)
    else
        tmp = (-4.5d0) * (t / (a / z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.02e+14) || !(x <= 5e-104)) {
		tmp = (x * 0.5) * (y / a);
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.02e+14) or not (x <= 5e-104):
		tmp = (x * 0.5) * (y / a)
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.02e+14) || !(x <= 5e-104))
		tmp = Float64(Float64(x * 0.5) * Float64(y / a));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.02e+14) || ~((x <= 5e-104)))
		tmp = (x * 0.5) * (y / a);
	else
		tmp = -4.5 * (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.02e+14], N[Not[LessEqual[x, 5e-104]], $MachinePrecision]], N[(N[(x * 0.5), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.02e14 or 4.99999999999999979e-104 < x

   1. Initial program 92.6%

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

   3. Taylor expanded in x around inf 65.2%

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

      1. associate-/l* 63.7%

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

      2. associate-*r/ 63.7%

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

   5. Simplified 63.7%

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

      1. div-inv 63.2%

         \[\leadsto \color{blue}{\left(0.5 \cdot x\right) \cdot \frac{1}{\frac{a}{y}}} \]

      2. *-commutative 63.2%

         \[\leadsto \color{blue}{\left(x \cdot 0.5\right)} \cdot \frac{1}{\frac{a}{y}} \]

      3. clear-num 63.2%

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

   7. Applied egg-rr 63.2%

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

   if -1.02e14 < x < 4.99999999999999979e-104

   1. Initial program 94.4%

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

   3. Taylor expanded in x around 0 68.1%

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

      1. associate-/l* 68.4%

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

   5. Simplified 68.4%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+14} \lor \neg \left(x \leq 5 \cdot 10^{-104}\right):\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 91.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \frac{0.5}{a} \cdot \left(x \cdot y + -9 \cdot \left(z \cdot t\right)\right) \end{array} \]

FPCore

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

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return (0.5 / a) * ((x * y) + (-9.0 * (z * t)));
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (0.5d0 / a) * ((x * y) + ((-9.0d0) * (z * t)))
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return (0.5 / a) * ((x * y) + (-9.0 * (z * t)));
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return (0.5 / a) * ((x * y) + (-9.0 * (z * t)))

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(Float64(0.5 / a) * Float64(Float64(x * y) + Float64(-9.0 * Float64(z * t))))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = (0.5 / a) * ((x * y) + (-9.0 * (z * t)));
end

Wolfram

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

Derivation

1. Initial program 93.4%

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

   1. div-inv 93.3%

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

   2. fma-neg 93.7%

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

   3. *-commutative 93.7%

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

   4. distribute-rgt-neg-in 93.7%

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

   5. distribute-rgt-neg-in 93.7%

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

   6. metadata-eval 93.7%

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

   7. *-commutative 93.7%

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

   8. associate-/r* 93.7%

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

   9. metadata-eval 93.7%

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

4. Applied egg-rr 93.7%

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

5. Taylor expanded in x around 0 93.3%

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

6. Final simplification 93.3%

   \[\leadsto \frac{0.5}{a} \cdot \left(x \cdot y + -9 \cdot \left(z \cdot t\right)\right) \]
7. Add Preprocessing

Alternative 11: 91.2% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* 9.0 (* z t))) (* a 2.0)))

C

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

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - (9.0d0 * (z * t))) / (a * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
end

Wolfram

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

Derivation

1. Initial program 93.4%

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

   1. fma-neg 93.8%

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

   2. associate-*l* 93.8%

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

   3. distribute-rgt-neg-in 93.8%

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

   4. *-commutative 93.8%

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

   5. distribute-rgt-neg-in 93.8%

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

   6. metadata-eval 93.8%

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

3. Simplified 93.8%

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

   1. *-commutative 93.8%

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

   2. associate-*r* 93.8%

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

   3. metadata-eval 93.8%

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

   4. distribute-rgt-neg-in 93.8%

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

   5. distribute-lft-neg-in 93.8%

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

   6. fma-neg 93.4%

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

   7. *-commutative 93.4%

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

   8. associate-*l* 93.4%

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

6. Applied egg-rr 93.4%

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

7. Final simplification 93.4%

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

Alternative 12: 51.2% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

3. Taylor expanded in x around 0 48.9%

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

   1. associate-/l* 49.5%

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

   2. associate-/r/ 50.2%

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

5. Simplified 50.2%

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

6. Final simplification 50.2%

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

Alternative 13: 50.8% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

3. Taylor expanded in x around 0 48.9%

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

   1. associate-/l* 49.5%

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

5. Simplified 49.5%

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

6. Final simplification 49.5%

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

Developer target: 93.4% 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 2024034 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :herbie-target
  (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)))