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

Percentage Accurate: 91.0% → 96.7%

Time: 13.5s

Alternatives: 18

Speedup: 0.1×

• 29.1% 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: 91.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+261}\right):\\ \;\;\;\;\mathsf{fma}\left(-4.5, z \cdot \frac{t}{a}, 0.5 \cdot \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+261)))
     (fma -4.5 (* z (/ t a)) (* 0.5 (/ y (/ a x))))
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+261)) {
		tmp = fma(-4.5, (z * (t / a)), (0.5 * (y / (a / x))));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+261))
		tmp = fma(-4.5, Float64(z * Float64(t / a)), Float64(0.5 * Float64(y / Float64(a / x))));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+261]], $MachinePrecision]], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * 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)) < -inf.0 or 9.9999999999999993e260 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 66.8%

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

      1. associate-*l* 68.2%

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

   3. Simplified 68.2%

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

   4. Taylor expanded in x around 0 65.6%

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

      1. fma-def 65.6%

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

      2. associate-/l* 76.3%

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

      3. associate-/r/ 76.3%

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

      4. associate-/l* 92.1%

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

      5. associate-/r/ 90.7%

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

   6. Simplified 90.7%

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

      1. *-commutative 90.7%

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

      2. clear-num 90.7%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, 0.5 \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right)\right) \]

      3. un-div-inv 90.7%

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

   8. Applied egg-rr 90.7%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 9.9999999999999993e260

   1. Initial program 97.8%

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

      1. associate-*l* 97.8%

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

   3. Simplified 97.8%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+261}\right):\\ \;\;\;\;\mathsf{fma}\left(-4.5, z \cdot \frac{t}{a}, 0.5 \cdot \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \]

Alternative 2: 96.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+261}\right):\\ \;\;\;\;\mathsf{fma}\left(-4.5, z \cdot \frac{t}{a}, 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+261)))
     (fma -4.5 (* z (/ t a)) (* 0.5 (* y (/ x a))))
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+261)) {
		tmp = fma(-4.5, (z * (t / a)), (0.5 * (y * (x / a))));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+261))
		tmp = fma(-4.5, Float64(z * Float64(t / a)), Float64(0.5 * Float64(y * Float64(x / a))));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+261]], $MachinePrecision]], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * 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)) < -inf.0 or 9.9999999999999993e260 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 66.8%

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

      1. associate-*l* 68.2%

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

   3. Simplified 68.2%

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

   4. Taylor expanded in x around 0 65.6%

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

      1. fma-def 65.6%

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

      2. associate-/l* 76.3%

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

      3. associate-/r/ 76.3%

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

      4. associate-/l* 92.1%

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

      5. associate-/r/ 90.7%

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

   6. Simplified 90.7%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 9.9999999999999993e260

   1. Initial program 97.8%

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

      1. associate-*l* 97.8%

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

   3. Simplified 97.8%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+261}\right):\\ \;\;\;\;\mathsf{fma}\left(-4.5, z \cdot \frac{t}{a}, 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \]

Alternative 3: 90.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{+263}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.5e+263)
   (* (fma x y (* z (* t -9.0))) (/ 0.5 a))
   (* 0.5 (/ x (/ a y)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.5e+263) {
		tmp = fma(x, y, (z * (t * -9.0))) * (0.5 / a);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.5e+263)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) * Float64(0.5 / a));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.5e+263], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.49999999999999995e263

   1. Initial program 89.4%

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

      1. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

      1. div-inv 89.8%

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

      2. fma-neg 90.6%

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

      3. distribute-rgt-neg-in 90.6%

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

      4. *-commutative 90.6%

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

      5. distribute-rgt-neg-in 90.6%

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

      6. metadata-eval 90.6%

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

      7. *-commutative 90.6%

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

      8. associate-/r* 90.6%

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

      9. metadata-eval 90.6%

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

   5. Applied egg-rr 90.6%

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

   if 1.49999999999999995e263 < y

   1. Initial program 68.7%

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

      1. associate-*l* 68.7%

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

   3. Simplified 68.7%

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

   4. Taylor expanded in x around inf 60.8%

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

      1. associate-/l* 84.0%

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

   6. Simplified 84.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{+263}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 4: 90.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 3.9 \cdot 10^{+264}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -9 \cdot \left(z \cdot t\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y 3.9e+264)
   (/ (fma x y (* -9.0 (* z t))) (* a 2.0))
   (* 0.5 (/ x (/ a y)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 3.9e+264) {
		tmp = fma(x, y, (-9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 3.9e+264)
		tmp = Float64(fma(x, y, Float64(-9.0 * Float64(z * t))) / Float64(a * 2.0));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, 3.9e+264], N[(N[(x * y + N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.89999999999999994e264

   1. Initial program 89.4%

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

      1. fma-neg 90.3%

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

      2. *-commutative 90.3%

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

      3. associate-*l* 90.7%

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

      4. distribute-lft-neg-in 90.7%

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

      5. metadata-eval 90.7%

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

   3. Simplified 90.7%

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

   if 3.89999999999999994e264 < y

   1. Initial program 68.7%

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

      1. associate-*l* 68.7%

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

   3. Simplified 68.7%

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

   4. Taylor expanded in x around inf 60.8%

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

      1. associate-/l* 84.0%

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

   6. Simplified 84.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.9 \cdot 10^{+264}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -9 \cdot \left(z \cdot t\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 75.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a \cdot 2}\\ \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-61}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+74}:\\ \;\;\;\;\frac{t \cdot -9}{a} \cdot \frac{z}{2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) (* a 2.0))))
   (if (<= (* x y) (- INFINITY))
     (* 0.5 (/ y (/ a x)))
     (if (<= (* x y) -2e-66)
       t_1
       (if (<= (* x y) 5e-61)
         (/ (* t (* z -4.5)) a)
         (if (<= (* x y) 2.0)
           t_1
           (if (<= (* x y) 4e+74)
             (* (/ (* t -9.0) a) (/ z 2.0))
             (* 0.5 (/ x (/ a y))))))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = 0.5 * (y / (a / x));
	} else if ((x * y) <= -2e-66) {
		tmp = t_1;
	} else if ((x * y) <= 5e-61) {
		tmp = (t * (z * -4.5)) / a;
	} else if ((x * y) <= 2.0) {
		tmp = t_1;
	} else if ((x * y) <= 4e+74) {
		tmp = ((t * -9.0) / a) * (z / 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = 0.5 * (y / (a / x));
	} else if ((x * y) <= -2e-66) {
		tmp = t_1;
	} else if ((x * y) <= 5e-61) {
		tmp = (t * (z * -4.5)) / a;
	} else if ((x * y) <= 2.0) {
		tmp = t_1;
	} else if ((x * y) <= 4e+74) {
		tmp = ((t * -9.0) / a) * (z / 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) / (a * 2.0)
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = 0.5 * (y / (a / x))
	elif (x * y) <= -2e-66:
		tmp = t_1
	elif (x * y) <= 5e-61:
		tmp = (t * (z * -4.5)) / a
	elif (x * y) <= 2.0:
		tmp = t_1
	elif (x * y) <= 4e+74:
		tmp = ((t * -9.0) / a) * (z / 2.0)
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / Float64(a * 2.0))
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	elseif (Float64(x * y) <= -2e-66)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-61)
		tmp = Float64(Float64(t * Float64(z * -4.5)) / a);
	elseif (Float64(x * y) <= 2.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e+74)
		tmp = Float64(Float64(Float64(t * -9.0) / a) * Float64(z / 2.0));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / (a * 2.0);
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = 0.5 * (y / (a / x));
	elseif ((x * y) <= -2e-66)
		tmp = t_1;
	elseif ((x * y) <= 5e-61)
		tmp = (t * (z * -4.5)) / a;
	elseif ((x * y) <= 2.0)
		tmp = t_1;
	elseif ((x * y) <= 4e+74)
		tmp = ((t * -9.0) / a) * (z / 2.0);
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-66], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-61], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e+74], N[(N[(N[(t * -9.0), $MachinePrecision] / a), $MachinePrecision] * N[(z / 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 64.1%

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

      1. associate-*l* 64.1%

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

   3. Simplified 64.1%

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

   4. Taylor expanded in x around inf 64.1%

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

      1. associate-/l* 93.8%

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

      2. associate-/r/ 93.6%

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

   6. Simplified 93.6%

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

      1. *-commutative 81.1%

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

      2. clear-num 81.1%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, 0.5 \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right)\right) \]

      3. un-div-inv 81.0%

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

   8. Applied egg-rr 93.5%

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

   if -inf.0 < (*.f64 x y) < -2e-66 or 4.9999999999999999e-61 < (*.f64 x y) < 2

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in x around inf 73.1%

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

   if -2e-66 < (*.f64 x y) < 4.9999999999999999e-61

   1. Initial program 92.3%

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

      1. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 86.5%

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

      1. associate-*r/ 86.5%

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

      2. *-commutative 86.5%

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

      3. associate-*r* 86.6%

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

   6. Simplified 86.6%

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

   if 2 < (*.f64 x y) < 3.99999999999999981e74

   1. Initial program 90.4%

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

      1. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in x around 0 70.9%

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

      1. associate-*r* 70.9%

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

      2. *-commutative 70.9%

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

      3. times-frac 75.6%

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

   6. Applied egg-rr 75.6%

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

   if 3.99999999999999981e74 < (*.f64 x y)

   1. Initial program 79.4%

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

      1. associate-*l* 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in x around inf 75.7%

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

      1. associate-/l* 89.2%

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

   6. Simplified 89.2%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-61}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+74}:\\ \;\;\;\;\frac{t \cdot -9}{a} \cdot \frac{z}{2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 75.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a \cdot 2}\\ \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-61}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+74}:\\ \;\;\;\;\frac{t \cdot -9}{a} \cdot \frac{z}{2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) (* a 2.0))))
   (if (<= (* x y) (- INFINITY))
     (* 0.5 (/ y (/ a x)))
     (if (<= (* x y) -2e-66)
       t_1
       (if (<= (* x y) 5e-61)
         (/ (* z (* t -9.0)) (* a 2.0))
         (if (<= (* x y) 2.0)
           t_1
           (if (<= (* x y) 4e+74)
             (* (/ (* t -9.0) a) (/ z 2.0))
             (* 0.5 (/ x (/ a y))))))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = 0.5 * (y / (a / x));
	} else if ((x * y) <= -2e-66) {
		tmp = t_1;
	} else if ((x * y) <= 5e-61) {
		tmp = (z * (t * -9.0)) / (a * 2.0);
	} else if ((x * y) <= 2.0) {
		tmp = t_1;
	} else if ((x * y) <= 4e+74) {
		tmp = ((t * -9.0) / a) * (z / 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = 0.5 * (y / (a / x));
	} else if ((x * y) <= -2e-66) {
		tmp = t_1;
	} else if ((x * y) <= 5e-61) {
		tmp = (z * (t * -9.0)) / (a * 2.0);
	} else if ((x * y) <= 2.0) {
		tmp = t_1;
	} else if ((x * y) <= 4e+74) {
		tmp = ((t * -9.0) / a) * (z / 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) / (a * 2.0)
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = 0.5 * (y / (a / x))
	elif (x * y) <= -2e-66:
		tmp = t_1
	elif (x * y) <= 5e-61:
		tmp = (z * (t * -9.0)) / (a * 2.0)
	elif (x * y) <= 2.0:
		tmp = t_1
	elif (x * y) <= 4e+74:
		tmp = ((t * -9.0) / a) * (z / 2.0)
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / Float64(a * 2.0))
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	elseif (Float64(x * y) <= -2e-66)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-61)
		tmp = Float64(Float64(z * Float64(t * -9.0)) / Float64(a * 2.0));
	elseif (Float64(x * y) <= 2.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e+74)
		tmp = Float64(Float64(Float64(t * -9.0) / a) * Float64(z / 2.0));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / (a * 2.0);
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = 0.5 * (y / (a / x));
	elseif ((x * y) <= -2e-66)
		tmp = t_1;
	elseif ((x * y) <= 5e-61)
		tmp = (z * (t * -9.0)) / (a * 2.0);
	elseif ((x * y) <= 2.0)
		tmp = t_1;
	elseif ((x * y) <= 4e+74)
		tmp = ((t * -9.0) / a) * (z / 2.0);
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-66], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-61], N[(N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e+74], N[(N[(N[(t * -9.0), $MachinePrecision] / a), $MachinePrecision] * N[(z / 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 64.1%

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

      1. associate-*l* 64.1%

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

   3. Simplified 64.1%

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

   4. Taylor expanded in x around inf 64.1%

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

      1. associate-/l* 93.8%

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

      2. associate-/r/ 93.6%

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

   6. Simplified 93.6%

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

      1. *-commutative 81.1%

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

      2. clear-num 81.1%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, 0.5 \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right)\right) \]

      3. un-div-inv 81.0%

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

   8. Applied egg-rr 93.5%

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

   if -inf.0 < (*.f64 x y) < -2e-66 or 4.9999999999999999e-61 < (*.f64 x y) < 2

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in x around inf 73.1%

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

   if -2e-66 < (*.f64 x y) < 4.9999999999999999e-61

   1. Initial program 92.3%

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

      1. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 86.5%

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

      1. *-commutative 86.5%

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

      2. *-commutative 86.5%

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

      3. associate-*r* 86.6%

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

   6. Simplified 86.6%

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

   if 2 < (*.f64 x y) < 3.99999999999999981e74

   1. Initial program 90.4%

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

      1. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in x around 0 70.9%

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

      1. associate-*r* 70.9%

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

      2. *-commutative 70.9%

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

      3. times-frac 75.6%

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

   6. Applied egg-rr 75.6%

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

   if 3.99999999999999981e74 < (*.f64 x y)

   1. Initial program 79.4%

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

      1. associate-*l* 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in x around inf 75.7%

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

      1. associate-/l* 89.2%

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

   6. Simplified 89.2%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-61}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+74}:\\ \;\;\;\;\frac{t \cdot -9}{a} \cdot \frac{z}{2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a \cdot 2}\\ \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-61}:\\ \;\;\;\;\frac{-4.5}{a} \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+74}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) (* a 2.0))))
   (if (<= (* x y) (- INFINITY))
     (* 0.5 (/ y (/ a x)))
     (if (<= (* x y) -2e-66)
       t_1
       (if (<= (* x y) 5e-61)
         (* (/ -4.5 a) (* z t))
         (if (<= (* x y) 2.0)
           t_1
           (if (<= (* x y) 4e+74)
             (* -4.5 (* z (/ t a)))
             (* 0.5 (/ x (/ a y))))))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = 0.5 * (y / (a / x));
	} else if ((x * y) <= -2e-66) {
		tmp = t_1;
	} else if ((x * y) <= 5e-61) {
		tmp = (-4.5 / a) * (z * t);
	} else if ((x * y) <= 2.0) {
		tmp = t_1;
	} else if ((x * y) <= 4e+74) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = 0.5 * (y / (a / x));
	} else if ((x * y) <= -2e-66) {
		tmp = t_1;
	} else if ((x * y) <= 5e-61) {
		tmp = (-4.5 / a) * (z * t);
	} else if ((x * y) <= 2.0) {
		tmp = t_1;
	} else if ((x * y) <= 4e+74) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) / (a * 2.0)
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = 0.5 * (y / (a / x))
	elif (x * y) <= -2e-66:
		tmp = t_1
	elif (x * y) <= 5e-61:
		tmp = (-4.5 / a) * (z * t)
	elif (x * y) <= 2.0:
		tmp = t_1
	elif (x * y) <= 4e+74:
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / Float64(a * 2.0))
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	elseif (Float64(x * y) <= -2e-66)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-61)
		tmp = Float64(Float64(-4.5 / a) * Float64(z * t));
	elseif (Float64(x * y) <= 2.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e+74)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / (a * 2.0);
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = 0.5 * (y / (a / x));
	elseif ((x * y) <= -2e-66)
		tmp = t_1;
	elseif ((x * y) <= 5e-61)
		tmp = (-4.5 / a) * (z * t);
	elseif ((x * y) <= 2.0)
		tmp = t_1;
	elseif ((x * y) <= 4e+74)
		tmp = -4.5 * (z * (t / a));
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-66], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-61], N[(N[(-4.5 / a), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e+74], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 64.1%

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

      1. associate-*l* 64.1%

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

   3. Simplified 64.1%

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

   4. Taylor expanded in x around inf 64.1%

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

      1. associate-/l* 93.8%

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

      2. associate-/r/ 93.6%

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

   6. Simplified 93.6%

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

      1. *-commutative 81.1%

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

      2. clear-num 81.1%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, 0.5 \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right)\right) \]

      3. un-div-inv 81.0%

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

   8. Applied egg-rr 93.5%

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

   if -inf.0 < (*.f64 x y) < -2e-66 or 4.9999999999999999e-61 < (*.f64 x y) < 2

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in x around inf 73.1%

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

   if -2e-66 < (*.f64 x y) < 4.9999999999999999e-61

   1. Initial program 92.3%

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

      1. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 86.5%

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

      1. associate-/l* 80.0%

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

   6. Simplified 80.0%

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

      1. clear-num 78.9%

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

      2. un-div-inv 79.0%

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

   8. Applied egg-rr 79.0%

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

      1. associate-/l/ 85.8%

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

      2. associate-/r/ 86.5%

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

   10. Applied egg-rr 86.5%

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

   if 2 < (*.f64 x y) < 3.99999999999999981e74

   1. Initial program 90.4%

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

      1. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in x around 0 70.9%

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

      1. *-commutative 70.9%

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

      2. times-frac 70.8%

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

      3. associate-*l/ 75.6%

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

      4. metadata-eval 75.6%

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

      5. *-commutative 75.6%

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

   6. Applied egg-rr 75.6%

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

   if 3.99999999999999981e74 < (*.f64 x y)

   1. Initial program 79.4%

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

      1. associate-*l* 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in x around inf 75.7%

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

      1. associate-/l* 89.2%

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

   6. Simplified 89.2%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-61}:\\ \;\;\;\;\frac{-4.5}{a} \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+74}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{a \cdot 2}\\ \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-61}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+74}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x y) (* a 2.0))))
   (if (<= (* x y) (- INFINITY))
     (* 0.5 (/ y (/ a x)))
     (if (<= (* x y) -2e-66)
       t_1
       (if (<= (* x y) 5e-61)
         (/ (* t (* z -4.5)) a)
         (if (<= (* x y) 2.0)
           t_1
           (if (<= (* x y) 4e+74)
             (* -4.5 (* z (/ t a)))
             (* 0.5 (/ x (/ a y))))))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = 0.5 * (y / (a / x));
	} else if ((x * y) <= -2e-66) {
		tmp = t_1;
	} else if ((x * y) <= 5e-61) {
		tmp = (t * (z * -4.5)) / a;
	} else if ((x * y) <= 2.0) {
		tmp = t_1;
	} else if ((x * y) <= 4e+74) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / (a * 2.0);
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = 0.5 * (y / (a / x));
	} else if ((x * y) <= -2e-66) {
		tmp = t_1;
	} else if ((x * y) <= 5e-61) {
		tmp = (t * (z * -4.5)) / a;
	} else if ((x * y) <= 2.0) {
		tmp = t_1;
	} else if ((x * y) <= 4e+74) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) / (a * 2.0)
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = 0.5 * (y / (a / x))
	elif (x * y) <= -2e-66:
		tmp = t_1
	elif (x * y) <= 5e-61:
		tmp = (t * (z * -4.5)) / a
	elif (x * y) <= 2.0:
		tmp = t_1
	elif (x * y) <= 4e+74:
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / Float64(a * 2.0))
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	elseif (Float64(x * y) <= -2e-66)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-61)
		tmp = Float64(Float64(t * Float64(z * -4.5)) / a);
	elseif (Float64(x * y) <= 2.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e+74)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / (a * 2.0);
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = 0.5 * (y / (a / x));
	elseif ((x * y) <= -2e-66)
		tmp = t_1;
	elseif ((x * y) <= 5e-61)
		tmp = (t * (z * -4.5)) / a;
	elseif ((x * y) <= 2.0)
		tmp = t_1;
	elseif ((x * y) <= 4e+74)
		tmp = -4.5 * (z * (t / a));
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-66], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-61], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e+74], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 64.1%

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

      1. associate-*l* 64.1%

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

   3. Simplified 64.1%

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

   4. Taylor expanded in x around inf 64.1%

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

      1. associate-/l* 93.8%

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

      2. associate-/r/ 93.6%

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

   6. Simplified 93.6%

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

      1. *-commutative 81.1%

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

      2. clear-num 81.1%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, 0.5 \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right)\right) \]

      3. un-div-inv 81.0%

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

   8. Applied egg-rr 93.5%

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

   if -inf.0 < (*.f64 x y) < -2e-66 or 4.9999999999999999e-61 < (*.f64 x y) < 2

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in x around inf 73.1%

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

   if -2e-66 < (*.f64 x y) < 4.9999999999999999e-61

   1. Initial program 92.3%

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

      1. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 86.5%

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

      1. associate-*r/ 86.5%

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

      2. *-commutative 86.5%

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

      3. associate-*r* 86.6%

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

   6. Simplified 86.6%

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

   if 2 < (*.f64 x y) < 3.99999999999999981e74

   1. Initial program 90.4%

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

      1. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in x around 0 70.9%

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

      1. *-commutative 70.9%

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

      2. times-frac 70.8%

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

      3. associate-*l/ 75.6%

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

      4. metadata-eval 75.6%

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

      5. *-commutative 75.6%

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

   6. Applied egg-rr 75.6%

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

   if 3.99999999999999981e74 < (*.f64 x y)

   1. Initial program 79.4%

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

      1. associate-*l* 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in x around inf 75.7%

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

      1. associate-/l* 89.2%

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

   6. Simplified 89.2%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-61}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 2:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+74}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 9: 90.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -1 \cdot 10^{-149}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a} - \frac{z}{a} \cdot \frac{9 \cdot t}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) -1e-149)
   (- (* (* x y) (/ 0.5 a)) (* (/ z a) (/ (* 9.0 t) 2.0)))
   (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= -1e-149) {
		tmp = ((x * y) * (0.5 / a)) - ((z / a) * ((9.0 * t) / 2.0));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 ((a * 2.0d0) <= (-1d-149)) then
        tmp = ((x * y) * (0.5d0 / a)) - ((z / a) * ((9.0d0 * t) / 2.0d0))
    else
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= -1e-149) {
		tmp = ((x * y) * (0.5 / a)) - ((z / a) * ((9.0 * t) / 2.0));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (a * 2.0) <= -1e-149:
		tmp = ((x * y) * (0.5 / a)) - ((z / a) * ((9.0 * t) / 2.0))
	else:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= -1e-149)
		tmp = Float64(Float64(Float64(x * y) * Float64(0.5 / a)) - Float64(Float64(z / a) * Float64(Float64(9.0 * t) / 2.0)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 2.0) <= -1e-149)
		tmp = ((x * y) * (0.5 / a)) - ((z / a) * ((9.0 * t) / 2.0));
	else
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], -1e-149], N[(N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision] - N[(N[(z / a), $MachinePrecision] * N[(N[(9.0 * t), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < -9.99999999999999979e-150

   1. Initial program 83.4%

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

      1. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

      1. div-sub 83.4%

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

      2. div-inv 83.4%

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

      3. *-commutative 83.4%

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

      4. associate-/r* 83.4%

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

      5. metadata-eval 83.4%

         \[\leadsto \left(x \cdot y\right) \cdot \frac{\color{blue}{0.5}}{a} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2} \]

      6. times-frac 87.5%

         \[\leadsto \left(x \cdot y\right) \cdot \frac{0.5}{a} - \color{blue}{\frac{z}{a} \cdot \frac{9 \cdot t}{2}} \]

   5. Applied egg-rr 87.5%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a} - \frac{z}{a} \cdot \frac{9 \cdot t}{2}} \]

   if -9.99999999999999979e-150 < (*.f64 a 2)

   1. Initial program 91.4%

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

      1. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -1 \cdot 10^{-149}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a} - \frac{z}{a} \cdot \frac{9 \cdot t}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \]

Alternative 10: 90.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{+264}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y 6e+264)
   (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
   (* 0.5 (/ x (/ a y)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 6e+264) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 6d+264) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = 0.5d0 * (x / (a / y))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 6e+264) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if y <= 6e+264:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 6e+264)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 6e+264)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, 6e+264], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6e264

   1. Initial program 89.4%

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

      1. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

   if 6e264 < y

   1. Initial program 68.7%

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

      1. associate-*l* 68.7%

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

   3. Simplified 68.7%

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

   4. Taylor expanded in x around inf 60.8%

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

      1. associate-/l* 84.0%

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

   6. Simplified 84.0%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{+264}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 11: 66.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-128} \lor \neg \left(t \leq 1.3 \cdot 10^{+39}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.5e-128) (not (<= t 1.3e+39)))
   (* -4.5 (/ t (/ a z)))
   (* 0.5 (* x (/ y a)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.5e-128) || !(t <= 1.3e+39)) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 ((t <= (-3.5d-128)) .or. (.not. (t <= 1.3d+39))) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = 0.5d0 * (x * (y / a))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.5e-128) || !(t <= 1.3e+39)) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.5e-128) or not (t <= 1.3e+39):
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = 0.5 * (x * (y / a))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.5e-128) || !(t <= 1.3e+39))
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.5e-128) || ~((t <= 1.3e+39)))
		tmp = -4.5 * (t / (a / z));
	else
		tmp = 0.5 * (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.5e-128], N[Not[LessEqual[t, 1.3e+39]], $MachinePrecision]], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5e-128 or 1.3e39 < t

   1. Initial program 85.9%

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

      1. associate-*l* 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in x around 0 58.0%

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

      1. associate-/l* 60.6%

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

   6. Simplified 60.6%

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

   if -3.5e-128 < t < 1.3e39

   1. Initial program 91.3%

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

      1. associate-*l* 92.2%

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

   3. Simplified 92.2%

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

      1. div-inv 92.1%

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

      2. fma-neg 92.1%

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

      3. distribute-rgt-neg-in 92.1%

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

      4. *-commutative 92.1%

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

      5. distribute-rgt-neg-in 92.1%

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

      6. metadata-eval 92.1%

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

      7. *-commutative 92.1%

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

      8. associate-/r* 92.1%

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

      9. metadata-eval 92.1%

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

   5. Applied egg-rr 92.1%

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

   6. Taylor expanded in x around inf 68.0%

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

      1. associate-*r/ 70.4%

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

   8. Simplified 70.4%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-128} \lor \neg \left(t \leq 1.3 \cdot 10^{+39}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \]

Alternative 12: 66.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-128} \lor \neg \left(t \leq 5 \cdot 10^{+55}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1e-128) (not (<= t 5e+55)))
   (* -4.5 (/ t (/ a z)))
   (* 0.5 (* y (/ x a)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1e-128) || !(t <= 5e+55)) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 ((t <= (-1d-128)) .or. (.not. (t <= 5d+55))) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = 0.5d0 * (y * (x / a))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1e-128) || !(t <= 5e+55)) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1e-128) or not (t <= 5e+55):
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = 0.5 * (y * (x / a))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1e-128) || !(t <= 5e+55))
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1e-128) || ~((t <= 5e+55)))
		tmp = -4.5 * (t / (a / z));
	else
		tmp = 0.5 * (y * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1e-128], N[Not[LessEqual[t, 5e+55]], $MachinePrecision]], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.00000000000000005e-128 or 5.00000000000000046e55 < t

   1. Initial program 85.6%

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

      1. associate-*l* 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in x around 0 57.8%

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

      1. associate-/l* 60.5%

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

   6. Simplified 60.5%

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

   if -1.00000000000000005e-128 < t < 5.00000000000000046e55

   1. Initial program 91.5%

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

      1. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in x around inf 67.2%

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

      1. associate-/l* 69.6%

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

      2. associate-/r/ 66.7%

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

   6. Simplified 66.7%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-128} \lor \neg \left(t \leq 5 \cdot 10^{+55}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]

Alternative 13: 66.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-128} \lor \neg \left(t \leq 1.6 \cdot 10^{+56}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.5e-128) (not (<= t 1.6e+56)))
   (* -4.5 (/ t (/ a z)))
   (* 0.5 (/ y (/ a x)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.5e-128) || !(t <= 1.6e+56)) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (y / (a / x));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 ((t <= (-3.5d-128)) .or. (.not. (t <= 1.6d+56))) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = 0.5d0 * (y / (a / x))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.5e-128) || !(t <= 1.6e+56)) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = 0.5 * (y / (a / x));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.5e-128) or not (t <= 1.6e+56):
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = 0.5 * (y / (a / x))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.5e-128) || !(t <= 1.6e+56))
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.5e-128) || ~((t <= 1.6e+56)))
		tmp = -4.5 * (t / (a / z));
	else
		tmp = 0.5 * (y / (a / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.5e-128], N[Not[LessEqual[t, 1.6e+56]], $MachinePrecision]], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5e-128 or 1.60000000000000002e56 < t

   1. Initial program 85.6%

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

      1. associate-*l* 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in x around 0 57.8%

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

      1. associate-/l* 60.5%

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

   6. Simplified 60.5%

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

   if -3.5e-128 < t < 1.60000000000000002e56

   1. Initial program 91.5%

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

      1. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in x around inf 67.2%

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

      1. associate-/l* 69.6%

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

      2. associate-/r/ 66.7%

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

   6. Simplified 66.7%

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

      1. *-commutative 87.6%

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

      2. clear-num 87.0%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, 0.5 \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right)\right) \]

      3. un-div-inv 88.4%

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

   8. Applied egg-rr 66.7%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-128} \lor \neg \left(t \leq 1.6 \cdot 10^{+56}\right):\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 14: 66.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-128}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+55}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.5e-128)
   (* -4.5 (/ t (/ a z)))
   (if (<= t 1.65e+55) (* 0.5 (/ y (/ a x))) (* (/ z a) (* t -4.5)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e-128) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 1.65e+55) {
		tmp = 0.5 * (y / (a / x));
	} else {
		tmp = (z / a) * (t * -4.5);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 (t <= (-2.5d-128)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if (t <= 1.65d+55) then
        tmp = 0.5d0 * (y / (a / x))
    else
        tmp = (z / a) * (t * (-4.5d0))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e-128) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 1.65e+55) {
		tmp = 0.5 * (y / (a / x));
	} else {
		tmp = (z / a) * (t * -4.5);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.5e-128:
		tmp = -4.5 * (t / (a / z))
	elif t <= 1.65e+55:
		tmp = 0.5 * (y / (a / x))
	else:
		tmp = (z / a) * (t * -4.5)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.5e-128)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (t <= 1.65e+55)
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	else
		tmp = Float64(Float64(z / a) * Float64(t * -4.5));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.5e-128)
		tmp = -4.5 * (t / (a / z));
	elseif (t <= 1.65e+55)
		tmp = 0.5 * (y / (a / x));
	else
		tmp = (z / a) * (t * -4.5);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.5e-128], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e+55], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5000000000000001e-128

   1. Initial program 86.1%

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

      1. associate-*l* 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in x around 0 49.8%

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

      1. associate-/l* 55.9%

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

   6. Simplified 55.9%

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

   if -2.5000000000000001e-128 < t < 1.65e55

   1. Initial program 91.5%

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

      1. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in x around inf 67.2%

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

      1. associate-/l* 69.6%

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

      2. associate-/r/ 66.7%

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

   6. Simplified 66.7%

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

      1. *-commutative 87.6%

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

      2. clear-num 87.0%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, 0.5 \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right)\right) \]

      3. un-div-inv 88.4%

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

   8. Applied egg-rr 66.7%

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

   if 1.65e55 < t

   1. Initial program 85.0%

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

      1. associate-*l* 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in x around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. times-frac 68.1%

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

      3. metadata-eval 68.1%

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

      4. associate-*l/ 76.1%

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

      5. associate-/r/ 66.3%

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

      6. associate-*r/ 66.3%

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

      7. div-inv 66.4%

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

      8. clear-num 66.5%

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

   6. Applied egg-rr 66.5%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-128}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+55}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \end{array} \]

Alternative 15: 67.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-128}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+55}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1e-128)
   (* -4.5 (/ t (/ a z)))
   (if (<= t 5.6e+55) (* 0.5 (/ y (/ a x))) (* (/ t a) (* z -4.5)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1e-128) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 5.6e+55) {
		tmp = 0.5 * (y / (a / x));
	} else {
		tmp = (t / a) * (z * -4.5);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 (t <= (-1d-128)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if (t <= 5.6d+55) then
        tmp = 0.5d0 * (y / (a / x))
    else
        tmp = (t / a) * (z * (-4.5d0))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1e-128) {
		tmp = -4.5 * (t / (a / z));
	} else if (t <= 5.6e+55) {
		tmp = 0.5 * (y / (a / x));
	} else {
		tmp = (t / a) * (z * -4.5);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -1e-128:
		tmp = -4.5 * (t / (a / z))
	elif t <= 5.6e+55:
		tmp = 0.5 * (y / (a / x))
	else:
		tmp = (t / a) * (z * -4.5)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1e-128)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (t <= 5.6e+55)
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	else
		tmp = Float64(Float64(t / a) * Float64(z * -4.5));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1e-128)
		tmp = -4.5 * (t / (a / z));
	elseif (t <= 5.6e+55)
		tmp = 0.5 * (y / (a / x));
	else
		tmp = (t / a) * (z * -4.5);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1e-128], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+55], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * N[(z * -4.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.00000000000000005e-128

   1. Initial program 86.1%

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

      1. associate-*l* 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in x around 0 49.8%

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

      1. associate-/l* 55.9%

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

   6. Simplified 55.9%

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

   if -1.00000000000000005e-128 < t < 5.6000000000000002e55

   1. Initial program 91.5%

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

      1. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in x around inf 67.2%

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

      1. associate-/l* 69.6%

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

      2. associate-/r/ 66.7%

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

   6. Simplified 66.7%

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

      1. *-commutative 87.6%

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

      2. clear-num 87.0%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, 0.5 \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right)\right) \]

      3. un-div-inv 88.4%

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

   8. Applied egg-rr 66.7%

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

   if 5.6000000000000002e55 < t

   1. Initial program 85.0%

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

      1. associate-*l* 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in x around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. times-frac 68.1%

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

      3. metadata-eval 68.1%

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

      4. associate-*l/ 76.1%

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

      5. *-commutative 76.1%

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

      6. associate-*r* 76.1%

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

   6. Applied egg-rr 76.1%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-128}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+55}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \end{array} \]

Alternative 16: 67.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-129}:\\ \;\;\;\;\frac{-4.5}{\frac{\frac{a}{z}}{t}}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+56}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.9e-129)
   (/ -4.5 (/ (/ a z) t))
   (if (<= t 6.6e+56) (* 0.5 (/ y (/ a x))) (* (/ t a) (* z -4.5)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e-129) {
		tmp = -4.5 / ((a / z) / t);
	} else if (t <= 6.6e+56) {
		tmp = 0.5 * (y / (a / x));
	} else {
		tmp = (t / a) * (z * -4.5);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 (t <= (-2.9d-129)) then
        tmp = (-4.5d0) / ((a / z) / t)
    else if (t <= 6.6d+56) then
        tmp = 0.5d0 * (y / (a / x))
    else
        tmp = (t / a) * (z * (-4.5d0))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e-129) {
		tmp = -4.5 / ((a / z) / t);
	} else if (t <= 6.6e+56) {
		tmp = 0.5 * (y / (a / x));
	} else {
		tmp = (t / a) * (z * -4.5);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.9e-129:
		tmp = -4.5 / ((a / z) / t)
	elif t <= 6.6e+56:
		tmp = 0.5 * (y / (a / x))
	else:
		tmp = (t / a) * (z * -4.5)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.9e-129)
		tmp = Float64(-4.5 / Float64(Float64(a / z) / t));
	elseif (t <= 6.6e+56)
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	else
		tmp = Float64(Float64(t / a) * Float64(z * -4.5));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.9e-129)
		tmp = -4.5 / ((a / z) / t);
	elseif (t <= 6.6e+56)
		tmp = 0.5 * (y / (a / x));
	else
		tmp = (t / a) * (z * -4.5);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.9e-129], N[(-4.5 / N[(N[(a / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e+56], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * N[(z * -4.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.90000000000000017e-129

   1. Initial program 86.1%

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

      1. associate-*l* 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in x around 0 49.8%

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

      1. associate-/l* 55.9%

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

   6. Simplified 55.9%

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

      1. clear-num 55.9%

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

      2. un-div-inv 55.9%

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

   8. Applied egg-rr 55.9%

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

   if -2.90000000000000017e-129 < t < 6.60000000000000004e56

   1. Initial program 91.5%

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

      1. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in x around inf 67.2%

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

      1. associate-/l* 69.6%

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

      2. associate-/r/ 66.7%

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

   6. Simplified 66.7%

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

      1. *-commutative 87.6%

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

      2. clear-num 87.0%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, 0.5 \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right)\right) \]

      3. un-div-inv 88.4%

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

   8. Applied egg-rr 66.7%

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

   if 6.60000000000000004e56 < t

   1. Initial program 85.0%

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

      1. associate-*l* 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in x around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. times-frac 68.1%

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

      3. metadata-eval 68.1%

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

      4. associate-*l/ 76.1%

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

      5. *-commutative 76.1%

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

      6. associate-*r* 76.1%

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

   6. Applied egg-rr 76.1%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-129}:\\ \;\;\;\;\frac{-4.5}{\frac{\frac{a}{z}}{t}}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+56}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right)\\ \end{array} \]

Alternative 17: 52.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-176}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e-176) (* -4.5 (/ t (/ a z))) (* -4.5 (/ (* z t) a))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e-176) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 (z <= (-1d-176)) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e-176) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e-176:
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e-176)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1e-176)
		tmp = -4.5 * (t / (a / z));
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e-176], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e-176

   1. Initial program 91.6%

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

      1. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in x around 0 57.9%

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

      1. associate-/l* 59.5%

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

   6. Simplified 59.5%

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

   if -1e-176 < z

   1. Initial program 86.3%

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

      1. associate-*l* 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in x around 0 43.9%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-176}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]

Alternative 18: 51.5% accurate, 1.9× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t / (a / z));
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t / (a / z));
}

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 88.5%

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

   1. associate-*l* 88.9%

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

3. Simplified 88.9%

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

4. Taylor expanded in x around 0 49.6%

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

   1. associate-/l* 49.2%

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

6. Simplified 49.2%

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

7. Final simplification 49.2%

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

Developer target: 93.1% accurate, 0.7× 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 2023275 
(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)))