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

Percentage Accurate: 91.6% → 95.1%

Time: 9.5s

Alternatives: 13

Speedup: 0.5×

• 28.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+217}:\\ \;\;\;\;\mathsf{fma}\left(0.5, y, z \cdot \frac{t \cdot -4.5}{x}\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(\frac{0.5}{a} - 4.5 \cdot \left(t \cdot \frac{z}{y \cdot \left(x \cdot a\right)}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 -2e+217)
     (* (fma 0.5 y (* z (/ (* t -4.5) x))) (/ x a))
     (if (<= t_1 1e+308)
       (/ t_1 (* a 2.0))
       (* x (* y (- (/ 0.5 a) (* 4.5 (* t (/ z (* y (* x a))))))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -2e+217) {
		tmp = fma(0.5, y, (z * ((t * -4.5) / x))) * (x / a);
	} else if (t_1 <= 1e+308) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = x * (y * ((0.5 / a) - (4.5 * (t * (z / (y * (x * a)))))));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= -2e+217)
		tmp = Float64(fma(0.5, y, Float64(z * Float64(Float64(t * -4.5) / x))) * Float64(x / a));
	elseif (t_1 <= 1e+308)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = Float64(x * Float64(y * Float64(Float64(0.5 / a) - Float64(4.5 * Float64(t * Float64(z / Float64(y * Float64(x * a))))))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+217], N[(N[(0.5 * y + N[(z * N[(N[(t * -4.5), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+308], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(N[(0.5 / a), $MachinePrecision] - N[(4.5 * N[(t * N[(z / N[(y * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -1.99999999999999992e217

   1. Initial program 76.6%

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

   3. Taylor expanded in x around inf 89.2%

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

   4. Taylor expanded in a around 0 76.6%

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

      1. *-commutative 76.6%

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

      2. associate-/l* 91.8%

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

      3. +-commutative 91.8%

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

      4. fma-define 91.8%

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

      5. associate-*r/ 91.8%

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

      6. associate-*r* 91.8%

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

      7. *-commutative 91.8%

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

      8. *-commutative 91.8%

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

      9. associate-/l* 91.8%

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

      10. *-commutative 91.8%

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

   6. Simplified 91.8%

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

   if -1.99999999999999992e217 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 1e308

   1. Initial program 98.2%

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

   if 1e308 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 60.3%

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

   3. Taylor expanded in x around inf 65.2%

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

   4. Taylor expanded in y around -inf 65.4%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(4.5 \cdot \frac{t \cdot z}{a \cdot \left(x \cdot y\right)} - 0.5 \cdot \frac{1}{a}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 65.4%

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

      2. mul-1-neg 65.4%

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

      3. associate-/l* 87.5%

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

      4. associate-*r* 84.4%

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

      5. associate-*r/ 84.4%

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

      6. metadata-eval 84.4%

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

   6. Simplified 84.4%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -2 \cdot 10^{+217}:\\ \;\;\;\;\mathsf{fma}\left(0.5, y, z \cdot \frac{t \cdot -4.5}{x}\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+308}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(\frac{0.5}{a} - 4.5 \cdot \left(t \cdot \frac{z}{y \cdot \left(x \cdot a\right)}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+308}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(\frac{0.5}{a} - 4.5 \cdot \left(t \cdot \frac{z}{y \cdot \left(x \cdot a\right)}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+308)))
     (* x (* y (- (/ 0.5 a) (* 4.5 (* t (/ z (* y (* x a))))))))
     (/ t_1 (* a 2.0)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+308)) {
		tmp = x * (y * ((0.5 / a) - (4.5 * (t * (z / (y * (x * a)))))));
	} else {
		tmp = t_1 / (a * 2.0);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+308)) {
		tmp = x * (y * ((0.5 / a) - (4.5 * (t * (z / (y * (x * a)))))));
	} else {
		tmp = t_1 / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+308):
		tmp = x * (y * ((0.5 / a) - (4.5 * (t * (z / (y * (x * a)))))))
	else:
		tmp = t_1 / (a * 2.0)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+308))
		tmp = Float64(x * Float64(y * Float64(Float64(0.5 / a) - Float64(4.5 * Float64(t * Float64(z / Float64(y * Float64(x * a))))))));
	else
		tmp = Float64(t_1 / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+308)))
		tmp = x * (y * ((0.5 / a) - (4.5 * (t * (z / (y * (x * a)))))));
	else
		tmp = t_1 / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := 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+308]], $MachinePrecision]], N[(x * N[(y * N[(N[(0.5 / a), $MachinePrecision] - N[(4.5 * N[(t * N[(z / N[(y * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -inf.0 or 1e308 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 65.5%

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

   3. Taylor expanded in x around inf 75.6%

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

   4. Taylor expanded in y around -inf 77.4%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(4.5 \cdot \frac{t \cdot z}{a \cdot \left(x \cdot y\right)} - 0.5 \cdot \frac{1}{a}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 77.4%

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

      2. mul-1-neg 77.4%

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

      3. associate-/l* 93.5%

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

      4. associate-*r* 91.9%

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

      5. associate-*r/ 91.9%

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

      6. metadata-eval 91.9%

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

   6. Simplified 91.9%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 1e308

   1. Initial program 98.3%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+308}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(\frac{0.5}{a} - 4.5 \cdot \left(t \cdot \frac{z}{y \cdot \left(x \cdot a\right)}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \left(-4.5 \cdot \frac{z \cdot t}{y \cdot a} + 0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+305}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a} + 0.5 \cdot \frac{x \cdot y}{t \cdot a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 -2e+217)
     (* y (+ (* -4.5 (/ (* z t) (* y a))) (* 0.5 (/ x a))))
     (if (<= t_1 1e+305)
       (/ t_1 (* a 2.0))
       (* t (+ (* -4.5 (/ z a)) (* 0.5 (/ (* x y) (* t a)))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -2e+217) {
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / a)));
	} else if (t_1 <= 1e+305) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = t * ((-4.5 * (z / a)) + (0.5 * ((x * y) / (t * a))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - ((z * 9.0d0) * t)
    if (t_1 <= (-2d+217)) then
        tmp = y * (((-4.5d0) * ((z * t) / (y * a))) + (0.5d0 * (x / a)))
    else if (t_1 <= 1d+305) then
        tmp = t_1 / (a * 2.0d0)
    else
        tmp = t * (((-4.5d0) * (z / a)) + (0.5d0 * ((x * y) / (t * a))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -2e+217) {
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / a)));
	} else if (t_1 <= 1e+305) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = t * ((-4.5 * (z / a)) + (0.5 * ((x * y) / (t * a))));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_1 <= -2e+217:
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / a)))
	elif t_1 <= 1e+305:
		tmp = t_1 / (a * 2.0)
	else:
		tmp = t * ((-4.5 * (z / a)) + (0.5 * ((x * y) / (t * a))))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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 <= -2e+217)
		tmp = Float64(y * Float64(Float64(-4.5 * Float64(Float64(z * t) / Float64(y * a))) + Float64(0.5 * Float64(x / a))));
	elseif (t_1 <= 1e+305)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = Float64(t * Float64(Float64(-4.5 * Float64(z / a)) + Float64(0.5 * Float64(Float64(x * y) / Float64(t * a)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_1 <= -2e+217)
		tmp = y * ((-4.5 * ((z * t) / (y * a))) + (0.5 * (x / a)));
	elseif (t_1 <= 1e+305)
		tmp = t_1 / (a * 2.0);
	else
		tmp = t * ((-4.5 * (z / a)) + (0.5 * ((x * y) / (t * a))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+217], N[(y * N[(N[(-4.5 * N[(N[(z * t), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+305], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(-4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[(x * y), $MachinePrecision] / N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -1.99999999999999992e217

   1. Initial program 76.6%

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

   3. Taylor expanded in y around inf 86.2%

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

   if -1.99999999999999992e217 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 9.9999999999999994e304

   1. Initial program 98.2%

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

   if 9.9999999999999994e304 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 62.7%

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

   3. Taylor expanded in t around inf 81.9%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -2 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \left(-4.5 \cdot \frac{z \cdot t}{y \cdot a} + 0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+305}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a} + 0.5 \cdot \frac{x \cdot y}{t \cdot a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \frac{x}{a \cdot 2}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+67}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ x (* a 2.0)))))
   (if (<= (* x y) -2e+217)
     t_1
     (if (<= (* x y) -1e-53)
       (* (* x y) (/ 0.5 a))
       (if (<= (* x y) 5e+67) (* -4.5 (/ t (/ a z))) t_1)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (x / (a * 2.0));
	double tmp;
	if ((x * y) <= -2e+217) {
		tmp = t_1;
	} else if ((x * y) <= -1e-53) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e+67) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x / (a * 2.0d0))
    if ((x * y) <= (-2d+217)) then
        tmp = t_1
    else if ((x * y) <= (-1d-53)) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 5d+67) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (x / (a * 2.0));
	double tmp;
	if ((x * y) <= -2e+217) {
		tmp = t_1;
	} else if ((x * y) <= -1e-53) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e+67) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = y * (x / (a * 2.0))
	tmp = 0
	if (x * y) <= -2e+217:
		tmp = t_1
	elif (x * y) <= -1e-53:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 5e+67:
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(x / Float64(a * 2.0)))
	tmp = 0.0
	if (Float64(x * y) <= -2e+217)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e-53)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 5e+67)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (x / (a * 2.0));
	tmp = 0.0;
	if ((x * y) <= -2e+217)
		tmp = t_1;
	elseif ((x * y) <= -1e-53)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 5e+67)
		tmp = -4.5 * (t / (a / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+217], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e-53], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+67], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999992e217 or 4.99999999999999976e67 < (*.f64 x y)

   1. Initial program 83.3%

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

      1. div-inv 83.2%

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

      2. fmm-def 83.2%

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

      3. *-commutative 83.2%

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

      4. distribute-rgt-neg-in 83.2%

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

      5. distribute-rgt-neg-in 83.2%

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

      6. metadata-eval 83.2%

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

      7. *-commutative 83.2%

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

      8. associate-/r* 83.2%

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

      9. metadata-eval 83.2%

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

   4. Applied egg-rr 83.2%

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

   5. Taylor expanded in x around inf 79.5%

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

      1. clear-num 79.5%

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

      2. un-div-inv 79.6%

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

      3. *-commutative 79.6%

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

      4. div-inv 79.6%

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

      5. metadata-eval 79.6%

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

   7. Applied egg-rr 79.6%

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

      1. associate-/l* 86.6%

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

   9. Simplified 86.6%

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

   if -1.99999999999999992e217 < (*.f64 x y) < -1.00000000000000003e-53

   1. Initial program 97.8%

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

      1. div-inv 97.7%

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

      2. fmm-def 97.7%

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

      3. *-commutative 97.7%

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

      4. distribute-rgt-neg-in 97.7%

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

      5. distribute-rgt-neg-in 97.7%

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

      6. metadata-eval 97.7%

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

      7. *-commutative 97.7%

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

      8. associate-/r* 97.7%

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

      9. metadata-eval 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in x around inf 74.9%

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

   if -1.00000000000000003e-53 < (*.f64 x y) < 4.99999999999999976e67

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0 75.2%

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

      1. associate-/l* 74.4%

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

   5. Simplified 74.4%

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

      1. clear-num 74.4%

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

      2. un-div-inv 75.0%

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

   7. Applied egg-rr 75.0%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+67}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+67}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+217)
   (* y (* x (/ 0.5 a)))
   (if (<= (* x y) -1e-53)
     (* (* x y) (/ 0.5 a))
     (if (<= (* x y) 5e+67) (* -4.5 (/ t (/ a z))) (* y (/ x (* a 2.0)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+217) {
		tmp = y * (x * (0.5 / a));
	} else if ((x * y) <= -1e-53) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e+67) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = y * (x / (a * 2.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-2d+217)) then
        tmp = y * (x * (0.5d0 / a))
    else if ((x * y) <= (-1d-53)) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 5d+67) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = y * (x / (a * 2.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+217) {
		tmp = y * (x * (0.5 / a));
	} else if ((x * y) <= -1e-53) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e+67) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = y * (x / (a * 2.0));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+217:
		tmp = y * (x * (0.5 / a))
	elif (x * y) <= -1e-53:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 5e+67:
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = y * (x / (a * 2.0))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+217)
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	elseif (Float64(x * y) <= -1e-53)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 5e+67)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(y * Float64(x / Float64(a * 2.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e+217)
		tmp = y * (x * (0.5 / a));
	elseif ((x * y) <= -1e-53)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 5e+67)
		tmp = -4.5 * (t / (a / z));
	else
		tmp = y * (x / (a * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+217], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-53], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+67], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.99999999999999992e217

   1. Initial program 74.7%

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

      1. div-inv 74.7%

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

      2. fmm-def 74.7%

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

      3. *-commutative 74.7%

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

      4. distribute-rgt-neg-in 74.7%

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

      5. distribute-rgt-neg-in 74.7%

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

      6. metadata-eval 74.7%

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

      7. *-commutative 74.7%

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

      8. associate-/r* 74.7%

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

      9. metadata-eval 74.7%

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

   4. Applied egg-rr 74.7%

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

   5. Taylor expanded in x around inf 70.2%

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

      1. associate-*r/ 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-*l* 70.2%

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

   7. Applied egg-rr 70.2%

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

      1. associate-/l* 95.2%

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

      2. *-commutative 95.2%

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

      3. *-un-lft-identity 95.2%

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

      4. times-frac 95.2%

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

      5. metadata-eval 95.2%

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

      6. metadata-eval 95.2%

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

      7. times-frac 95.2%

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

      8. *-un-lft-identity 95.2%

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

      9. *-commutative 95.2%

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

      10. *-commutative 95.2%

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

      11. div-inv 95.3%

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

      12. metadata-eval 95.3%

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

      13. div-inv 95.3%

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

      14. clear-num 95.3%

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

   9. Applied egg-rr 95.3%

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

   if -1.99999999999999992e217 < (*.f64 x y) < -1.00000000000000003e-53

   1. Initial program 97.8%

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

      1. div-inv 97.7%

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

      2. fmm-def 97.7%

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

      3. *-commutative 97.7%

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

      4. distribute-rgt-neg-in 97.7%

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

      5. distribute-rgt-neg-in 97.7%

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

      6. metadata-eval 97.7%

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

      7. *-commutative 97.7%

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

      8. associate-/r* 97.7%

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

      9. metadata-eval 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in x around inf 74.9%

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

   if -1.00000000000000003e-53 < (*.f64 x y) < 4.99999999999999976e67

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0 75.2%

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

      1. associate-/l* 74.4%

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

   5. Simplified 74.4%

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

      1. clear-num 74.4%

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

      2. un-div-inv 75.0%

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

   7. Applied egg-rr 75.0%

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

   if 4.99999999999999976e67 < (*.f64 x y)

   1. Initial program 86.7%

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

      1. div-inv 86.5%

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

      2. fmm-def 86.5%

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

      3. *-commutative 86.5%

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

      4. distribute-rgt-neg-in 86.5%

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

      5. distribute-rgt-neg-in 86.5%

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

      6. metadata-eval 86.5%

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

      7. *-commutative 86.5%

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

      8. associate-/r* 86.5%

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

      9. metadata-eval 86.5%

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

   4. Applied egg-rr 86.5%

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

   5. Taylor expanded in x around inf 83.2%

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

      1. clear-num 83.2%

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

      2. un-div-inv 83.3%

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

      3. *-commutative 83.3%

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

      4. div-inv 83.3%

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

      5. metadata-eval 83.3%

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

   7. Applied egg-rr 83.3%

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

      1. associate-/l* 83.2%

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

   9. Simplified 83.2%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a \cdot 2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+67}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+217)
   (* y (* x (/ 0.5 a)))
   (if (<= (* x y) -1e-53)
     (* (* x y) (/ 0.5 a))
     (if (<= (* x y) 5e+67) (* t (* -4.5 (/ z a))) (* y (/ x (* a 2.0)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+217) {
		tmp = y * (x * (0.5 / a));
	} else if ((x * y) <= -1e-53) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e+67) {
		tmp = t * (-4.5 * (z / a));
	} else {
		tmp = y * (x / (a * 2.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-2d+217)) then
        tmp = y * (x * (0.5d0 / a))
    else if ((x * y) <= (-1d-53)) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 5d+67) then
        tmp = t * ((-4.5d0) * (z / a))
    else
        tmp = y * (x / (a * 2.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+217) {
		tmp = y * (x * (0.5 / a));
	} else if ((x * y) <= -1e-53) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e+67) {
		tmp = t * (-4.5 * (z / a));
	} else {
		tmp = y * (x / (a * 2.0));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+217:
		tmp = y * (x * (0.5 / a))
	elif (x * y) <= -1e-53:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 5e+67:
		tmp = t * (-4.5 * (z / a))
	else:
		tmp = y * (x / (a * 2.0))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+217)
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	elseif (Float64(x * y) <= -1e-53)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 5e+67)
		tmp = Float64(t * Float64(-4.5 * Float64(z / a)));
	else
		tmp = Float64(y * Float64(x / Float64(a * 2.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e+217)
		tmp = y * (x * (0.5 / a));
	elseif ((x * y) <= -1e-53)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 5e+67)
		tmp = t * (-4.5 * (z / a));
	else
		tmp = y * (x / (a * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+217], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-53], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+67], N[(t * N[(-4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.99999999999999992e217

   1. Initial program 74.7%

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

      1. div-inv 74.7%

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

      2. fmm-def 74.7%

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

      3. *-commutative 74.7%

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

      4. distribute-rgt-neg-in 74.7%

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

      5. distribute-rgt-neg-in 74.7%

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

      6. metadata-eval 74.7%

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

      7. *-commutative 74.7%

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

      8. associate-/r* 74.7%

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

      9. metadata-eval 74.7%

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

   4. Applied egg-rr 74.7%

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

   5. Taylor expanded in x around inf 70.2%

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

      1. associate-*r/ 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-*l* 70.2%

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

   7. Applied egg-rr 70.2%

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

      1. associate-/l* 95.2%

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

      2. *-commutative 95.2%

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

      3. *-un-lft-identity 95.2%

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

      4. times-frac 95.2%

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

      5. metadata-eval 95.2%

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

      6. metadata-eval 95.2%

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

      7. times-frac 95.2%

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

      8. *-un-lft-identity 95.2%

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

      9. *-commutative 95.2%

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

      10. *-commutative 95.2%

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

      11. div-inv 95.3%

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

      12. metadata-eval 95.3%

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

      13. div-inv 95.3%

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

      14. clear-num 95.3%

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

   9. Applied egg-rr 95.3%

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

   if -1.99999999999999992e217 < (*.f64 x y) < -1.00000000000000003e-53

   1. Initial program 97.8%

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

      1. div-inv 97.7%

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

      2. fmm-def 97.7%

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

      3. *-commutative 97.7%

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

      4. distribute-rgt-neg-in 97.7%

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

      5. distribute-rgt-neg-in 97.7%

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

      6. metadata-eval 97.7%

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

      7. *-commutative 97.7%

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

      8. associate-/r* 97.7%

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

      9. metadata-eval 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in x around inf 74.9%

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

   if -1.00000000000000003e-53 < (*.f64 x y) < 4.99999999999999976e67

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0 75.2%

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

      1. *-commutative 75.2%

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

      2. associate-*r* 75.2%

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

   5. Simplified 75.2%

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

      1. associate-*r* 75.2%

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

      2. times-frac 75.2%

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

      3. associate-*r/ 74.4%

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

      4. metadata-eval 74.4%

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

      5. *-commutative 74.4%

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

      6. *-commutative 74.4%

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

      7. associate-*r* 74.4%

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

      8. metadata-eval 74.4%

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

      9. times-frac 74.4%

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

      10. *-commutative 74.4%

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

      11. *-commutative 74.4%

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

      12. times-frac 74.4%

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

      13. metadata-eval 74.4%

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

   7. Applied egg-rr 74.4%

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

   if 4.99999999999999976e67 < (*.f64 x y)

   1. Initial program 86.7%

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

      1. div-inv 86.5%

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

      2. fmm-def 86.5%

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

      3. *-commutative 86.5%

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

      4. distribute-rgt-neg-in 86.5%

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

      5. distribute-rgt-neg-in 86.5%

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

      6. metadata-eval 86.5%

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

      7. *-commutative 86.5%

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

      8. associate-/r* 86.5%

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

      9. metadata-eval 86.5%

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

   4. Applied egg-rr 86.5%

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

   5. Taylor expanded in x around inf 83.2%

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

      1. clear-num 83.2%

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

      2. un-div-inv 83.3%

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

      3. *-commutative 83.3%

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

      4. div-inv 83.3%

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

      5. metadata-eval 83.3%

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

   7. Applied egg-rr 83.3%

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

      1. associate-/l* 83.2%

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

   9. Simplified 83.2%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a \cdot 2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+67}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+217)
   (* y (* x (/ 0.5 a)))
   (if (<= (* x y) -1e-53)
     (* (* x y) (/ 0.5 a))
     (if (<= (* x y) 5e+67) (/ (* t -4.5) (/ a z)) (* y (/ x (* a 2.0)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+217) {
		tmp = y * (x * (0.5 / a));
	} else if ((x * y) <= -1e-53) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e+67) {
		tmp = (t * -4.5) / (a / z);
	} else {
		tmp = y * (x / (a * 2.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-2d+217)) then
        tmp = y * (x * (0.5d0 / a))
    else if ((x * y) <= (-1d-53)) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 5d+67) then
        tmp = (t * (-4.5d0)) / (a / z)
    else
        tmp = y * (x / (a * 2.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+217) {
		tmp = y * (x * (0.5 / a));
	} else if ((x * y) <= -1e-53) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 5e+67) {
		tmp = (t * -4.5) / (a / z);
	} else {
		tmp = y * (x / (a * 2.0));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+217:
		tmp = y * (x * (0.5 / a))
	elif (x * y) <= -1e-53:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 5e+67:
		tmp = (t * -4.5) / (a / z)
	else:
		tmp = y * (x / (a * 2.0))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+217)
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	elseif (Float64(x * y) <= -1e-53)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 5e+67)
		tmp = Float64(Float64(t * -4.5) / Float64(a / z));
	else
		tmp = Float64(y * Float64(x / Float64(a * 2.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e+217)
		tmp = y * (x * (0.5 / a));
	elseif ((x * y) <= -1e-53)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 5e+67)
		tmp = (t * -4.5) / (a / z);
	else
		tmp = y * (x / (a * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+217], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-53], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+67], N[(N[(t * -4.5), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.99999999999999992e217

   1. Initial program 74.7%

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

      1. div-inv 74.7%

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

      2. fmm-def 74.7%

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

      3. *-commutative 74.7%

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

      4. distribute-rgt-neg-in 74.7%

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

      5. distribute-rgt-neg-in 74.7%

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

      6. metadata-eval 74.7%

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

      7. *-commutative 74.7%

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

      8. associate-/r* 74.7%

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

      9. metadata-eval 74.7%

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

   4. Applied egg-rr 74.7%

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

   5. Taylor expanded in x around inf 70.2%

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

      1. associate-*r/ 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-*l* 70.2%

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

   7. Applied egg-rr 70.2%

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

      1. associate-/l* 95.2%

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

      2. *-commutative 95.2%

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

      3. *-un-lft-identity 95.2%

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

      4. times-frac 95.2%

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

      5. metadata-eval 95.2%

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

      6. metadata-eval 95.2%

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

      7. times-frac 95.2%

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

      8. *-un-lft-identity 95.2%

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

      9. *-commutative 95.2%

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

      10. *-commutative 95.2%

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

      11. div-inv 95.3%

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

      12. metadata-eval 95.3%

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

      13. div-inv 95.3%

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

      14. clear-num 95.3%

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

   9. Applied egg-rr 95.3%

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

   if -1.99999999999999992e217 < (*.f64 x y) < -1.00000000000000003e-53

   1. Initial program 97.8%

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

      1. div-inv 97.7%

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

      2. fmm-def 97.7%

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

      3. *-commutative 97.7%

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

      4. distribute-rgt-neg-in 97.7%

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

      5. distribute-rgt-neg-in 97.7%

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

      6. metadata-eval 97.7%

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

      7. *-commutative 97.7%

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

      8. associate-/r* 97.7%

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

      9. metadata-eval 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in x around inf 74.9%

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

   if -1.00000000000000003e-53 < (*.f64 x y) < 4.99999999999999976e67

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0 75.2%

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

      1. associate-/l* 74.4%

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

   5. Simplified 74.4%

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

      1. associate-*r* 74.3%

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

      2. clear-num 74.3%

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

      3. un-div-inv 75.0%

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

      4. *-commutative 75.0%

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

   7. Applied egg-rr 75.0%

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

   if 4.99999999999999976e67 < (*.f64 x y)

   1. Initial program 86.7%

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

      1. div-inv 86.5%

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

      2. fmm-def 86.5%

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

      3. *-commutative 86.5%

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

      4. distribute-rgt-neg-in 86.5%

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

      5. distribute-rgt-neg-in 86.5%

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

      6. metadata-eval 86.5%

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

      7. *-commutative 86.5%

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

      8. associate-/r* 86.5%

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

      9. metadata-eval 86.5%

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

   4. Applied egg-rr 86.5%

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

   5. Taylor expanded in x around inf 83.2%

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

      1. clear-num 83.2%

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

      2. un-div-inv 83.3%

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

      3. *-commutative 83.3%

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

      4. div-inv 83.3%

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

      5. metadata-eval 83.3%

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

   7. Applied egg-rr 83.3%

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

      1. associate-/l* 83.2%

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

   9. Simplified 83.2%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a \cdot 2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+67}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+67}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+217)
   (* y (* x (/ 0.5 a)))
   (if (<= (* x y) -1e-53)
     (/ (* x y) (* a 2.0))
     (if (<= (* x y) 5e+67) (/ (* t -4.5) (/ a z)) (* y (/ x (* a 2.0)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+217) {
		tmp = y * (x * (0.5 / a));
	} else if ((x * y) <= -1e-53) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 5e+67) {
		tmp = (t * -4.5) / (a / z);
	} else {
		tmp = y * (x / (a * 2.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-2d+217)) then
        tmp = y * (x * (0.5d0 / a))
    else if ((x * y) <= (-1d-53)) then
        tmp = (x * y) / (a * 2.0d0)
    else if ((x * y) <= 5d+67) then
        tmp = (t * (-4.5d0)) / (a / z)
    else
        tmp = y * (x / (a * 2.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+217) {
		tmp = y * (x * (0.5 / a));
	} else if ((x * y) <= -1e-53) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= 5e+67) {
		tmp = (t * -4.5) / (a / z);
	} else {
		tmp = y * (x / (a * 2.0));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+217:
		tmp = y * (x * (0.5 / a))
	elif (x * y) <= -1e-53:
		tmp = (x * y) / (a * 2.0)
	elif (x * y) <= 5e+67:
		tmp = (t * -4.5) / (a / z)
	else:
		tmp = y * (x / (a * 2.0))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+217)
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	elseif (Float64(x * y) <= -1e-53)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (Float64(x * y) <= 5e+67)
		tmp = Float64(Float64(t * -4.5) / Float64(a / z));
	else
		tmp = Float64(y * Float64(x / Float64(a * 2.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e+217)
		tmp = y * (x * (0.5 / a));
	elseif ((x * y) <= -1e-53)
		tmp = (x * y) / (a * 2.0);
	elseif ((x * y) <= 5e+67)
		tmp = (t * -4.5) / (a / z);
	else
		tmp = y * (x / (a * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+217], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-53], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+67], N[(N[(t * -4.5), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.99999999999999992e217

   1. Initial program 74.7%

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

      1. div-inv 74.7%

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

      2. fmm-def 74.7%

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

      3. *-commutative 74.7%

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

      4. distribute-rgt-neg-in 74.7%

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

      5. distribute-rgt-neg-in 74.7%

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

      6. metadata-eval 74.7%

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

      7. *-commutative 74.7%

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

      8. associate-/r* 74.7%

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

      9. metadata-eval 74.7%

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

   4. Applied egg-rr 74.7%

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

   5. Taylor expanded in x around inf 70.2%

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

      1. associate-*r/ 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-*l* 70.2%

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

   7. Applied egg-rr 70.2%

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

      1. associate-/l* 95.2%

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

      2. *-commutative 95.2%

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

      3. *-un-lft-identity 95.2%

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

      4. times-frac 95.2%

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

      5. metadata-eval 95.2%

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

      6. metadata-eval 95.2%

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

      7. times-frac 95.2%

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

      8. *-un-lft-identity 95.2%

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

      9. *-commutative 95.2%

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

      10. *-commutative 95.2%

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

      11. div-inv 95.3%

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

      12. metadata-eval 95.3%

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

      13. div-inv 95.3%

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

      14. clear-num 95.3%

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

   9. Applied egg-rr 95.3%

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

   if -1.99999999999999992e217 < (*.f64 x y) < -1.00000000000000003e-53

   1. Initial program 97.8%

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

   3. Taylor expanded in x around inf 75.0%

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

   if -1.00000000000000003e-53 < (*.f64 x y) < 4.99999999999999976e67

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0 75.2%

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

      1. associate-/l* 74.4%

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

   5. Simplified 74.4%

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

      1. associate-*r* 74.3%

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

      2. clear-num 74.3%

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

      3. un-div-inv 75.0%

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

      4. *-commutative 75.0%

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

   7. Applied egg-rr 75.0%

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

   if 4.99999999999999976e67 < (*.f64 x y)

   1. Initial program 86.7%

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

      1. div-inv 86.5%

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

      2. fmm-def 86.5%

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

      3. *-commutative 86.5%

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

      4. distribute-rgt-neg-in 86.5%

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

      5. distribute-rgt-neg-in 86.5%

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

      6. metadata-eval 86.5%

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

      7. *-commutative 86.5%

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

      8. associate-/r* 86.5%

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

      9. metadata-eval 86.5%

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

   4. Applied egg-rr 86.5%

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

   5. Taylor expanded in x around inf 83.2%

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

      1. clear-num 83.2%

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

      2. un-div-inv 83.3%

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

      3. *-commutative 83.3%

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

      4. div-inv 83.3%

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

      5. metadata-eval 83.3%

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

   7. Applied egg-rr 83.3%

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

      1. associate-/l* 83.2%

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

   9. Simplified 83.2%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a \cdot 2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-53}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+67}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y \cdot 0.5}{a}\\ t_2 := t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+173}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -185000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (* y 0.5) a))) (t_2 (* t (* z (/ -4.5 a)))))
   (if (<= z -1.35e+173)
     t_2
     (if (<= z -9.8e+145)
       t_1
       (if (<= z -185000000000.0)
         t_2
         (if (<= z 2.8e+64) t_1 (* -4.5 (* t (/ z a)))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y * 0.5) / a);
	double t_2 = t * (z * (-4.5 / a));
	double tmp;
	if (z <= -1.35e+173) {
		tmp = t_2;
	} else if (z <= -9.8e+145) {
		tmp = t_1;
	} else if (z <= -185000000000.0) {
		tmp = t_2;
	} else if (z <= 2.8e+64) {
		tmp = t_1;
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * 0.5d0) / a)
    t_2 = t * (z * ((-4.5d0) / a))
    if (z <= (-1.35d+173)) then
        tmp = t_2
    else if (z <= (-9.8d+145)) then
        tmp = t_1
    else if (z <= (-185000000000.0d0)) then
        tmp = t_2
    else if (z <= 2.8d+64) then
        tmp = t_1
    else
        tmp = (-4.5d0) * (t * (z / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y * 0.5) / a);
	double t_2 = t * (z * (-4.5 / a));
	double tmp;
	if (z <= -1.35e+173) {
		tmp = t_2;
	} else if (z <= -9.8e+145) {
		tmp = t_1;
	} else if (z <= -185000000000.0) {
		tmp = t_2;
	} else if (z <= 2.8e+64) {
		tmp = t_1;
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x * ((y * 0.5) / a)
	t_2 = t * (z * (-4.5 / a))
	tmp = 0
	if z <= -1.35e+173:
		tmp = t_2
	elif z <= -9.8e+145:
		tmp = t_1
	elif z <= -185000000000.0:
		tmp = t_2
	elif z <= 2.8e+64:
		tmp = t_1
	else:
		tmp = -4.5 * (t * (z / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y * 0.5) / a))
	t_2 = Float64(t * Float64(z * Float64(-4.5 / a)))
	tmp = 0.0
	if (z <= -1.35e+173)
		tmp = t_2;
	elseif (z <= -9.8e+145)
		tmp = t_1;
	elseif (z <= -185000000000.0)
		tmp = t_2;
	elseif (z <= 2.8e+64)
		tmp = t_1;
	else
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y * 0.5) / a);
	t_2 = t * (z * (-4.5 / a));
	tmp = 0.0;
	if (z <= -1.35e+173)
		tmp = t_2;
	elseif (z <= -9.8e+145)
		tmp = t_1;
	elseif (z <= -185000000000.0)
		tmp = t_2;
	elseif (z <= 2.8e+64)
		tmp = t_1;
	else
		tmp = -4.5 * (t * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+173], t$95$2, If[LessEqual[z, -9.8e+145], t$95$1, If[LessEqual[z, -185000000000.0], t$95$2, If[LessEqual[z, 2.8e+64], t$95$1, N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3500000000000001e173 or -9.80000000000000006e145 < z < -1.85e11

   1. Initial program 90.6%

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

      1. div-inv 90.6%

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

      2. fmm-def 90.6%

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

      3. *-commutative 90.6%

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

      4. distribute-rgt-neg-in 90.6%

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

      5. distribute-rgt-neg-in 90.6%

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

      6. metadata-eval 90.6%

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

      7. *-commutative 90.6%

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

      8. associate-/r* 90.6%

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

      9. metadata-eval 90.6%

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

   4. Applied egg-rr 90.6%

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

   5. Taylor expanded in x around 0 69.9%

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

      1. *-commutative 69.9%

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

      2. metadata-eval 69.9%

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

      3. times-frac 69.9%

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

      4. associate-*r* 69.9%

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

      5. associate-/l* 74.6%

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

      6. times-frac 74.6%

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

      7. metadata-eval 74.6%

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

      8. associate-*l/ 74.6%

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

      9. associate-/l* 74.6%

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

   7. Simplified 74.6%

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

   if -1.3500000000000001e173 < z < -9.80000000000000006e145 or -1.85e11 < z < 2.80000000000000024e64

   1. Initial program 92.1%

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

   3. Taylor expanded in x around inf 65.5%

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

      1. *-commutative 65.5%

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

      2. associate-/l* 64.2%

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

      3. associate-*r* 64.2%

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

      4. *-commutative 64.2%

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

      5. associate-*r/ 64.2%

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

   5. Simplified 64.2%

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

   if 2.80000000000000024e64 < z

   1. Initial program 84.6%

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

   3. Taylor expanded in x around 0 54.0%

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

      1. associate-/l* 64.0%

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

   5. Simplified 64.0%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+173}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;z \leq -185000000000:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \mathbf{elif}\;z \leq -480000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (* z (/ -4.5 a)))))
   (if (<= z -1.35e+173)
     t_1
     (if (<= z -9.8e+145)
       (* y (/ x (* a 2.0)))
       (if (<= z -480000000000.0)
         t_1
         (if (<= z 2.8e+64) (* x (/ (* y 0.5) a)) (* -4.5 (* t (/ z a)))))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z * (-4.5 / a));
	double tmp;
	if (z <= -1.35e+173) {
		tmp = t_1;
	} else if (z <= -9.8e+145) {
		tmp = y * (x / (a * 2.0));
	} else if (z <= -480000000000.0) {
		tmp = t_1;
	} else if (z <= 2.8e+64) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (z * ((-4.5d0) / a))
    if (z <= (-1.35d+173)) then
        tmp = t_1
    else if (z <= (-9.8d+145)) then
        tmp = y * (x / (a * 2.0d0))
    else if (z <= (-480000000000.0d0)) then
        tmp = t_1
    else if (z <= 2.8d+64) then
        tmp = x * ((y * 0.5d0) / a)
    else
        tmp = (-4.5d0) * (t * (z / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (z * (-4.5 / a));
	double tmp;
	if (z <= -1.35e+173) {
		tmp = t_1;
	} else if (z <= -9.8e+145) {
		tmp = y * (x / (a * 2.0));
	} else if (z <= -480000000000.0) {
		tmp = t_1;
	} else if (z <= 2.8e+64) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = t * (z * (-4.5 / a))
	tmp = 0
	if z <= -1.35e+173:
		tmp = t_1
	elif z <= -9.8e+145:
		tmp = y * (x / (a * 2.0))
	elif z <= -480000000000.0:
		tmp = t_1
	elif z <= 2.8e+64:
		tmp = x * ((y * 0.5) / a)
	else:
		tmp = -4.5 * (t * (z / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(z * Float64(-4.5 / a)))
	tmp = 0.0
	if (z <= -1.35e+173)
		tmp = t_1;
	elseif (z <= -9.8e+145)
		tmp = Float64(y * Float64(x / Float64(a * 2.0)));
	elseif (z <= -480000000000.0)
		tmp = t_1;
	elseif (z <= 2.8e+64)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (z * (-4.5 / a));
	tmp = 0.0;
	if (z <= -1.35e+173)
		tmp = t_1;
	elseif (z <= -9.8e+145)
		tmp = y * (x / (a * 2.0));
	elseif (z <= -480000000000.0)
		tmp = t_1;
	elseif (z <= 2.8e+64)
		tmp = x * ((y * 0.5) / a);
	else
		tmp = -4.5 * (t * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+173], t$95$1, If[LessEqual[z, -9.8e+145], N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -480000000000.0], t$95$1, If[LessEqual[z, 2.8e+64], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3500000000000001e173 or -9.80000000000000006e145 < z < -4.8e11

   1. Initial program 90.6%

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

      1. div-inv 90.6%

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

      2. fmm-def 90.6%

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

      3. *-commutative 90.6%

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

      4. distribute-rgt-neg-in 90.6%

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

      5. distribute-rgt-neg-in 90.6%

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

      6. metadata-eval 90.6%

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

      7. *-commutative 90.6%

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

      8. associate-/r* 90.6%

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

      9. metadata-eval 90.6%

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

   4. Applied egg-rr 90.6%

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

   5. Taylor expanded in x around 0 69.9%

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

      1. *-commutative 69.9%

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

      2. metadata-eval 69.9%

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

      3. times-frac 69.9%

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

      4. associate-*r* 69.9%

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

      5. associate-/l* 74.6%

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

      6. times-frac 74.6%

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

      7. metadata-eval 74.6%

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

      8. associate-*l/ 74.6%

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

      9. associate-/l* 74.6%

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

   7. Simplified 74.6%

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

   if -1.3500000000000001e173 < z < -9.80000000000000006e145

   1. Initial program 86.5%

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

      1. div-inv 87.0%

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

      2. fmm-def 87.0%

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

      3. *-commutative 87.0%

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

      4. distribute-rgt-neg-in 87.0%

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

      5. distribute-rgt-neg-in 87.0%

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

      6. metadata-eval 87.0%

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

      7. *-commutative 87.0%

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

      8. associate-/r* 87.0%

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

      9. metadata-eval 87.0%

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

   4. Applied egg-rr 87.0%

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

   5. Taylor expanded in x around inf 58.7%

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

      1. clear-num 58.7%

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

      2. un-div-inv 58.7%

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

      3. *-commutative 58.7%

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

      4. div-inv 58.7%

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

      5. metadata-eval 58.7%

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

   7. Applied egg-rr 58.7%

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

      1. associate-/l* 58.7%

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

   9. Simplified 58.7%

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

   if -4.8e11 < z < 2.80000000000000024e64

   1. Initial program 92.3%

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

   3. Taylor expanded in x around inf 65.8%

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

      1. *-commutative 65.8%

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

      2. associate-/l* 64.4%

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

      3. associate-*r* 64.4%

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

      4. *-commutative 64.4%

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

      5. associate-*r/ 64.4%

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

   5. Simplified 64.4%

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

   if 2.80000000000000024e64 < z

   1. Initial program 84.6%

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

   3. Taylor expanded in x around 0 54.0%

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

      1. associate-/l* 64.0%

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

   5. Simplified 64.0%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+173}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \mathbf{elif}\;z \leq -480000000000:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 95.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+274}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* y (* x (/ 0.5 a)))
   (if (<= (* x y) 5e+274)
     (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0))
     (* y (/ x (* a 2.0))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = y * (x * (0.5 / a));
	} else if ((x * y) <= 5e+274) {
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	} else {
		tmp = y * (x / (a * 2.0));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x * (0.5 / a));
	} else if ((x * y) <= 5e+274) {
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	} else {
		tmp = y * (x / (a * 2.0));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = y * (x * (0.5 / a))
	elif (x * y) <= 5e+274:
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0)
	else:
		tmp = y * (x / (a * 2.0))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(y * Float64(x * Float64(0.5 / a)));
	elseif (Float64(x * y) <= 5e+274)
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0));
	else
		tmp = Float64(y * Float64(x / Float64(a * 2.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = y * (x * (0.5 / a));
	elseif ((x * y) <= 5e+274)
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	else
		tmp = y * (x / (a * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+274], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 65.3%

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

      1. div-inv 65.3%

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

      2. fmm-def 65.3%

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

      3. *-commutative 65.3%

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

      4. distribute-rgt-neg-in 65.3%

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

      5. distribute-rgt-neg-in 65.3%

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

      6. metadata-eval 65.3%

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

      7. *-commutative 65.3%

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

      8. associate-/r* 65.3%

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

      9. metadata-eval 65.3%

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

   4. Applied egg-rr 65.3%

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

   5. Taylor expanded in x around inf 65.3%

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

      1. associate-*r/ 65.3%

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

      2. *-commutative 65.3%

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

      3. associate-*l* 65.3%

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

   7. Applied egg-rr 65.3%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

      3. *-un-lft-identity 99.8%

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

      4. times-frac 99.8%

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

      5. metadata-eval 99.8%

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

      6. metadata-eval 99.8%

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

      7. times-frac 99.8%

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

      8. *-un-lft-identity 99.8%

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

      9. *-commutative 99.8%

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

      10. *-commutative 99.8%

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

      11. div-inv 99.9%

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

      12. metadata-eval 99.9%

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

      13. div-inv 99.9%

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

      14. clear-num 99.9%

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

   9. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 x y) < 4.9999999999999998e274

   1. Initial program 94.1%

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

   if 4.9999999999999998e274 < (*.f64 x y)

   1. Initial program 74.2%

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

      1. div-inv 74.2%

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

      2. fmm-def 74.2%

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

      3. *-commutative 74.2%

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

      4. distribute-rgt-neg-in 74.2%

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

      5. distribute-rgt-neg-in 74.2%

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

      6. metadata-eval 74.2%

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

      7. *-commutative 74.2%

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

      8. associate-/r* 74.2%

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

      9. metadata-eval 74.2%

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

   4. Applied egg-rr 74.2%

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

   5. Taylor expanded in x around inf 83.3%

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

      1. clear-num 83.3%

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

      2. un-div-inv 83.3%

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

      3. *-commutative 83.3%

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

      4. div-inv 83.3%

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

      5. metadata-eval 83.3%

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

   7. Applied egg-rr 83.3%

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

      1. associate-/l* 95.6%

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

   9. Simplified 95.6%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+274}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.5% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

3. Taylor expanded in x around 0 46.6%

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

   1. associate-/l* 46.9%

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

5. Simplified 46.9%

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

6. Final simplification 46.9%

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

Alternative 13: 50.5% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

   1. div-inv 90.5%

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

   2. fmm-def 90.5%

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

   3. *-commutative 90.5%

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

   4. distribute-rgt-neg-in 90.5%

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

   5. distribute-rgt-neg-in 90.5%

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

   6. metadata-eval 90.5%

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

   7. *-commutative 90.5%

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

   8. associate-/r* 90.5%

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

   9. metadata-eval 90.5%

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

4. Applied egg-rr 90.5%

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

5. Taylor expanded in x around 0 46.6%

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

   1. *-commutative 46.6%

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

   2. metadata-eval 46.6%

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

   3. times-frac 46.6%

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

   4. associate-*r* 46.6%

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

   5. associate-/l* 47.3%

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

   6. times-frac 47.3%

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

   7. metadata-eval 47.3%

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

   8. associate-*l/ 47.3%

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

   9. associate-/l* 47.3%

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

7. Simplified 47.3%

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

8. Final simplification 47.3%

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

Developer target: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (< a -2.090464557976709e+86)
   (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z))))
   (if (< a 2.144030707833976e+99)
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
     (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a < (-2.090464557976709d+86)) then
        tmp = (0.5d0 * ((y * x) / a)) - (4.5d0 * (t / (a / z)))
    else if (a < 2.144030707833976d+99) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = ((y / a) * (x * 0.5d0)) - ((t / a) * (z * 4.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a < -2.090464557976709e+86:
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)))
	elif a < 2.144030707833976e+99:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a < -2.090464557976709e+86)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / a)) - Float64(4.5 * Float64(t / Float64(a / z))));
	elseif (a < 2.144030707833976e+99)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(y / a) * Float64(x * 0.5)) - Float64(Float64(t / a) * Float64(z * 4.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a < -2.090464557976709e+86)
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	elseif (a < 2.144030707833976e+99)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Less[a, -2.090464557976709e+86], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[a, 2.144030707833976e+99], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024076 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

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

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