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

Percentage Accurate: 90.8% → 93.7%

Time: 9.5s

Alternatives: 13

Speedup: 0.8×

• 27.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.8% 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: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot x - t \cdot \left(9 \cdot z\right)\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+204}:\\ \;\;\;\;\frac{t\_1}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, \left(-4.5\right) \cdot t, \left(\frac{0.5}{a} \cdot x\right) \cdot y\right)\\ \end{array} \end{array} \]

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 (- (* y x) (* t (* 9.0 z)))))
   (if (<= t_1 5e+204)
     (/ t_1 (* 2.0 a))
     (fma (/ z a) (* (- 4.5) t) (* (* (/ 0.5 a) x) y)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * x) - (t * (9.0 * z));
	double tmp;
	if (t_1 <= 5e+204) {
		tmp = t_1 / (2.0 * a);
	} else {
		tmp = fma((z / a), (-4.5 * t), (((0.5 / a) * x) * y));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * x) - Float64(t * Float64(9.0 * z)))
	tmp = 0.0
	if (t_1 <= 5e+204)
		tmp = Float64(t_1 / Float64(2.0 * a));
	else
		tmp = fma(Float64(z / a), Float64(Float64(-4.5) * t), Float64(Float64(Float64(0.5 / a) * x) * y));
	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[(y * x), $MachinePrecision] - N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+204], N[(t$95$1 / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * N[((-4.5) * t), $MachinePrecision] + N[(N[(N[(0.5 / a), $MachinePrecision] * x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 5.00000000000000008e204

   1. Initial program 95.7%

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

   if 5.00000000000000008e204 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 73.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. times-frac N/A

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

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

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

      12. lower-fma.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-/l* N/A

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

      17. lower-*.f64 N/A

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

      18. metadata-eval N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. associate-/l* N/A

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

   4. Applied rewrites 98.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{a}, -t \cdot 4.5, \left(x \cdot \frac{0.5}{a}\right) \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x - t \cdot \left(9 \cdot z\right) \leq 5 \cdot 10^{+204}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(9 \cdot z\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, \left(-4.5\right) \cdot t, \left(\frac{0.5}{a} \cdot x\right) \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 54.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{y \cdot x - t \cdot \left(9 \cdot z\right)}{2 \cdot a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(\frac{-4.5}{a} \cdot z\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;\frac{-4.5}{a} \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{a} \cdot -4.5\right) \cdot z\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- (* y x) (* t (* 9.0 z))) (* 2.0 a))))
   (if (<= t_1 (- INFINITY))
     (* (* (/ -4.5 a) z) t)
     (if (<= t_1 2e+299) (* (/ -4.5 a) (* t z)) (* (* (/ t a) -4.5) z)))))

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) - (t * (9.0 * z))) / (2.0 * a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((-4.5 / a) * z) * t;
	} else if (t_1 <= 2e+299) {
		tmp = (-4.5 / a) * (t * z);
	} else {
		tmp = ((t / a) * -4.5) * z;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y * x) - (t * (9.0 * z))) / (2.0 * a);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((-4.5 / a) * z) * t;
	} else if (t_1 <= 2e+299) {
		tmp = (-4.5 / a) * (t * z);
	} else {
		tmp = ((t / a) * -4.5) * z;
	}
	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) - (t * (9.0 * z))) / (2.0 * a)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((-4.5 / a) * z) * t
	elif t_1 <= 2e+299:
		tmp = (-4.5 / a) * (t * z)
	else:
		tmp = ((t / a) * -4.5) * z
	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(Float64(y * x) - Float64(t * Float64(9.0 * z))) / Float64(2.0 * a))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(-4.5 / a) * z) * t);
	elseif (t_1 <= 2e+299)
		tmp = Float64(Float64(-4.5 / a) * Float64(t * z));
	else
		tmp = Float64(Float64(Float64(t / a) * -4.5) * z);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y * x) - (t * (9.0 * z))) / (2.0 * a);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((-4.5 / a) * z) * t;
	elseif (t_1 <= 2e+299)
		tmp = (-4.5 / a) * (t * z);
	else
		tmp = ((t / a) * -4.5) * z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y * x), $MachinePrecision] - N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(-4.5 / a), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2e+299], N[(N[(-4.5 / a), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / a), $MachinePrecision] * -4.5), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 77.6%

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

   3. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 53.5

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

   5. Applied rewrites 53.5%

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

   7. Applied rewrites 53.4%

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

   if -inf.0 < (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) (*.f64 a #s(literal 2 binary64))) < 2.0000000000000001e299

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 44.8

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

   5. Applied rewrites 44.8%

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

   7. Applied rewrites 51.1%

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

   if 2.0000000000000001e299 < (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) (*.f64 a #s(literal 2 binary64)))

   1. Initial program 80.6%

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

   3. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 58.3

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

   5. Applied rewrites 58.3%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot x - t \cdot \left(9 \cdot z\right)}{2 \cdot a} \leq -\infty:\\ \;\;\;\;\left(\frac{-4.5}{a} \cdot z\right) \cdot t\\ \mathbf{elif}\;\frac{y \cdot x - t \cdot \left(9 \cdot z\right)}{2 \cdot a} \leq 2 \cdot 10^{+299}:\\ \;\;\;\;\frac{-4.5}{a} \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{a} \cdot -4.5\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(\frac{-4.5}{a} \cdot z\right) \cdot t\\ t_2 := \frac{y \cdot x - t \cdot \left(9 \cdot z\right)}{2 \cdot a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+104}:\\ \;\;\;\;\frac{-4.5}{a} \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* (/ -4.5 a) z) t))
        (t_2 (/ (- (* y x) (* t (* 9.0 z))) (* 2.0 a))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 2e+104) (* (/ -4.5 a) (* t 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 = ((-4.5 / a) * z) * t;
	double t_2 = ((y * x) - (t * (9.0 * z))) / (2.0 * a);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 2e+104) {
		tmp = (-4.5 / a) * (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((-4.5 / a) * z) * t;
	double t_2 = ((y * x) - (t * (9.0 * z))) / (2.0 * a);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 2e+104) {
		tmp = (-4.5 / a) * (t * 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 = ((-4.5 / a) * z) * t
	t_2 = ((y * x) - (t * (9.0 * z))) / (2.0 * a)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 2e+104:
		tmp = (-4.5 / a) * (t * 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(Float64(Float64(-4.5 / a) * z) * t)
	t_2 = Float64(Float64(Float64(y * x) - Float64(t * Float64(9.0 * z))) / Float64(2.0 * a))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 2e+104)
		tmp = Float64(Float64(-4.5 / a) * Float64(t * 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 = ((-4.5 / a) * z) * t;
	t_2 = ((y * x) - (t * (9.0 * z))) / (2.0 * a);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 2e+104)
		tmp = (-4.5 / a) * (t * 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[(N[(N[(-4.5 / a), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * x), $MachinePrecision] - N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 2e+104], N[(N[(-4.5 / a), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) (*.f64 a #s(literal 2 binary64))) < -inf.0 or 2e104 < (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) (*.f64 a #s(literal 2 binary64)))

   1. Initial program 83.9%

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

   3. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 48.0

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

   5. Applied rewrites 48.0%

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

   7. Applied rewrites 48.6%

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

   if -inf.0 < (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) (*.f64 a #s(literal 2 binary64))) < 2e104

   1. Initial program 97.1%

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

   3. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 50.2

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

   5. Applied rewrites 50.2%

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

   7. Applied rewrites 57.1%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot x - t \cdot \left(9 \cdot z\right)}{2 \cdot a} \leq -\infty:\\ \;\;\;\;\left(\frac{-4.5}{a} \cdot z\right) \cdot t\\ \mathbf{elif}\;\frac{y \cdot x - t \cdot \left(9 \cdot z\right)}{2 \cdot a} \leq 2 \cdot 10^{+104}:\\ \;\;\;\;\frac{-4.5}{a} \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{-4.5}{a} \cdot z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot x - t \cdot \left(9 \cdot z\right)\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+204}:\\ \;\;\;\;\frac{t\_1}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{0.5}{a} \cdot x, y, \left(4.5 \cdot \frac{z}{a}\right) \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

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 (- (* y x) (* t (* 9.0 z)))))
   (if (<= t_1 5e+204)
     (/ t_1 (* 2.0 a))
     (fma (* (/ 0.5 a) x) y (* (* 4.5 (/ z a)) (- t))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * x) - (t * (9.0 * z));
	double tmp;
	if (t_1 <= 5e+204) {
		tmp = t_1 / (2.0 * a);
	} else {
		tmp = fma(((0.5 / a) * x), y, ((4.5 * (z / a)) * -t));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * x) - Float64(t * Float64(9.0 * z)))
	tmp = 0.0
	if (t_1 <= 5e+204)
		tmp = Float64(t_1 / Float64(2.0 * a));
	else
		tmp = fma(Float64(Float64(0.5 / a) * x), y, Float64(Float64(4.5 * Float64(z / a)) * Float64(-t)));
	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[(y * x), $MachinePrecision] - N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+204], N[(t$95$1 / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(0.5 / a), $MachinePrecision] * x), $MachinePrecision] * y + N[(N[(4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision] * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 5.00000000000000008e204

   1. Initial program 95.7%

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

   if 5.00000000000000008e204 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 73.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. div-inv N/A

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

      11. lower-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

      15. lower-/.f64 N/A

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

      16. metadata-eval N/A

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

      17. lift-*.f64 N/A

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

      18. *-commutative N/A

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

      19. associate-/l* N/A

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

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

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

      21. lower-*.f64 N/A

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

      22. lower-neg.f64 N/A

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

   4. Applied rewrites 96.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \frac{0.5}{a}, y, \left(-t\right) \cdot \left(4.5 \cdot \frac{z}{a}\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x - t \cdot \left(9 \cdot z\right) \leq 5 \cdot 10^{+204}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(9 \cdot z\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{0.5}{a} \cdot x, y, \left(4.5 \cdot \frac{z}{a}\right) \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(9 \cdot z\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\left(\frac{-4.5}{a} \cdot z\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\frac{y \cdot x}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5 \cdot \left(t \cdot z\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (* 9.0 z))))
   (if (<= t_1 -2e+91)
     (* (* (/ -4.5 a) z) t)
     (if (<= t_1 2e+29) (/ (* y x) (* 2.0 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 * (9.0 * z);
	double tmp;
	if (t_1 <= -2e+91) {
		tmp = ((-4.5 / a) * z) * t;
	} else if (t_1 <= 2e+29) {
		tmp = (y * x) / (2.0 * 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 * (9.0d0 * z)
    if (t_1 <= (-2d+91)) then
        tmp = (((-4.5d0) / a) * z) * t
    else if (t_1 <= 2d+29) then
        tmp = (y * x) / (2.0d0 * 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 * (9.0 * z);
	double tmp;
	if (t_1 <= -2e+91) {
		tmp = ((-4.5 / a) * z) * t;
	} else if (t_1 <= 2e+29) {
		tmp = (y * x) / (2.0 * 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 * (9.0 * z)
	tmp = 0
	if t_1 <= -2e+91:
		tmp = ((-4.5 / a) * z) * t
	elif t_1 <= 2e+29:
		tmp = (y * x) / (2.0 * 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(9.0 * z))
	tmp = 0.0
	if (t_1 <= -2e+91)
		tmp = Float64(Float64(Float64(-4.5 / a) * z) * t);
	elseif (t_1 <= 2e+29)
		tmp = Float64(Float64(y * x) / Float64(2.0 * a));
	else
		tmp = Float64(Float64(-4.5 * Float64(t * 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 * (9.0 * z);
	tmp = 0.0;
	if (t_1 <= -2e+91)
		tmp = ((-4.5 / a) * z) * t;
	elseif (t_1 <= 2e+29)
		tmp = (y * x) / (2.0 * 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[(9.0 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+91], N[(N[(N[(-4.5 / a), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2e+29], N[(N[(y * x), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(-4.5 * N[(t * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -2.00000000000000016e91

   1. Initial program 81.7%

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

   3. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 79.2

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

   5. Applied rewrites 79.2%

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

   7. Applied rewrites 82.7%

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

   if -2.00000000000000016e91 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.99999999999999983e29

   1. Initial program 95.1%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 75.8

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

   5. Applied rewrites 75.8%

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

   if 1.99999999999999983e29 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 87.1%

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

   3. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 79.1

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

   5. Applied rewrites 79.1%

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

   7. Applied rewrites 79.1%

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

   9. Applied rewrites 80.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(9 \cdot z\right) \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\left(\frac{-4.5}{a} \cdot z\right) \cdot t\\ \mathbf{elif}\;t \cdot \left(9 \cdot z\right) \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\frac{y \cdot x}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5 \cdot \left(t \cdot z\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(9 \cdot z\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\left(\frac{-4.5}{a} \cdot z\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5 \cdot \left(t \cdot z\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (* 9.0 z))))
   (if (<= t_1 -2e+91)
     (* (* (/ -4.5 a) z) t)
     (if (<= t_1 2e+29) (* (* y x) (/ 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 * (9.0 * z);
	double tmp;
	if (t_1 <= -2e+91) {
		tmp = ((-4.5 / a) * z) * t;
	} else if (t_1 <= 2e+29) {
		tmp = (y * x) * (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 * (9.0d0 * z)
    if (t_1 <= (-2d+91)) then
        tmp = (((-4.5d0) / a) * z) * t
    else if (t_1 <= 2d+29) then
        tmp = (y * x) * (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 * (9.0 * z);
	double tmp;
	if (t_1 <= -2e+91) {
		tmp = ((-4.5 / a) * z) * t;
	} else if (t_1 <= 2e+29) {
		tmp = (y * x) * (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 * (9.0 * z)
	tmp = 0
	if t_1 <= -2e+91:
		tmp = ((-4.5 / a) * z) * t
	elif t_1 <= 2e+29:
		tmp = (y * x) * (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(9.0 * z))
	tmp = 0.0
	if (t_1 <= -2e+91)
		tmp = Float64(Float64(Float64(-4.5 / a) * z) * t);
	elseif (t_1 <= 2e+29)
		tmp = Float64(Float64(y * x) * Float64(0.5 / a));
	else
		tmp = Float64(Float64(-4.5 * Float64(t * 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 * (9.0 * z);
	tmp = 0.0;
	if (t_1 <= -2e+91)
		tmp = ((-4.5 / a) * z) * t;
	elseif (t_1 <= 2e+29)
		tmp = (y * x) * (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[(9.0 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+91], N[(N[(N[(-4.5 / a), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2e+29], N[(N[(y * x), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(-4.5 * N[(t * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -2.00000000000000016e91

   1. Initial program 81.7%

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

   3. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 79.2

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

   5. Applied rewrites 79.2%

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

   7. Applied rewrites 82.7%

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

   if -2.00000000000000016e91 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.99999999999999983e29

   1. Initial program 95.1%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 75.8

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

   5. Applied rewrites 75.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. lift-/.f64 N/A

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

      9. lower-*.f64 75.7

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

   7. Applied rewrites 75.7%

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

   if 1.99999999999999983e29 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 87.1%

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

   3. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 79.1

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

   5. Applied rewrites 79.1%

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

   7. Applied rewrites 79.1%

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

   9. Applied rewrites 80.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(9 \cdot z\right) \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\left(\frac{-4.5}{a} \cdot z\right) \cdot t\\ \mathbf{elif}\;t \cdot \left(9 \cdot z\right) \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5 \cdot \left(t \cdot z\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(9 \cdot z\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\left(\frac{-4.5}{a} \cdot z\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\left(\frac{y}{a} \cdot 0.5\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5 \cdot \left(t \cdot z\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (* 9.0 z))))
   (if (<= t_1 -2e+91)
     (* (* (/ -4.5 a) z) t)
     (if (<= t_1 2e+29) (* (* (/ y a) 0.5) x) (/ (* -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 * (9.0 * z);
	double tmp;
	if (t_1 <= -2e+91) {
		tmp = ((-4.5 / a) * z) * t;
	} else if (t_1 <= 2e+29) {
		tmp = ((y / a) * 0.5) * x;
	} 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 * (9.0d0 * z)
    if (t_1 <= (-2d+91)) then
        tmp = (((-4.5d0) / a) * z) * t
    else if (t_1 <= 2d+29) then
        tmp = ((y / a) * 0.5d0) * x
    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 * (9.0 * z);
	double tmp;
	if (t_1 <= -2e+91) {
		tmp = ((-4.5 / a) * z) * t;
	} else if (t_1 <= 2e+29) {
		tmp = ((y / a) * 0.5) * x;
	} 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 * (9.0 * z)
	tmp = 0
	if t_1 <= -2e+91:
		tmp = ((-4.5 / a) * z) * t
	elif t_1 <= 2e+29:
		tmp = ((y / a) * 0.5) * x
	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(9.0 * z))
	tmp = 0.0
	if (t_1 <= -2e+91)
		tmp = Float64(Float64(Float64(-4.5 / a) * z) * t);
	elseif (t_1 <= 2e+29)
		tmp = Float64(Float64(Float64(y / a) * 0.5) * x);
	else
		tmp = Float64(Float64(-4.5 * Float64(t * 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 * (9.0 * z);
	tmp = 0.0;
	if (t_1 <= -2e+91)
		tmp = ((-4.5 / a) * z) * t;
	elseif (t_1 <= 2e+29)
		tmp = ((y / a) * 0.5) * x;
	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[(9.0 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+91], N[(N[(N[(-4.5 / a), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2e+29], N[(N[(N[(y / a), $MachinePrecision] * 0.5), $MachinePrecision] * x), $MachinePrecision], N[(N[(-4.5 * N[(t * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -2.00000000000000016e91

   1. Initial program 81.7%

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

   3. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 79.2

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

   5. Applied rewrites 79.2%

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

   7. Applied rewrites 82.7%

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

   if -2.00000000000000016e91 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.99999999999999983e29

   1. Initial program 95.1%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 75.3

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

   5. Applied rewrites 75.3%

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

   if 1.99999999999999983e29 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 87.1%

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

   3. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 79.1

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

   5. Applied rewrites 79.1%

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

   7. Applied rewrites 79.1%

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

   9. Applied rewrites 80.6%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(9 \cdot z\right) \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\left(\frac{-4.5}{a} \cdot z\right) \cdot t\\ \mathbf{elif}\;t \cdot \left(9 \cdot z\right) \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\left(\frac{y}{a} \cdot 0.5\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5 \cdot \left(t \cdot z\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(9 \cdot z\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\left(\frac{-4.5}{a} \cdot z\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\left(\frac{y}{a} \cdot 0.5\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5}{a} \cdot \left(t \cdot z\right)\\ \end{array} \end{array} \]

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 (* 9.0 z))))
   (if (<= t_1 -2e+91)
     (* (* (/ -4.5 a) z) t)
     (if (<= t_1 2e+29) (* (* (/ y a) 0.5) x) (* (/ -4.5 a) (* t z))))))

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 * (9.0 * z);
	double tmp;
	if (t_1 <= -2e+91) {
		tmp = ((-4.5 / a) * z) * t;
	} else if (t_1 <= 2e+29) {
		tmp = ((y / a) * 0.5) * x;
	} else {
		tmp = (-4.5 / a) * (t * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (9.0d0 * z)
    if (t_1 <= (-2d+91)) then
        tmp = (((-4.5d0) / a) * z) * t
    else if (t_1 <= 2d+29) then
        tmp = ((y / a) * 0.5d0) * x
    else
        tmp = ((-4.5d0) / a) * (t * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (9.0 * z);
	double tmp;
	if (t_1 <= -2e+91) {
		tmp = ((-4.5 / a) * z) * t;
	} else if (t_1 <= 2e+29) {
		tmp = ((y / a) * 0.5) * x;
	} else {
		tmp = (-4.5 / a) * (t * z);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = t * (9.0 * z)
	tmp = 0
	if t_1 <= -2e+91:
		tmp = ((-4.5 / a) * z) * t
	elif t_1 <= 2e+29:
		tmp = ((y / a) * 0.5) * x
	else:
		tmp = (-4.5 / a) * (t * z)
	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(9.0 * z))
	tmp = 0.0
	if (t_1 <= -2e+91)
		tmp = Float64(Float64(Float64(-4.5 / a) * z) * t);
	elseif (t_1 <= 2e+29)
		tmp = Float64(Float64(Float64(y / a) * 0.5) * x);
	else
		tmp = Float64(Float64(-4.5 / a) * Float64(t * z));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (9.0 * z);
	tmp = 0.0;
	if (t_1 <= -2e+91)
		tmp = ((-4.5 / a) * z) * t;
	elseif (t_1 <= 2e+29)
		tmp = ((y / a) * 0.5) * x;
	else
		tmp = (-4.5 / a) * (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+91], N[(N[(N[(-4.5 / a), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2e+29], N[(N[(N[(y / a), $MachinePrecision] * 0.5), $MachinePrecision] * x), $MachinePrecision], N[(N[(-4.5 / a), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -2.00000000000000016e91

   1. Initial program 81.7%

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

   3. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 79.2

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

   5. Applied rewrites 79.2%

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

   7. Applied rewrites 82.7%

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

   if -2.00000000000000016e91 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.99999999999999983e29

   1. Initial program 95.1%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 75.3

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

   5. Applied rewrites 75.3%

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

   if 1.99999999999999983e29 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 87.1%

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

   3. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 79.1

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

   5. Applied rewrites 79.1%

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

   7. Applied rewrites 80.5%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(9 \cdot z\right) \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\left(\frac{-4.5}{a} \cdot z\right) \cdot t\\ \mathbf{elif}\;t \cdot \left(9 \cdot z\right) \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\left(\frac{y}{a} \cdot 0.5\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5}{a} \cdot \left(t \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 91.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq 5 \cdot 10^{+152}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(9 \cdot z\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{a} \cdot 0.5\right) \cdot x\\ \end{array} \end{array} \]

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 (<= (* y x) 5e+152)
   (/ (- (* y x) (* t (* 9.0 z))) (* 2.0 a))
   (* (* (/ y a) 0.5) x)))

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 ((y * x) <= 5e+152) {
		tmp = ((y * x) - (t * (9.0 * z))) / (2.0 * a);
	} else {
		tmp = ((y / a) * 0.5) * x;
	}
	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 ((y * x) <= 5d+152) then
        tmp = ((y * x) - (t * (9.0d0 * z))) / (2.0d0 * a)
    else
        tmp = ((y / a) * 0.5d0) * x
    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 ((y * x) <= 5e+152) {
		tmp = ((y * x) - (t * (9.0 * z))) / (2.0 * a);
	} else {
		tmp = ((y / a) * 0.5) * x;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (y * x) <= 5e+152:
		tmp = ((y * x) - (t * (9.0 * z))) / (2.0 * a)
	else:
		tmp = ((y / a) * 0.5) * x
	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(y * x) <= 5e+152)
		tmp = Float64(Float64(Float64(y * x) - Float64(t * Float64(9.0 * z))) / Float64(2.0 * a));
	else
		tmp = Float64(Float64(Float64(y / a) * 0.5) * x);
	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 ((y * x) <= 5e+152)
		tmp = ((y * x) - (t * (9.0 * z))) / (2.0 * a);
	else
		tmp = ((y / a) * 0.5) * x;
	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[(y * x), $MachinePrecision], 5e+152], N[(N[(N[(y * x), $MachinePrecision] - N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * 0.5), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 5e152

   1. Initial program 93.1%

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

   if 5e152 < (*.f64 x y)

   1. Initial program 76.1%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 99.6

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

   5. Applied rewrites 99.6%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq 5 \cdot 10^{+152}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(9 \cdot z\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{a} \cdot 0.5\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 92.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq 5 \cdot 10^{+152}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-9 \cdot z, t, y \cdot x\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{a} \cdot 0.5\right) \cdot x\\ \end{array} \end{array} \]

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 (<= (* y x) 5e+152)
   (/ (fma (* -9.0 z) t (* y x)) (* 2.0 a))
   (* (* (/ y a) 0.5) x)))

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 ((y * x) <= 5e+152) {
		tmp = fma((-9.0 * z), t, (y * x)) / (2.0 * a);
	} else {
		tmp = ((y / a) * 0.5) * x;
	}
	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(y * x) <= 5e+152)
		tmp = Float64(fma(Float64(-9.0 * z), t, Float64(y * x)) / Float64(2.0 * a));
	else
		tmp = Float64(Float64(Float64(y / a) * 0.5) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], 5e+152], N[(N[(N[(-9.0 * z), $MachinePrecision] * t + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * 0.5), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 5e152

   1. Initial program 93.1%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 93.1

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 93.1

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

   4. Applied rewrites 93.1%

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

   if 5e152 < (*.f64 x y)

   1. Initial program 76.1%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 99.6

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

   5. Applied rewrites 99.6%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq 5 \cdot 10^{+152}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-9 \cdot z, t, y \cdot x\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{a} \cdot 0.5\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 91.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq 5 \cdot 10^{+152}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-9 \cdot t, z, y \cdot x\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{a} \cdot 0.5\right) \cdot x\\ \end{array} \end{array} \]

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 (<= (* y x) 5e+152)
   (/ (fma (* -9.0 t) z (* y x)) (* 2.0 a))
   (* (* (/ y a) 0.5) x)))

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 ((y * x) <= 5e+152) {
		tmp = fma((-9.0 * t), z, (y * x)) / (2.0 * a);
	} else {
		tmp = ((y / a) * 0.5) * x;
	}
	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(y * x) <= 5e+152)
		tmp = Float64(fma(Float64(-9.0 * t), z, Float64(y * x)) / Float64(2.0 * a));
	else
		tmp = Float64(Float64(Float64(y / a) * 0.5) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], 5e+152], N[(N[(N[(-9.0 * t), $MachinePrecision] * z + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * 0.5), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 5e152

   1. Initial program 93.1%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. metadata-eval 93.1

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 93.1

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

   4. Applied rewrites 93.1%

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

   if 5e152 < (*.f64 x y)

   1. Initial program 76.1%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 99.6

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

   5. Applied rewrites 99.6%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq 5 \cdot 10^{+152}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-9 \cdot t, z, y \cdot x\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{a} \cdot 0.5\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 91.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq 5 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, -9, y \cdot x\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{a} \cdot 0.5\right) \cdot x\\ \end{array} \end{array} \]

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 (<= (* y x) 5e+152)
   (* (fma (* t z) -9.0 (* y x)) (/ 0.5 a))
   (* (* (/ y a) 0.5) x)))

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 ((y * x) <= 5e+152) {
		tmp = fma((t * z), -9.0, (y * x)) * (0.5 / a);
	} else {
		tmp = ((y / a) * 0.5) * x;
	}
	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(y * x) <= 5e+152)
		tmp = Float64(fma(Float64(t * z), -9.0, Float64(y * x)) * Float64(0.5 / a));
	else
		tmp = Float64(Float64(Float64(y / a) * 0.5) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], 5e+152], N[(N[(N[(t * z), $MachinePrecision] * -9.0 + N[(y * x), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * 0.5), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 5e152

   1. Initial program 93.1%

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

      1. lift-/.f64 N/A

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

      2. div-inv N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*r* N/A

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

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

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. associate-/r* N/A

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

      21. lower-/.f64 N/A

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

      22. metadata-eval 92.9

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

   4. Applied rewrites 92.9%

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

   if 5e152 < (*.f64 x y)

   1. Initial program 76.1%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 99.6

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

   5. Applied rewrites 99.6%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq 5 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, -9, y \cdot x\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{a} \cdot 0.5\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.6% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.7%

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

3. Taylor expanded in t around inf

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

   1. associate-*l/ N/A

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

   2. associate-*l* N/A

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

   3. lower-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 49.1

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

5. Applied rewrites 49.1%

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

7. Applied rewrites 49.6%

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

8. Final simplification 49.6%

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

Developer Target 1: 93.4% accurate, 0.6× 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 2024248 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< a -209046455797670900000000000000000000000000000000000000000000000000000000000000000000000) (- (* 1/2 (/ (* y x) a)) (* 9/2 (/ t (/ a z)))) (if (< a 2144030707833976000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z (* 9 t))) (* a 2)) (- (* (/ y a) (* x 1/2)) (* (/ t a) (* z 9/2))))))

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