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

Percentage Accurate: 91.4% → 97.1%

Time: 13.2s

Alternatives: 13

Speedup: 0.5×

• 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: 91.4% 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: 97.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ t_2 := -4.5 \cdot \frac{z}{a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+251}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a \cdot 2}, y, t \cdot t\_2\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, t, x \cdot \frac{y}{a \cdot 2}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))) (t_2 (* -4.5 (/ z a))))
   (if (<= t_1 -4e+251)
     (fma (/ x (* a 2.0)) y (* t t_2))
     (if (<= t_1 5e+299)
       (/ (fma y x (* z (* t -9.0))) (* a 2.0))
       (fma t_2 t (* x (/ y (* a 2.0))))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double t_2 = -4.5 * (z / a);
	double tmp;
	if (t_1 <= -4e+251) {
		tmp = fma((x / (a * 2.0)), y, (t * t_2));
	} else if (t_1 <= 5e+299) {
		tmp = fma(y, x, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = fma(t_2, t, (x * (y / (a * 2.0))));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	t_2 = Float64(-4.5 * Float64(z / a))
	tmp = 0.0
	if (t_1 <= -4e+251)
		tmp = fma(Float64(x / Float64(a * 2.0)), y, Float64(t * t_2));
	elseif (t_1 <= 5e+299)
		tmp = Float64(fma(y, x, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = fma(t_2, t, Float64(x * Float64(y / Float64(a * 2.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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]}, Block[{t$95$2 = N[(-4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+251], N[(N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision] * y + N[(t * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+299], N[(N[(y * x + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(t$95$2 * t + N[(x * N[(y / N[(a * 2.0), $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)) < -4.0000000000000002e251

   1. Initial program 79.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. lower-*.f64 N/A

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

      14. metadata-eval 79.4

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

   4. Applied rewrites 79.4%

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

   6. Applied rewrites 97.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{a \cdot 2}, y, \left(-4.5 \cdot \frac{z}{a}\right) \cdot t\right)} \]

   if -4.0000000000000002e251 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 5.0000000000000003e299

   1. Initial program 97.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. lower-*.f64 N/A

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

      14. metadata-eval 97.6

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

   4. Applied rewrites 97.6%

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

   if 5.0000000000000003e299 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 75.7%

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

      1. lift--.f64 N/A

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

      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. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. lower-*.f64 N/A

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

      14. metadata-eval 75.9

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

   4. Applied rewrites 75.9%

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

   6. Applied rewrites 99.8%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -4 \cdot 10^{+251}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a \cdot 2}, y, t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5 \cdot \frac{z}{a}, t, x \cdot \frac{y}{a \cdot 2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4.5 \cdot \frac{z}{a}, t, x \cdot \frac{y}{a \cdot 2}\right)\\ t_2 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+264}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (fma (* -4.5 (/ z a)) t (* x (/ y (* a 2.0)))))
        (t_2 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_2 -1e+264)
     t_1
     (if (<= t_2 5e+299) (/ (fma y x (* z (* t -9.0))) (* a 2.0)) t_1))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((-4.5 * (z / a)), t, (x * (y / (a * 2.0))));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -1e+264) {
		tmp = t_1;
	} else if (t_2 <= 5e+299) {
		tmp = fma(y, x, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = fma(Float64(-4.5 * Float64(z / a)), t, Float64(x * Float64(y / Float64(a * 2.0))))
	t_2 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_2 <= -1e+264)
		tmp = t_1;
	elseif (t_2 <= 5e+299)
		tmp = Float64(fma(y, x, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(-4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision] * t + N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+264], t$95$1, If[LessEqual[t$95$2, 5e+299], N[(N[(y * x + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -1.00000000000000004e264 or 5.0000000000000003e299 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 76.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. lower-*.f64 N/A

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

      14. metadata-eval 77.0

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

   4. Applied rewrites 77.0%

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

   6. Applied rewrites 98.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5 \cdot \frac{z}{a}, t, x \cdot \frac{y}{a \cdot 2}\right)} \]

   if -1.00000000000000004e264 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 5.0000000000000003e299

   1. Initial program 97.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. lower-*.f64 N/A

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

      14. metadata-eval 97.7

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

   4. Applied rewrites 97.7%

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

Alternative 3: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+248}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 (- INFINITY))
     (* -4.5 (* t (/ z a)))
     (if (<= t_1 5e+248)
       (/ (fma y x (* z (* t -9.0))) (* a 2.0))
       (* t (* z (/ -4.5 a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = -4.5 * (t * (z / a));
	} else if (t_1 <= 5e+248) {
		tmp = fma(y, x, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = t * (z * (-4.5 / a));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (t_1 <= 5e+248)
		tmp = Float64(fma(y, x, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+248], N[(N[(y * x + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 70.1%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 4.9999999999999996e248

   1. Initial program 95.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. lower-*.f64 N/A

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

      14. metadata-eval 95.0

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

   4. Applied rewrites 95.0%

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

   if 4.9999999999999996e248 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 78.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 99.6

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

   5. Applied rewrites 99.6%

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

   7. Applied rewrites 99.9%

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

Alternative 4: 95.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+248}:\\ \;\;\;\;\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 (- INFINITY))
     (* -4.5 (* t (/ z a)))
     (if (<= t_1 5e+248)
       (* (fma z (* t -9.0) (* x y)) (/ 0.5 a))
       (* t (* z (/ -4.5 a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = -4.5 * (t * (z / a));
	} else if (t_1 <= 5e+248) {
		tmp = fma(z, (t * -9.0), (x * y)) * (0.5 / a);
	} else {
		tmp = t * (z * (-4.5 / a));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (t_1 <= 5e+248)
		tmp = Float64(fma(z, Float64(t * -9.0), Float64(x * y)) * Float64(0.5 / a));
	else
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+248], N[(N[(z * N[(t * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 70.1%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 4.9999999999999996e248

   1. Initial program 95.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

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

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. associate-/r* N/A

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

      19. lower-/.f64 N/A

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

      20. metadata-eval 94.9

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

   4. Applied rewrites 94.9%

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

   if 4.9999999999999996e248 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 78.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 99.6

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

   5. Applied rewrites 99.6%

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

   7. Applied rewrites 99.9%

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

Alternative 5: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -20000000000:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;\frac{-9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot y\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -20000000000.0)
   (* y (* 0.5 (/ x a)))
   (if (<= (* x y) 5e+19)
     (/ (* -9.0 (* z t)) (* a 2.0))
     (/ (* 0.5 (* x y)) a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -20000000000.0) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 5e+19) {
		tmp = (-9.0 * (z * t)) / (a * 2.0);
	} else {
		tmp = (0.5 * (x * y)) / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-20000000000.0d0)) then
        tmp = y * (0.5d0 * (x / a))
    else if ((x * y) <= 5d+19) then
        tmp = ((-9.0d0) * (z * t)) / (a * 2.0d0)
    else
        tmp = (0.5d0 * (x * y)) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -20000000000.0) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 5e+19) {
		tmp = (-9.0 * (z * t)) / (a * 2.0);
	} else {
		tmp = (0.5 * (x * y)) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -20000000000.0:
		tmp = y * (0.5 * (x / a))
	elif (x * y) <= 5e+19:
		tmp = (-9.0 * (z * t)) / (a * 2.0)
	else:
		tmp = (0.5 * (x * y)) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -20000000000.0)
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	elseif (Float64(x * y) <= 5e+19)
		tmp = Float64(Float64(-9.0 * Float64(z * t)) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(0.5 * Float64(x * y)) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -20000000000.0)
		tmp = y * (0.5 * (x / a));
	elseif ((x * y) <= 5e+19)
		tmp = (-9.0 * (z * t)) / (a * 2.0);
	else
		tmp = (0.5 * (x * y)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -20000000000.0], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+19], N[(N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e10

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 22.4

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

   5. Applied rewrites 22.4%

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

   7. Applied rewrites 22.5%

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

   9. Applied rewrites 22.6%

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

   10. Taylor expanded in x around inf

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

       1. associate-*r/ N/A

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

       2. associate-*r* N/A

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

       3. associate-*l/ N/A

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

       4. associate-*r/ N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. lower-*.f64 N/A

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

       8. lower-/.f64 78.5

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

   12. Applied rewrites 78.5%

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

   if -2e10 < (*.f64 x y) < 5e19

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 81.0

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

   5. Applied rewrites 81.0%

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

   if 5e19 < (*.f64 x y)

   1. Initial program 94.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

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

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. associate-/r* N/A

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

      19. lower-/.f64 N/A

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

      20. metadata-eval 94.3

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

   4. Applied rewrites 94.3%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot \frac{\frac{1}{2}}{a} \]
   6. Step-by-step derivation

      1. lower-*.f64 74.9

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

   7. Applied rewrites 74.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 75.0

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

   9. Applied rewrites 75.0%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -20000000000:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;\frac{-9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot y\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -20000000000:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;\frac{-4.5 \cdot \left(z \cdot t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot y\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -20000000000.0)
   (* y (* 0.5 (/ x a)))
   (if (<= (* x y) 5e+19) (/ (* -4.5 (* z t)) a) (/ (* 0.5 (* x y)) a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -20000000000.0) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 5e+19) {
		tmp = (-4.5 * (z * t)) / a;
	} else {
		tmp = (0.5 * (x * y)) / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-20000000000.0d0)) then
        tmp = y * (0.5d0 * (x / a))
    else if ((x * y) <= 5d+19) then
        tmp = ((-4.5d0) * (z * t)) / a
    else
        tmp = (0.5d0 * (x * y)) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -20000000000.0) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 5e+19) {
		tmp = (-4.5 * (z * t)) / a;
	} else {
		tmp = (0.5 * (x * y)) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -20000000000.0:
		tmp = y * (0.5 * (x / a))
	elif (x * y) <= 5e+19:
		tmp = (-4.5 * (z * t)) / a
	else:
		tmp = (0.5 * (x * y)) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -20000000000.0)
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	elseif (Float64(x * y) <= 5e+19)
		tmp = Float64(Float64(-4.5 * Float64(z * t)) / a);
	else
		tmp = Float64(Float64(0.5 * Float64(x * y)) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -20000000000.0)
		tmp = y * (0.5 * (x / a));
	elseif ((x * y) <= 5e+19)
		tmp = (-4.5 * (z * t)) / a;
	else
		tmp = (0.5 * (x * y)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -20000000000.0], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+19], N[(N[(-4.5 * N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e10

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 22.4

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

   5. Applied rewrites 22.4%

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

   7. Applied rewrites 22.5%

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

   9. Applied rewrites 22.6%

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

   10. Taylor expanded in x around inf

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

       1. associate-*r/ N/A

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

       2. associate-*r* N/A

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

       3. associate-*l/ N/A

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

       4. associate-*r/ N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. lower-*.f64 N/A

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

       8. lower-/.f64 78.5

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

   12. Applied rewrites 78.5%

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

   if -2e10 < (*.f64 x y) < 5e19

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 78.8

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

   5. Applied rewrites 78.8%

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

   7. Applied rewrites 81.0%

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

   if 5e19 < (*.f64 x y)

   1. Initial program 94.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

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

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. associate-/r* N/A

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

      19. lower-/.f64 N/A

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

      20. metadata-eval 94.3

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

   4. Applied rewrites 94.3%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot \frac{\frac{1}{2}}{a} \]
   6. Step-by-step derivation

      1. lower-*.f64 74.9

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

   7. Applied rewrites 74.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 75.0

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

   9. Applied rewrites 75.0%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -20000000000:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;\frac{-4.5 \cdot \left(z \cdot t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot y\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -20000000000:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;\frac{-4.5 \cdot \left(z \cdot t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -20000000000.0)
   (* y (* 0.5 (/ x a)))
   (if (<= (* x y) 5e+19) (/ (* -4.5 (* z t)) a) (/ (* x y) (* a 2.0)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -20000000000.0) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 5e+19) {
		tmp = (-4.5 * (z * t)) / a;
	} else {
		tmp = (x * y) / (a * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-20000000000.0d0)) then
        tmp = y * (0.5d0 * (x / a))
    else if ((x * y) <= 5d+19) then
        tmp = ((-4.5d0) * (z * t)) / a
    else
        tmp = (x * y) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -20000000000.0) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 5e+19) {
		tmp = (-4.5 * (z * t)) / a;
	} else {
		tmp = (x * y) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -20000000000.0:
		tmp = y * (0.5 * (x / a))
	elif (x * y) <= 5e+19:
		tmp = (-4.5 * (z * t)) / a
	else:
		tmp = (x * y) / (a * 2.0)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -20000000000.0)
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	elseif (Float64(x * y) <= 5e+19)
		tmp = Float64(Float64(-4.5 * Float64(z * t)) / a);
	else
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -20000000000.0)
		tmp = y * (0.5 * (x / a));
	elseif ((x * y) <= 5e+19)
		tmp = (-4.5 * (z * t)) / a;
	else
		tmp = (x * y) / (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.
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], -20000000000.0], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+19], N[(N[(-4.5 * N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e10

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 22.4

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

   5. Applied rewrites 22.4%

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

   7. Applied rewrites 22.5%

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

   9. Applied rewrites 22.6%

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

   10. Taylor expanded in x around inf

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

       1. associate-*r/ N/A

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

       2. associate-*r* N/A

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

       3. associate-*l/ N/A

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

       4. associate-*r/ N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. lower-*.f64 N/A

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

       8. lower-/.f64 78.5

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

   12. Applied rewrites 78.5%

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

   if -2e10 < (*.f64 x y) < 5e19

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 78.8

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

   5. Applied rewrites 78.8%

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

   7. Applied rewrites 81.0%

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

   if 5e19 < (*.f64 x y)

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 75.0

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

   5. Applied rewrites 75.0%

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

Alternative 8: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -20000000000:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;\frac{-4.5 \cdot \left(z \cdot t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -20000000000.0)
   (* y (* 0.5 (/ x a)))
   (if (<= (* x y) 5e+19) (/ (* -4.5 (* z t)) a) (* (/ 0.5 a) (* x y)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -20000000000.0) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 5e+19) {
		tmp = (-4.5 * (z * t)) / a;
	} else {
		tmp = (0.5 / a) * (x * y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-20000000000.0d0)) then
        tmp = y * (0.5d0 * (x / a))
    else if ((x * y) <= 5d+19) then
        tmp = ((-4.5d0) * (z * t)) / a
    else
        tmp = (0.5d0 / a) * (x * y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -20000000000.0) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 5e+19) {
		tmp = (-4.5 * (z * t)) / a;
	} else {
		tmp = (0.5 / a) * (x * y);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -20000000000.0:
		tmp = y * (0.5 * (x / a))
	elif (x * y) <= 5e+19:
		tmp = (-4.5 * (z * t)) / a
	else:
		tmp = (0.5 / a) * (x * y)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -20000000000.0)
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	elseif (Float64(x * y) <= 5e+19)
		tmp = Float64(Float64(-4.5 * Float64(z * t)) / a);
	else
		tmp = Float64(Float64(0.5 / a) * Float64(x * y));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -20000000000.0)
		tmp = y * (0.5 * (x / a));
	elseif ((x * y) <= 5e+19)
		tmp = (-4.5 * (z * t)) / a;
	else
		tmp = (0.5 / a) * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -20000000000.0], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+19], N[(N[(-4.5 * N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(0.5 / a), $MachinePrecision] * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e10

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 22.4

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

   5. Applied rewrites 22.4%

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

   7. Applied rewrites 22.5%

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

   9. Applied rewrites 22.6%

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

   10. Taylor expanded in x around inf

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

       1. associate-*r/ N/A

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

       2. associate-*r* N/A

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

       3. associate-*l/ N/A

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

       4. associate-*r/ N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. lower-*.f64 N/A

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

       8. lower-/.f64 78.5

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

   12. Applied rewrites 78.5%

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

   if -2e10 < (*.f64 x y) < 5e19

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 78.8

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

   5. Applied rewrites 78.8%

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

   7. Applied rewrites 81.0%

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

   if 5e19 < (*.f64 x y)

   1. Initial program 94.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

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

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

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

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

      14. lower-*.f64 N/A

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

      15. metadata-eval N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. associate-/r* N/A

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

      19. lower-/.f64 N/A

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

      20. metadata-eval 94.3

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

   4. Applied rewrites 94.3%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot \frac{\frac{1}{2}}{a} \]
   6. Step-by-step derivation

      1. lower-*.f64 74.9

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

   7. Applied rewrites 74.9%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -20000000000:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;\frac{-4.5 \cdot \left(z \cdot t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{if}\;x \cdot y \leq -20000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;\frac{-4.5 \cdot \left(z \cdot t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (* 0.5 (/ x a)))))
   (if (<= (* x y) -20000000000.0)
     t_1
     (if (<= (* x y) 5e+19) (/ (* -4.5 (* z t)) a) t_1))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (0.5 * (x / a));
	double tmp;
	if ((x * y) <= -20000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e+19) {
		tmp = (-4.5 * (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 * (0.5d0 * (x / a))
    if ((x * y) <= (-20000000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= 5d+19) then
        tmp = ((-4.5d0) * (z * t)) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 * (0.5 * (x / a));
	double tmp;
	if ((x * y) <= -20000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e+19) {
		tmp = (-4.5 * (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = y * (0.5 * (x / a))
	tmp = 0
	if (x * y) <= -20000000000.0:
		tmp = t_1
	elif (x * y) <= 5e+19:
		tmp = (-4.5 * (z * t)) / a
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(0.5 * Float64(x / a)))
	tmp = 0.0
	if (Float64(x * y) <= -20000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+19)
		tmp = Float64(Float64(-4.5 * Float64(z * t)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (0.5 * (x / a));
	tmp = 0.0;
	if ((x * y) <= -20000000000.0)
		tmp = t_1;
	elseif ((x * y) <= 5e+19)
		tmp = (-4.5 * (z * t)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -20000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+19], N[(N[(-4.5 * N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2e10 or 5e19 < (*.f64 x y)

   1. Initial program 90.1%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 23.7

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

   5. Applied rewrites 23.7%

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

   7. Applied rewrites 23.8%

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

   9. Applied rewrites 23.8%

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

   10. Taylor expanded in x around inf

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

       1. associate-*r/ N/A

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

       2. associate-*r* N/A

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

       3. associate-*l/ N/A

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

       4. associate-*r/ N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. lower-*.f64 N/A

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

       8. lower-/.f64 76.1

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

   12. Applied rewrites 76.1%

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

   if -2e10 < (*.f64 x y) < 5e19

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 78.8

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

   5. Applied rewrites 78.8%

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

   7. Applied rewrites 81.0%

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

Alternative 10: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{if}\;x \cdot y \leq -20000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (* 0.5 (/ x a)))))
   (if (<= (* x y) -20000000000.0)
     t_1
     (if (<= (* x y) 5e+19) (* -4.5 (/ (* z t) a)) t_1))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (0.5 * (x / a));
	double tmp;
	if ((x * y) <= -20000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e+19) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 * (0.5d0 * (x / a))
    if ((x * y) <= (-20000000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= 5d+19) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 * (0.5 * (x / a));
	double tmp;
	if ((x * y) <= -20000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e+19) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = y * (0.5 * (x / a))
	tmp = 0
	if (x * y) <= -20000000000.0:
		tmp = t_1
	elif (x * y) <= 5e+19:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(0.5 * Float64(x / a)))
	tmp = 0.0
	if (Float64(x * y) <= -20000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+19)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (0.5 * (x / a));
	tmp = 0.0;
	if ((x * y) <= -20000000000.0)
		tmp = t_1;
	elseif ((x * y) <= 5e+19)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -20000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+19], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2e10 or 5e19 < (*.f64 x y)

   1. Initial program 90.1%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 23.7

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

   5. Applied rewrites 23.7%

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

   7. Applied rewrites 23.8%

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

   9. Applied rewrites 23.8%

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

   10. Taylor expanded in x around inf

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

       1. associate-*r/ N/A

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

       2. associate-*r* N/A

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

       3. associate-*l/ N/A

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

       4. associate-*r/ N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. lower-*.f64 N/A

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

       8. lower-/.f64 76.1

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

   12. Applied rewrites 76.1%

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

   if -2e10 < (*.f64 x y) < 5e19

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 78.8

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

   5. Applied rewrites 78.8%

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

   7. Applied rewrites 81.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -20000000000:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{if}\;x \cdot y \leq -20000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (* 0.5 (/ x a)))))
   (if (<= (* x y) -20000000000.0)
     t_1
     (if (<= (* x y) 5e+19) (* t (* z (/ -4.5 a))) t_1))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (0.5 * (x / a));
	double tmp;
	if ((x * y) <= -20000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e+19) {
		tmp = t * (z * (-4.5 / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (0.5d0 * (x / a))
    if ((x * y) <= (-20000000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= 5d+19) then
        tmp = t * (z * ((-4.5d0) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (0.5 * (x / a));
	double tmp;
	if ((x * y) <= -20000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e+19) {
		tmp = t * (z * (-4.5 / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = y * (0.5 * (x / a))
	tmp = 0
	if (x * y) <= -20000000000.0:
		tmp = t_1
	elif (x * y) <= 5e+19:
		tmp = t * (z * (-4.5 / a))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(0.5 * Float64(x / a)))
	tmp = 0.0
	if (Float64(x * y) <= -20000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+19)
		tmp = Float64(t * Float64(z * Float64(-4.5 / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (0.5 * (x / a));
	tmp = 0.0;
	if ((x * y) <= -20000000000.0)
		tmp = t_1;
	elseif ((x * y) <= 5e+19)
		tmp = t * (z * (-4.5 / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -20000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+19], N[(t * N[(z * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2e10 or 5e19 < (*.f64 x y)

   1. Initial program 90.1%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 23.7

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

   5. Applied rewrites 23.7%

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

   7. Applied rewrites 23.8%

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

   9. Applied rewrites 23.8%

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

   10. Taylor expanded in x around inf

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

       1. associate-*r/ N/A

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

       2. associate-*r* N/A

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

       3. associate-*l/ N/A

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

       4. associate-*r/ N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. lower-*.f64 N/A

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

       8. lower-/.f64 76.1

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

   12. Applied rewrites 76.1%

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

   if -2e10 < (*.f64 x y) < 5e19

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 78.8

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

   5. Applied rewrites 78.8%

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

   7. Applied rewrites 78.8%

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

Alternative 12: 51.8% accurate, 1.6× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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);
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.
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;
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])
[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])
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])){:}
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.
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 92.0%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 N/A

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

   2. associate-/l* N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 53.8

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

5. Applied rewrites 53.8%

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

7. Applied rewrites 53.9%

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

Alternative 13: 51.7% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.0%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 N/A

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

   2. associate-/l* N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 53.8

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

5. Applied rewrites 53.8%

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

Developer Target 1: 93.3% 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 2024221 
(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)))