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

Percentage Accurate: 91.5% → 96.3%

Time: 13.2s

Alternatives: 10

Speedup: 0.6×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+251}:\\ \;\;\;\;\frac{x \cdot \frac{y}{a}}{2} - \frac{t \cdot 4.5}{\frac{a}{z}}\\ \mathbf{elif}\;t\_1 \leq 10^{+216}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a \cdot 2}, x, \frac{t \cdot 4.5}{a} \cdot \left(0 - z\right)\right)\\ \end{array} \end{array} \]

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))))
   (if (<= t_1 -1e+251)
     (- (/ (* x (/ y a)) 2.0) (/ (* t 4.5) (/ a z)))
     (if (<= t_1 1e+216)
       (/ t_1 (* a 2.0))
       (fma (/ y (* a 2.0)) x (* (/ (* t 4.5) a) (- 0.0 z)))))))

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 tmp;
	if (t_1 <= -1e+251) {
		tmp = ((x * (y / a)) / 2.0) - ((t * 4.5) / (a / z));
	} else if (t_1 <= 1e+216) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = fma((y / (a * 2.0)), x, (((t * 4.5) / a) * (0.0 - z)));
	}
	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))
	tmp = 0.0
	if (t_1 <= -1e+251)
		tmp = Float64(Float64(Float64(x * Float64(y / a)) / 2.0) - Float64(Float64(t * 4.5) / Float64(a / z)));
	elseif (t_1 <= 1e+216)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = fma(Float64(y / Float64(a * 2.0)), x, Float64(Float64(Float64(t * 4.5) / a) * Float64(0.0 - z)));
	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]}, If[LessEqual[t$95$1, -1e+251], N[(N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision] - N[(N[(t * 4.5), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+216], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision] * x + N[(N[(N[(t * 4.5), $MachinePrecision] / a), $MachinePrecision] * N[(0.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -1e251

   1. Initial program 74.4%

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

      1. div-sub N/A

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

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{a \cdot 2}\right), \color{blue}{\left(\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), \left(a \cdot 2\right)\right), \left(\frac{\color{blue}{\left(z \cdot 9\right) \cdot t}}{a \cdot 2}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(a \cdot 2\right)\right), \left(\frac{\color{blue}{\left(z \cdot 9\right)} \cdot t}{a \cdot 2}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \left(\frac{\left(z \cdot 9\right) \cdot \color{blue}{t}}{a \cdot 2}\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \left(\frac{z \cdot \left(9 \cdot t\right)}{\color{blue}{a} \cdot 2}\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \left(z \cdot \color{blue}{\frac{9 \cdot t}{a \cdot 2}}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{9 \cdot t}{a \cdot 2}\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \left(\frac{9 \cdot t}{2 \cdot \color{blue}{a}}\right)\right)\right) \]

      10. associate-/r* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \left(\frac{\frac{9 \cdot t}{2}}{\color{blue}{a}}\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(\frac{9 \cdot t}{2}\right), \color{blue}{a}\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(\frac{t \cdot 9}{2}\right), a\right)\right)\right) \]

      13. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(t \cdot \frac{9}{2}\right), a\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{9}{2}\right)\right), a\right)\right)\right) \]

      15. metadata-eval 78.4%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

   4. Applied egg-rr 78.4%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - z \cdot \frac{t \cdot 4.5}{a}} \]
   5. Step-by-step derivation

      1. times-frac N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x}{a} \cdot \frac{y}{2}\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{\frac{x}{a} \cdot y}{2}\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\frac{x}{a} \cdot y\right), 2\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\frac{x}{a}\right), y\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      5. /-lowering-/.f64 95.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, a\right), y\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

   6. Applied egg-rr 95.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{a} \cdot y}{2}} - z \cdot \frac{t \cdot 4.5}{a} \]
   7. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot y}{a}\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \frac{y}{a}\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{y}{a}\right)\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      4. /-lowering-/.f64 94.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

   8. Applied egg-rr 94.9%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{y}{a}}}{2} - z \cdot \frac{t \cdot 4.5}{a} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \left(\frac{t \cdot \frac{9}{2}}{a} \cdot \color{blue}{z}\right)\right) \]

      2. div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \left(\left(\left(t \cdot \frac{9}{2}\right) \cdot \frac{1}{a}\right) \cdot z\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \left(\left(t \cdot \frac{9}{2}\right) \cdot \color{blue}{\left(\frac{1}{a} \cdot z\right)}\right)\right) \]

      4. associate-/r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \left(\left(t \cdot \frac{9}{2}\right) \cdot \frac{1}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      5. div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \left(\frac{t \cdot \frac{9}{2}}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \mathsf{/.f64}\left(\left(t \cdot \frac{9}{2}\right), \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), \left(\frac{\color{blue}{a}}{z}\right)\right)\right) \]

      8. /-lowering-/.f64 97.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   10. Applied egg-rr 97.3%

       \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \color{blue}{\frac{t \cdot 4.5}{\frac{a}{z}}} \]

   if -1e251 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 1e216

   1. Initial program 98.6%

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

   if 1e216 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 73.5%

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\frac{y}{a \cdot 2}\right), \color{blue}{x}, \left(\mathsf{neg}\left(\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \left(a \cdot 2\right)\right), x, \left(\mathsf{neg}\left(\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \mathsf{*.f64}\left(a, 2\right)\right), x, \left(\mathsf{neg}\left(\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right)\right)\right) \]

      8. neg-sub0 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \mathsf{*.f64}\left(a, 2\right)\right), x, \left(0 - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \mathsf{*.f64}\left(a, 2\right)\right), x, \mathsf{\_.f64}\left(0, \left(\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \mathsf{*.f64}\left(a, 2\right)\right), x, \mathsf{\_.f64}\left(0, \left(\frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}\right)\right)\right) \]

      11. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \mathsf{*.f64}\left(a, 2\right)\right), x, \mathsf{\_.f64}\left(0, \left(z \cdot \frac{9 \cdot t}{a \cdot 2}\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \mathsf{*.f64}\left(a, 2\right)\right), x, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(\frac{9 \cdot t}{a \cdot 2}\right)\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \mathsf{*.f64}\left(a, 2\right)\right), x, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(\frac{9 \cdot t}{2 \cdot a}\right)\right)\right)\right) \]

      14. associate-/r* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \mathsf{*.f64}\left(a, 2\right)\right), x, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left(\frac{\frac{9 \cdot t}{2}}{a}\right)\right)\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \mathsf{*.f64}\left(a, 2\right)\right), x, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(\frac{9 \cdot t}{2}\right), a\right)\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \mathsf{*.f64}\left(a, 2\right)\right), x, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(\frac{t \cdot 9}{2}\right), a\right)\right)\right)\right) \]

      17. associate-/l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \mathsf{*.f64}\left(a, 2\right)\right), x, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(t \cdot \frac{9}{2}\right), a\right)\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \mathsf{*.f64}\left(a, 2\right)\right), x, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{9}{2}\right)\right), a\right)\right)\right)\right) \]

      19. metadata-eval 93.4%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \mathsf{*.f64}\left(a, 2\right)\right), x, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right)\right) \]

   4. Applied egg-rr 93.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a \cdot 2}, x, 0 - z \cdot \frac{t \cdot 4.5}{a}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -1 \cdot 10^{+251}:\\ \;\;\;\;\frac{x \cdot \frac{y}{a}}{2} - \frac{t \cdot 4.5}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+216}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a \cdot 2}, x, \frac{t \cdot 4.5}{a} \cdot \left(0 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{y}{a}}{2} - \frac{t \cdot 4.5}{\frac{a}{z}}\\ t_2 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+275}:\\ \;\;\;\;\frac{t\_2}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (- (/ (* x (/ y a)) 2.0) (/ (* t 4.5) (/ a z))))
        (t_2 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_2 -1e+251) t_1 (if (<= t_2 1e+275) (/ t_2 (* 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 = ((x * (y / a)) / 2.0) - ((t * 4.5) / (a / z));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -1e+251) {
		tmp = t_1;
	} else if (t_2 <= 1e+275) {
		tmp = t_2 / (a * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * (y / a)) / 2.0d0) - ((t * 4.5d0) / (a / z))
    t_2 = (x * y) - ((z * 9.0d0) * t)
    if (t_2 <= (-1d+251)) then
        tmp = t_1
    else if (t_2 <= 1d+275) then
        tmp = t_2 / (a * 2.0d0)
    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 = ((x * (y / a)) / 2.0) - ((t * 4.5) / (a / z));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -1e+251) {
		tmp = t_1;
	} else if (t_2 <= 1e+275) {
		tmp = t_2 / (a * 2.0);
	} 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 = ((x * (y / a)) / 2.0) - ((t * 4.5) / (a / z))
	t_2 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_2 <= -1e+251:
		tmp = t_1
	elif t_2 <= 1e+275:
		tmp = t_2 / (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 = Float64(Float64(Float64(x * Float64(y / a)) / 2.0) - Float64(Float64(t * 4.5) / Float64(a / z)))
	t_2 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_2 <= -1e+251)
		tmp = t_1;
	elseif (t_2 <= 1e+275)
		tmp = Float64(t_2 / Float64(a * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x * (y / a)) / 2.0) - ((t * 4.5) / (a / z));
	t_2 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_2 <= -1e+251)
		tmp = t_1;
	elseif (t_2 <= 1e+275)
		tmp = t_2 / (a * 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision] - N[(N[(t * 4.5), $MachinePrecision] / N[(a / z), $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+251], t$95$1, If[LessEqual[t$95$2, 1e+275], N[(t$95$2 / 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)) < -1e251 or 9.9999999999999996e274 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 70.2%

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

      1. div-sub N/A

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

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{a \cdot 2}\right), \color{blue}{\left(\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), \left(a \cdot 2\right)\right), \left(\frac{\color{blue}{\left(z \cdot 9\right) \cdot t}}{a \cdot 2}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(a \cdot 2\right)\right), \left(\frac{\color{blue}{\left(z \cdot 9\right)} \cdot t}{a \cdot 2}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \left(\frac{\left(z \cdot 9\right) \cdot \color{blue}{t}}{a \cdot 2}\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \left(\frac{z \cdot \left(9 \cdot t\right)}{\color{blue}{a} \cdot 2}\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \left(z \cdot \color{blue}{\frac{9 \cdot t}{a \cdot 2}}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{9 \cdot t}{a \cdot 2}\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \left(\frac{9 \cdot t}{2 \cdot \color{blue}{a}}\right)\right)\right) \]

      10. associate-/r* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \left(\frac{\frac{9 \cdot t}{2}}{\color{blue}{a}}\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(\frac{9 \cdot t}{2}\right), \color{blue}{a}\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(\frac{t \cdot 9}{2}\right), a\right)\right)\right) \]

      13. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(t \cdot \frac{9}{2}\right), a\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{9}{2}\right)\right), a\right)\right)\right) \]

      15. metadata-eval 78.5%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

   4. Applied egg-rr 78.5%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - z \cdot \frac{t \cdot 4.5}{a}} \]
   5. Step-by-step derivation

      1. times-frac N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x}{a} \cdot \frac{y}{2}\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{\frac{x}{a} \cdot y}{2}\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\frac{x}{a} \cdot y\right), 2\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\frac{x}{a}\right), y\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      5. /-lowering-/.f64 92.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, a\right), y\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

   6. Applied egg-rr 92.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{a} \cdot y}{2}} - z \cdot \frac{t \cdot 4.5}{a} \]
   7. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot y}{a}\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \frac{y}{a}\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{y}{a}\right)\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      4. /-lowering-/.f64 93.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

   8. Applied egg-rr 93.3%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{y}{a}}}{2} - z \cdot \frac{t \cdot 4.5}{a} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \left(\frac{t \cdot \frac{9}{2}}{a} \cdot \color{blue}{z}\right)\right) \]

      2. div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \left(\left(\left(t \cdot \frac{9}{2}\right) \cdot \frac{1}{a}\right) \cdot z\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \left(\left(t \cdot \frac{9}{2}\right) \cdot \color{blue}{\left(\frac{1}{a} \cdot z\right)}\right)\right) \]

      4. associate-/r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \left(\left(t \cdot \frac{9}{2}\right) \cdot \frac{1}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      5. div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \left(\frac{t \cdot \frac{9}{2}}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \mathsf{/.f64}\left(\left(t \cdot \frac{9}{2}\right), \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), \left(\frac{\color{blue}{a}}{z}\right)\right)\right) \]

      8. /-lowering-/.f64 94.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   10. Applied egg-rr 94.6%

       \[\leadsto \frac{x \cdot \frac{y}{a}}{2} - \color{blue}{\frac{t \cdot 4.5}{\frac{a}{z}}} \]

   if -1e251 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 9.9999999999999996e274

   1. Initial program 98.7%

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

Alternative 3: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+251}:\\ \;\;\;\;\frac{x}{\frac{2}{\frac{y}{a}}} - \frac{z}{\frac{a}{t \cdot 4.5}}\\ \mathbf{elif}\;t\_1 \leq 10^{+275}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}} - z \cdot \frac{t \cdot 4.5}{a}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 -1e+251)
     (- (/ x (/ 2.0 (/ y a))) (/ z (/ a (* t 4.5))))
     (if (<= t_1 1e+275)
       (/ t_1 (* a 2.0))
       (- (* x (/ y (/ a 0.5))) (* z (/ (* t 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 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -1e+251) {
		tmp = (x / (2.0 / (y / a))) - (z / (a / (t * 4.5)));
	} else if (t_1 <= 1e+275) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = (x * (y / (a / 0.5))) - (z * ((t * 4.5) / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - ((z * 9.0d0) * t)
    if (t_1 <= (-1d+251)) then
        tmp = (x / (2.0d0 / (y / a))) - (z / (a / (t * 4.5d0)))
    else if (t_1 <= 1d+275) then
        tmp = t_1 / (a * 2.0d0)
    else
        tmp = (x * (y / (a / 0.5d0))) - (z * ((t * 4.5d0) / 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 t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -1e+251) {
		tmp = (x / (2.0 / (y / a))) - (z / (a / (t * 4.5)));
	} else if (t_1 <= 1e+275) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = (x * (y / (a / 0.5))) - (z * ((t * 4.5) / 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):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_1 <= -1e+251:
		tmp = (x / (2.0 / (y / a))) - (z / (a / (t * 4.5)))
	elif t_1 <= 1e+275:
		tmp = t_1 / (a * 2.0)
	else:
		tmp = (x * (y / (a / 0.5))) - (z * ((t * 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(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= -1e+251)
		tmp = Float64(Float64(x / Float64(2.0 / Float64(y / a))) - Float64(z / Float64(a / Float64(t * 4.5))));
	elseif (t_1 <= 1e+275)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = Float64(Float64(x * Float64(y / Float64(a / 0.5))) - Float64(z * Float64(Float64(t * 4.5) / 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)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_1 <= -1e+251)
		tmp = (x / (2.0 / (y / a))) - (z / (a / (t * 4.5)));
	elseif (t_1 <= 1e+275)
		tmp = t_1 / (a * 2.0);
	else
		tmp = (x * (y / (a / 0.5))) - (z * ((t * 4.5) / 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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+251], N[(N[(x / N[(2.0 / N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / N[(t * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+275], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / N[(a / 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(t * 4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -1e251

   1. Initial program 74.4%

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

      1. div-sub N/A

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

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{a \cdot 2}\right), \color{blue}{\left(\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), \left(a \cdot 2\right)\right), \left(\frac{\color{blue}{\left(z \cdot 9\right) \cdot t}}{a \cdot 2}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(a \cdot 2\right)\right), \left(\frac{\color{blue}{\left(z \cdot 9\right)} \cdot t}{a \cdot 2}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \left(\frac{\left(z \cdot 9\right) \cdot \color{blue}{t}}{a \cdot 2}\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \left(\frac{z \cdot \left(9 \cdot t\right)}{\color{blue}{a} \cdot 2}\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \left(z \cdot \color{blue}{\frac{9 \cdot t}{a \cdot 2}}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{9 \cdot t}{a \cdot 2}\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \left(\frac{9 \cdot t}{2 \cdot \color{blue}{a}}\right)\right)\right) \]

      10. associate-/r* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \left(\frac{\frac{9 \cdot t}{2}}{\color{blue}{a}}\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(\frac{9 \cdot t}{2}\right), \color{blue}{a}\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(\frac{t \cdot 9}{2}\right), a\right)\right)\right) \]

      13. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(t \cdot \frac{9}{2}\right), a\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{9}{2}\right)\right), a\right)\right)\right) \]

      15. metadata-eval 78.4%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

   4. Applied egg-rr 78.4%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - z \cdot \frac{t \cdot 4.5}{a}} \]
   5. Step-by-step derivation

      1. times-frac N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x}{a} \cdot \frac{y}{2}\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{\frac{x}{a} \cdot y}{2}\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\frac{x}{a} \cdot y\right), 2\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\frac{x}{a}\right), y\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      5. /-lowering-/.f64 95.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, a\right), y\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

   6. Applied egg-rr 95.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{a} \cdot y}{2}} - z \cdot \frac{t \cdot 4.5}{a} \]
   7. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot y}{a}\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \frac{y}{a}\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{y}{a}\right)\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      4. /-lowering-/.f64 94.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, a\right)\right), 2\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

   8. Applied egg-rr 94.9%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{y}{a}}}{2} - z \cdot \frac{t \cdot 4.5}{a} \]
   9. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x \cdot \frac{y}{a}}{2}\right), \color{blue}{\left(z \cdot \frac{t \cdot \frac{9}{2}}{a}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \frac{\frac{y}{a}}{2}\right), \left(\color{blue}{z} \cdot \frac{t \cdot \frac{9}{2}}{a}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \frac{1}{\frac{2}{\frac{y}{a}}}\right), \left(z \cdot \frac{t \cdot \frac{9}{2}}{a}\right)\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x}{\frac{2}{\frac{y}{a}}}\right), \left(\color{blue}{z} \cdot \frac{t \cdot \frac{9}{2}}{a}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{2}{\frac{y}{a}}\right)\right), \left(\color{blue}{z} \cdot \frac{t \cdot \frac{9}{2}}{a}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(2, \left(\frac{y}{a}\right)\right)\right), \left(z \cdot \frac{t \cdot \frac{9}{2}}{a}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(2, \mathsf{/.f64}\left(y, a\right)\right)\right), \left(z \cdot \frac{t \cdot \frac{9}{2}}{a}\right)\right) \]

      8. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(2, \mathsf{/.f64}\left(y, a\right)\right)\right), \left(z \cdot \frac{1}{\color{blue}{\frac{a}{t \cdot \frac{9}{2}}}}\right)\right) \]

      9. un-div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(2, \mathsf{/.f64}\left(y, a\right)\right)\right), \left(\frac{z}{\color{blue}{\frac{a}{t \cdot \frac{9}{2}}}}\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(2, \mathsf{/.f64}\left(y, a\right)\right)\right), \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{a}{t \cdot \frac{9}{2}}\right)}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(2, \mathsf{/.f64}\left(y, a\right)\right)\right), \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(a, \color{blue}{\left(t \cdot \frac{9}{2}\right)}\right)\right)\right) \]

      12. *-lowering-*.f64 97.3%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(2, \mathsf{/.f64}\left(y, a\right)\right)\right), \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(t, \color{blue}{\frac{9}{2}}\right)\right)\right)\right) \]

   10. Applied egg-rr 97.3%

       \[\leadsto \color{blue}{\frac{x}{\frac{2}{\frac{y}{a}}} - \frac{z}{\frac{a}{t \cdot 4.5}}} \]

   if -1e251 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 9.9999999999999996e274

   1. Initial program 98.7%

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

   if 9.9999999999999996e274 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 65.6%

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

      1. div-sub N/A

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

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{a \cdot 2}\right), \color{blue}{\left(\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), \left(a \cdot 2\right)\right), \left(\frac{\color{blue}{\left(z \cdot 9\right) \cdot t}}{a \cdot 2}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(a \cdot 2\right)\right), \left(\frac{\color{blue}{\left(z \cdot 9\right)} \cdot t}{a \cdot 2}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \left(\frac{\left(z \cdot 9\right) \cdot \color{blue}{t}}{a \cdot 2}\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \left(\frac{z \cdot \left(9 \cdot t\right)}{\color{blue}{a} \cdot 2}\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \left(z \cdot \color{blue}{\frac{9 \cdot t}{a \cdot 2}}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{9 \cdot t}{a \cdot 2}\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \left(\frac{9 \cdot t}{2 \cdot \color{blue}{a}}\right)\right)\right) \]

      10. associate-/r* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \left(\frac{\frac{9 \cdot t}{2}}{\color{blue}{a}}\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(\frac{9 \cdot t}{2}\right), \color{blue}{a}\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(\frac{t \cdot 9}{2}\right), a\right)\right)\right) \]

      13. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(t \cdot \frac{9}{2}\right), a\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{9}{2}\right)\right), a\right)\right)\right) \]

      15. metadata-eval 78.5%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

   4. Applied egg-rr 78.5%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - z \cdot \frac{t \cdot 4.5}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \frac{y}{a \cdot 2}\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{y}{a \cdot 2} \cdot x\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\frac{y}{a \cdot 2}\right), x\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a \cdot 2\right)\right), x\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a \cdot \frac{1}{\frac{1}{2}}\right)\right), x\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      6. div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{a}{\frac{1}{2}}\right)\right), x\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      7. /-lowering-/.f64 91.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \frac{1}{2}\right)\right), x\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

   6. Applied egg-rr 91.5%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -1 \cdot 10^{+251}:\\ \;\;\;\;\frac{x}{\frac{2}{\frac{y}{a}}} - \frac{z}{\frac{a}{t \cdot 4.5}}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+275}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}} - z \cdot \frac{t \cdot 4.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y}{\frac{a}{0.5}} - z \cdot \frac{t \cdot 4.5}{a}\\ t_2 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+275}:\\ \;\;\;\;\frac{t\_2}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (- (* x (/ y (/ a 0.5))) (* z (/ (* t 4.5) a))))
        (t_2 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_2 -1e+251) t_1 (if (<= t_2 1e+275) (/ t_2 (* 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 = (x * (y / (a / 0.5))) - (z * ((t * 4.5) / a));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -1e+251) {
		tmp = t_1;
	} else if (t_2 <= 1e+275) {
		tmp = t_2 / (a * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * (y / (a / 0.5d0))) - (z * ((t * 4.5d0) / a))
    t_2 = (x * y) - ((z * 9.0d0) * t)
    if (t_2 <= (-1d+251)) then
        tmp = t_1
    else if (t_2 <= 1d+275) then
        tmp = t_2 / (a * 2.0d0)
    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 = (x * (y / (a / 0.5))) - (z * ((t * 4.5) / a));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -1e+251) {
		tmp = t_1;
	} else if (t_2 <= 1e+275) {
		tmp = t_2 / (a * 2.0);
	} 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 = (x * (y / (a / 0.5))) - (z * ((t * 4.5) / a))
	t_2 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_2 <= -1e+251:
		tmp = t_1
	elif t_2 <= 1e+275:
		tmp = t_2 / (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 = Float64(Float64(x * Float64(y / Float64(a / 0.5))) - Float64(z * Float64(Float64(t * 4.5) / a)))
	t_2 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_2 <= -1e+251)
		tmp = t_1;
	elseif (t_2 <= 1e+275)
		tmp = Float64(t_2 / Float64(a * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * (y / (a / 0.5))) - (z * ((t * 4.5) / a));
	t_2 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_2 <= -1e+251)
		tmp = t_1;
	elseif (t_2 <= 1e+275)
		tmp = t_2 / (a * 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 * N[(y / N[(a / 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(t * 4.5), $MachinePrecision] / a), $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+251], t$95$1, If[LessEqual[t$95$2, 1e+275], N[(t$95$2 / 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)) < -1e251 or 9.9999999999999996e274 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 70.2%

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

      1. div-sub N/A

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

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{x \cdot y}{a \cdot 2}\right), \color{blue}{\left(\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(x \cdot y\right), \left(a \cdot 2\right)\right), \left(\frac{\color{blue}{\left(z \cdot 9\right) \cdot t}}{a \cdot 2}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(a \cdot 2\right)\right), \left(\frac{\color{blue}{\left(z \cdot 9\right)} \cdot t}{a \cdot 2}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \left(\frac{\left(z \cdot 9\right) \cdot \color{blue}{t}}{a \cdot 2}\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \left(\frac{z \cdot \left(9 \cdot t\right)}{\color{blue}{a} \cdot 2}\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \left(z \cdot \color{blue}{\frac{9 \cdot t}{a \cdot 2}}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{9 \cdot t}{a \cdot 2}\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \left(\frac{9 \cdot t}{2 \cdot \color{blue}{a}}\right)\right)\right) \]

      10. associate-/r* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \left(\frac{\frac{9 \cdot t}{2}}{\color{blue}{a}}\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(\frac{9 \cdot t}{2}\right), \color{blue}{a}\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(\frac{t \cdot 9}{2}\right), a\right)\right)\right) \]

      13. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(t \cdot \frac{9}{2}\right), a\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{9}{2}\right)\right), a\right)\right)\right) \]

      15. metadata-eval 78.5%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, 2\right)\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

   4. Applied egg-rr 78.5%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - z \cdot \frac{t \cdot 4.5}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \frac{y}{a \cdot 2}\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{y}{a \cdot 2} \cdot x\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\frac{y}{a \cdot 2}\right), x\right), \mathsf{*.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a \cdot 2\right)\right), x\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a \cdot \frac{1}{\frac{1}{2}}\right)\right), x\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      6. div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{a}{\frac{1}{2}}\right)\right), x\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

      7. /-lowering-/.f64 93.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \frac{1}{2}\right)\right), x\right), \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{9}{2}\right), a\right)\right)\right) \]

   6. Applied egg-rr 93.3%

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

   if -1e251 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 9.9999999999999996e274

   1. Initial program 98.7%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -1 \cdot 10^{+251}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}} - z \cdot \frac{t \cdot 4.5}{a}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+275}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}} - z \cdot \frac{t \cdot 4.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{\frac{y}{\frac{a}{x}}}{2}\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+64}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ a x)) 2.0)))
   (if (<= (* x y) -5e-95)
     t_1
     (if (<= (* x y) 5e+64) (* (* z t) (/ -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 / (a / x)) / 2.0;
	double tmp;
	if ((x * y) <= -5e-95) {
		tmp = t_1;
	} else if ((x * y) <= 5e+64) {
		tmp = (z * t) * (-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 / (a / x)) / 2.0d0
    if ((x * y) <= (-5d-95)) then
        tmp = t_1
    else if ((x * y) <= 5d+64) then
        tmp = (z * t) * ((-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 / (a / x)) / 2.0;
	double tmp;
	if ((x * y) <= -5e-95) {
		tmp = t_1;
	} else if ((x * y) <= 5e+64) {
		tmp = (z * t) * (-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 / (a / x)) / 2.0
	tmp = 0
	if (x * y) <= -5e-95:
		tmp = t_1
	elif (x * y) <= 5e+64:
		tmp = (z * t) * (-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(Float64(y / Float64(a / x)) / 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -5e-95)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+64)
		tmp = Float64(Float64(z * t) * 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 / (a / x)) / 2.0;
	tmp = 0.0;
	if ((x * y) <= -5e-95)
		tmp = t_1;
	elseif ((x * y) <= 5e+64)
		tmp = (z * t) * (-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[(N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e-95], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+64], N[(N[(z * t), $MachinePrecision] * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.9999999999999998e-95 or 5e64 < (*.f64 x y)

   1. Initial program 85.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(a, 2\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 70.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{a}, 2\right)\right) \]

   5. Simplified 70.6%

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

      1. associate-/r* N/A

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

      2. associate-*l/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{a} \cdot y\right), \color{blue}{2}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{x}{a}\right), 2\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{1}{\frac{a}{x}}\right), 2\right) \]

      6. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{y}{\frac{a}{x}}\right), 2\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{a}{x}\right)\right), 2\right) \]

      8. /-lowering-/.f64 74.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, x\right)\right), 2\right) \]

   7. Applied egg-rr 74.8%

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

   if -4.9999999999999998e-95 < (*.f64 x y) < 5e64

   1. Initial program 94.9%

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

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-9}{2} \cdot \left(t \cdot z\right)\right), \color{blue}{a}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-9}{2}, \left(t \cdot z\right)\right), a\right) \]

      4. *-lowering-*.f64 75.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(t, z\right)\right), a\right) \]

   5. Simplified 75.6%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t \cdot z\right), \color{blue}{\left(\frac{\frac{-9}{2}}{a}\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot t\right), \left(\frac{\color{blue}{\frac{-9}{2}}}{a}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, t\right), \left(\frac{\color{blue}{\frac{-9}{2}}}{a}\right)\right) \]

      6. /-lowering-/.f64 75.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{/.f64}\left(\frac{-9}{2}, \color{blue}{a}\right)\right) \]

   7. Applied egg-rr 75.6%

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

Alternative 6: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+64}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* x (/ 0.5 a)))))
   (if (<= (* x y) -4e-32)
     t_1
     (if (<= (* x y) 5e+64) (* (* z t) (/ -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 * (x * (0.5 / a));
	double tmp;
	if ((x * y) <= -4e-32) {
		tmp = t_1;
	} else if ((x * y) <= 5e+64) {
		tmp = (z * t) * (-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 * (x * (0.5d0 / a))
    if ((x * y) <= (-4d-32)) then
        tmp = t_1
    else if ((x * y) <= 5d+64) then
        tmp = (z * t) * ((-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 * (x * (0.5 / a));
	double tmp;
	if ((x * y) <= -4e-32) {
		tmp = t_1;
	} else if ((x * y) <= 5e+64) {
		tmp = (z * t) * (-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 * (x * (0.5 / a))
	tmp = 0
	if (x * y) <= -4e-32:
		tmp = t_1
	elif (x * y) <= 5e+64:
		tmp = (z * t) * (-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(x * Float64(0.5 / a)))
	tmp = 0.0
	if (Float64(x * y) <= -4e-32)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e+64)
		tmp = Float64(Float64(z * t) * 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 * (x * (0.5 / a));
	tmp = 0.0;
	if ((x * y) <= -4e-32)
		tmp = t_1;
	elseif ((x * y) <= 5e+64)
		tmp = (z * t) * (-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[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e-32], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e+64], N[(N[(z * t), $MachinePrecision] * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.00000000000000022e-32 or 5e64 < (*.f64 x y)

   1. Initial program 84.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(a, 2\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 72.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{a}, 2\right)\right) \]

   5. Simplified 72.9%

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

      1. div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot \frac{1}{a \cdot 2}\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{a \cdot 2}\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \left(\frac{1}{2 \cdot \color{blue}{a}}\right)\right)\right) \]

      7. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \left(\frac{\frac{1}{2}}{\color{blue}{a}}\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \left(\frac{\frac{1}{2}}{a}\right)\right)\right) \]

      9. /-lowering-/.f64 77.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{a}\right)\right)\right) \]

   7. Applied egg-rr 77.8%

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

   if -4.00000000000000022e-32 < (*.f64 x y) < 5e64

   1. Initial program 94.6%

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

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-9}{2} \cdot \left(t \cdot z\right)\right), \color{blue}{a}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-9}{2}, \left(t \cdot z\right)\right), a\right) \]

      4. *-lowering-*.f64 73.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(t, z\right)\right), a\right) \]

   5. Simplified 73.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t \cdot z\right), \color{blue}{\left(\frac{\frac{-9}{2}}{a}\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot t\right), \left(\frac{\color{blue}{\frac{-9}{2}}}{a}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, t\right), \left(\frac{\color{blue}{\frac{-9}{2}}}{a}\right)\right) \]

      6. /-lowering-/.f64 73.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{/.f64}\left(\frac{-9}{2}, \color{blue}{a}\right)\right) \]

   7. Applied egg-rr 73.5%

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

Alternative 7: 93.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+256}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \end{array} \]

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) -2e+256)
   (* x (/ y (* a 2.0)))
   (/ (- (* x y) (* (* z 9.0) t)) (* 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) <= -2e+256) {
		tmp = x * (y / (a * 2.0));
	} else {
		tmp = ((x * y) - ((z * 9.0) * t)) / (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) <= (-2d+256)) then
        tmp = x * (y / (a * 2.0d0))
    else
        tmp = ((x * y) - ((z * 9.0d0) * t)) / (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) <= -2e+256) {
		tmp = x * (y / (a * 2.0));
	} else {
		tmp = ((x * y) - ((z * 9.0) * t)) / (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) <= -2e+256:
		tmp = x * (y / (a * 2.0))
	else:
		tmp = ((x * y) - ((z * 9.0) * t)) / (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) <= -2e+256)
		tmp = Float64(x * Float64(y / Float64(a * 2.0)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / 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) <= -2e+256)
		tmp = x * (y / (a * 2.0));
	else
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+256], N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.0000000000000001e256

   1. Initial program 65.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(a, 2\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 73.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{a}, 2\right)\right) \]

   5. Simplified 73.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a \cdot 2}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a \cdot 2\right)\right), x\right) \]

      5. *-lowering-*.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{*.f64}\left(a, 2\right)\right), x\right) \]

   7. Applied egg-rr 99.9%

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

   if -2.0000000000000001e256 < (*.f64 x y)

   1. Initial program 92.9%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+256}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+256}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + z \cdot \left(t \cdot -9\right)\right)\\ \end{array} \end{array} \]

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) -2e+256)
   (* x (/ y (* a 2.0)))
   (* (/ 0.5 a) (+ (* x y) (* z (* t -9.0))))))

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) <= -2e+256) {
		tmp = x * (y / (a * 2.0));
	} else {
		tmp = (0.5 / a) * ((x * y) + (z * (t * -9.0)));
	}
	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) <= (-2d+256)) then
        tmp = x * (y / (a * 2.0d0))
    else
        tmp = (0.5d0 / a) * ((x * y) + (z * (t * (-9.0d0))))
    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) <= -2e+256) {
		tmp = x * (y / (a * 2.0));
	} else {
		tmp = (0.5 / a) * ((x * y) + (z * (t * -9.0)));
	}
	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) <= -2e+256:
		tmp = x * (y / (a * 2.0))
	else:
		tmp = (0.5 / a) * ((x * y) + (z * (t * -9.0)))
	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) <= -2e+256)
		tmp = Float64(x * Float64(y / Float64(a * 2.0)));
	else
		tmp = Float64(Float64(0.5 / a) * Float64(Float64(x * y) + Float64(z * Float64(t * -9.0))));
	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) <= -2e+256)
		tmp = x * (y / (a * 2.0));
	else
		tmp = (0.5 / a) * ((x * y) + (z * (t * -9.0)));
	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], -2e+256], N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / a), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.0000000000000001e256

   1. Initial program 65.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(a, 2\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 73.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{a}, 2\right)\right) \]

   5. Simplified 73.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a \cdot 2}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(a \cdot 2\right)\right), x\right) \]

      5. *-lowering-*.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{*.f64}\left(a, 2\right)\right), x\right) \]

   7. Applied egg-rr 99.9%

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

   if -2.0000000000000001e256 < (*.f64 x y)

   1. Initial program 92.9%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{a \cdot 2}\right), \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{2 \cdot a}\right), \left(x \cdot \color{blue}{y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      5. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{2}}{a}\right), \left(\color{blue}{x \cdot y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2}\right), a\right), \left(\color{blue}{x \cdot y} - \left(z \cdot 9\right) \cdot t\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \left(\color{blue}{x} \cdot y - \left(z \cdot 9\right) \cdot t\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)}\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\mathsf{neg}\left(\left(z \cdot 9\right) \cdot t\right)\right)}\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(\color{blue}{\left(z \cdot 9\right) \cdot t}\right)\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\mathsf{neg}\left(z \cdot \left(9 \cdot t\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot t\right)\right)}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9 \cdot t\right)\right)}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t \cdot 9\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right) \]

      17. metadata-eval 92.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{2}, a\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, -9\right)\right)\right)\right) \]

   4. Applied egg-rr 92.9%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+256}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + z \cdot \left(t \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(t \cdot -4.5\right) \cdot \frac{z}{a}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* t -4.5) (/ z a))))
   (if (<= z -1.6e+23) t_1 (if (<= z 2.3e-27) (* y (* x (/ 0.5 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 = (t * -4.5) * (z / a);
	double tmp;
	if (z <= -1.6e+23) {
		tmp = t_1;
	} else if (z <= 2.3e-27) {
		tmp = y * (x * (0.5 / 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 = (t * (-4.5d0)) * (z / a)
    if (z <= (-1.6d+23)) then
        tmp = t_1
    else if (z <= 2.3d-27) then
        tmp = y * (x * (0.5d0 / 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 = (t * -4.5) * (z / a);
	double tmp;
	if (z <= -1.6e+23) {
		tmp = t_1;
	} else if (z <= 2.3e-27) {
		tmp = y * (x * (0.5 / 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 = (t * -4.5) * (z / a)
	tmp = 0
	if z <= -1.6e+23:
		tmp = t_1
	elif z <= 2.3e-27:
		tmp = y * (x * (0.5 / 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(Float64(t * -4.5) * Float64(z / a))
	tmp = 0.0
	if (z <= -1.6e+23)
		tmp = t_1;
	elseif (z <= 2.3e-27)
		tmp = Float64(y * Float64(x * Float64(0.5 / 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 = (t * -4.5) * (z / a);
	tmp = 0.0;
	if (z <= -1.6e+23)
		tmp = t_1;
	elseif (z <= 2.3e-27)
		tmp = y * (x * (0.5 / 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[(N[(t * -4.5), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+23], t$95$1, If[LessEqual[z, 2.3e-27], N[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e23 or 2.2999999999999999e-27 < z

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-9}{2} \cdot \left(t \cdot z\right)\right), \color{blue}{a}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-9}{2}, \left(t \cdot z\right)\right), a\right) \]

      4. *-lowering-*.f64 62.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-9}{2}, \mathsf{*.f64}\left(t, z\right)\right), a\right) \]

   5. Simplified 62.9%

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

      1. associate-*r* N/A

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

      2. metadata-eval N/A

         \[\leadsto \frac{\left(\left(\mathsf{neg}\left(\frac{9}{2}\right)\right) \cdot t\right) \cdot z}{a} \]

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

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{9}{2} \cdot t\right)\right) \cdot z}{a} \]

      4. *-commutative N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(t \cdot \frac{9}{2}\right)\right) \cdot z}{a} \]

      5. associate-/l* N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(t \cdot \frac{9}{2}\right)\right), \color{blue}{\left(\frac{z}{a}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(t \cdot \left(\mathsf{neg}\left(\frac{9}{2}\right)\right)\right), \left(\frac{\color{blue}{z}}{a}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t \cdot \frac{-9}{2}\right), \left(\frac{z}{a}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \frac{-9}{2}\right), \left(\frac{\color{blue}{z}}{a}\right)\right) \]

      10. /-lowering-/.f64 66.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \frac{-9}{2}\right), \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right) \]

   7. Applied egg-rr 66.8%

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

   if -1.6e23 < z < 2.2999999999999999e-27

   1. Initial program 91.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(a, 2\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 66.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{a}, 2\right)\right) \]

   5. Simplified 66.5%

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

      1. div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot \frac{1}{a \cdot 2}\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{a \cdot 2}\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \left(\frac{1}{2 \cdot \color{blue}{a}}\right)\right)\right) \]

      7. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \left(\frac{\frac{1}{2}}{\color{blue}{a}}\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \left(\frac{\frac{1}{2}}{a}\right)\right)\right) \]

      9. /-lowering-/.f64 68.5%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{a}\right)\right)\right) \]

   7. Applied egg-rr 68.5%

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

Alternative 10: 52.1% accurate, 1.9× speedup

Math

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

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 (* y (* x (/ 0.5 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 y * (x * (0.5 / 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 = y * (x * (0.5d0 / 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 y * (x * (0.5 / 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 y * (x * (0.5 / 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(y * Float64(x * Float64(0.5 / 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 = y * (x * (0.5 / 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[(y * N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.2%

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

3. Taylor expanded in x around inf

   \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(a, 2\right)\right) \]
4. Step-by-step derivation

   1. *-lowering-*.f64 49.6%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{a}, 2\right)\right) \]

5. Simplified 49.6%

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

   1. div-inv N/A

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

   2. *-commutative N/A

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

   3. associate-*l* N/A

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

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot \frac{1}{a \cdot 2}\right)}\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{a \cdot 2}\right)}\right)\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \left(\frac{1}{2 \cdot \color{blue}{a}}\right)\right)\right) \]

   7. associate-/r* N/A

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \left(\frac{\frac{1}{2}}{\color{blue}{a}}\right)\right)\right) \]

   8. metadata-eval N/A

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \left(\frac{\frac{1}{2}}{a}\right)\right)\right) \]

   9. /-lowering-/.f64 50.2%

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{2}, \color{blue}{a}\right)\right)\right) \]

7. Applied egg-rr 50.2%

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

Developer Target 1: 93.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024191 
(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)))