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

Percentage Accurate: 91.8% → 96.9%

Time: 13.8s

Alternatives: 13

Speedup: 0.6×

• 27.4% 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: 91.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{2}, \frac{x}{a}, \left(t \cdot -4.5\right) \cdot \frac{z}{a}\right)\\ t_2 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+254}:\\ \;\;\;\;\frac{t\_2}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y 2.0) (/ x a) (* (* t -4.5) (/ z a))))
        (t_2 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_2 -5e+211) t_1 (if (<= t_2 1e+254) (/ t_2 (* 2.0 a)) t_1))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / 2.0), (x / a), ((t * -4.5) * (z / a)));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -5e+211) {
		tmp = t_1;
	} else if (t_2 <= 1e+254) {
		tmp = t_2 / (2.0 * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = fma(Float64(y / 2.0), Float64(x / a), Float64(Float64(t * -4.5) * Float64(z / a)))
	t_2 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_2 <= -5e+211)
		tmp = t_1;
	elseif (t_2 <= 1e+254)
		tmp = Float64(t_2 / Float64(2.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / 2.0), $MachinePrecision] * N[(x / a), $MachinePrecision] + N[(N[(t * -4.5), $MachinePrecision] * N[(z / 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, -5e+211], t$95$1, If[LessEqual[t$95$2, 1e+254], N[(t$95$2 / N[(2.0 * a), $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)) < -4.9999999999999995e211 or 9.9999999999999994e253 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 73.1%

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

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

      4. *-commutative N/A

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

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

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

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

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

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

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

      8. neg-sub0 N/A

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

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

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

      10. associate-*l* N/A

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

      11. associate-/l* N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-/r* N/A

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

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

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

      16. *-commutative N/A

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

      17. associate-/l* N/A

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

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

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

      19. metadata-eval 92.4%

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

   4. Applied egg-rr 92.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{2}, \frac{x}{a}, 0 - z \cdot \frac{t \cdot 4.5}{a}\right)} \]
   5. Step-by-step derivation

      1. sub0-neg N/A

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

      2. associate-*r/ N/A

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

      3. distribute-neg-frac2 N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. metadata-eval N/A

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

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

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

      8. *-commutative N/A

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

      9. frac-2neg N/A

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

      10. associate-*r* N/A

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

      11. metadata-eval N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-/l* N/A

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

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

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

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

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

      17. metadata-eval N/A

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

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

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

      19. /-lowering-/.f64 96.1%

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

   6. Applied egg-rr 96.1%

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

   if -4.9999999999999995e211 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 9.9999999999999994e253

   1. Initial program 98.5%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+211}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{2}, \frac{x}{a}, \left(t \cdot -4.5\right) \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+254}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{2}, \frac{x}{a}, \left(t \cdot -4.5\right) \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\frac{t\_1}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{\frac{-4.5 \cdot \left(z \cdot t\right)}{x}}{a} + \frac{y \cdot 0.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 5e+290)
     (/ t_1 (* 2.0 a))
     (* x (+ (/ (/ (* -4.5 (* z t)) x) a) (/ (* y 0.5) a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= 5e+290) {
		tmp = t_1 / (2.0 * a);
	} else {
		tmp = x * ((((-4.5 * (z * t)) / x) / a) + ((y * 0.5) / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - ((z * 9.0d0) * t)
    if (t_1 <= 5d+290) then
        tmp = t_1 / (2.0d0 * a)
    else
        tmp = x * (((((-4.5d0) * (z * t)) / x) / a) + ((y * 0.5d0) / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= 5e+290) {
		tmp = t_1 / (2.0 * a);
	} else {
		tmp = x * ((((-4.5 * (z * t)) / x) / a) + ((y * 0.5) / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_1 <= 5e+290:
		tmp = t_1 / (2.0 * a)
	else:
		tmp = x * ((((-4.5 * (z * t)) / x) / a) + ((y * 0.5) / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= 5e+290)
		tmp = Float64(t_1 / Float64(2.0 * a));
	else
		tmp = Float64(x * Float64(Float64(Float64(Float64(-4.5 * Float64(z * t)) / x) / a) + Float64(Float64(y * 0.5) / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_1 <= 5e+290)
		tmp = t_1 / (2.0 * a);
	else
		tmp = x * ((((-4.5 * (z * t)) / x) / a) + ((y * 0.5) / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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, 5e+290], N[(t$95$1 / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(N[(-4.5 * N[(z * t), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / a), $MachinePrecision] + N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 4.9999999999999998e290

   1. Initial program 94.9%

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

   if 4.9999999999999998e290 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 63.2%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

      5. cancel-sign-sub-inv N/A

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

      6. metadata-eval N/A

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

      12. /-lowering-/.f64 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{-9}{2} \cdot \frac{t \cdot z}{a \cdot x} + \frac{1}{2} \cdot \frac{y}{a}\right)} \]
   7. Step-by-step derivation

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

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

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

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/r* N/A

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

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

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

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

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

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

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

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

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

      10. associate-*r/ N/A

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

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

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

      12. *-lowering-*.f64 84.0%

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

   8. Simplified 84.0%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{\frac{-4.5 \cdot \left(z \cdot t\right)}{x}}{a} + \frac{y \cdot 0.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;y \cdot \frac{\frac{x}{2}}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+191}:\\ \;\;\;\;\left(x \cdot y + \left(z \cdot t\right) \cdot -9\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{a}{x}}}{2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* y (/ (/ x 2.0) a))
   (if (<= (* x y) 5e+191)
     (* (+ (* x y) (* (* z t) -9.0)) (/ 0.5 a))
     (/ (/ y (/ a x)) 2.0))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = y * ((x / 2.0) / a);
	} else if ((x * y) <= 5e+191) {
		tmp = ((x * y) + ((z * t) * -9.0)) * (0.5 / a);
	} else {
		tmp = (y / (a / x)) / 2.0;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((x / 2.0) / a);
	} else if ((x * y) <= 5e+191) {
		tmp = ((x * y) + ((z * t) * -9.0)) * (0.5 / a);
	} else {
		tmp = (y / (a / x)) / 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = y * ((x / 2.0) / a)
	elif (x * y) <= 5e+191:
		tmp = ((x * y) + ((z * t) * -9.0)) * (0.5 / a)
	else:
		tmp = (y / (a / x)) / 2.0
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(x / 2.0) / a));
	elseif (Float64(x * y) <= 5e+191)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) * -9.0)) * Float64(0.5 / a));
	else
		tmp = Float64(Float64(y / Float64(a / x)) / 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = y * ((x / 2.0) / a);
	elseif ((x * y) <= 5e+191)
		tmp = ((x * y) + ((z * t) * -9.0)) * (0.5 / a);
	else
		tmp = (y / (a / x)) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(y * N[(N[(x / 2.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+191], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 65.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 65.0%

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

   5. Simplified 65.0%

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

      1. times-frac N/A

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

      2. *-commutative N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. associate-*r* N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

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

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. div-inv N/A

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

      13. /-lowering-/.f64 89.8%

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

   7. Applied egg-rr 89.8%

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

   if -inf.0 < (*.f64 x y) < 5.0000000000000002e191

   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 a around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

      5. cancel-sign-sub-inv N/A

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

      6. metadata-eval N/A

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

      12. /-lowering-/.f64 94.5%

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

   5. Simplified 94.5%

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

   if 5.0000000000000002e191 < (*.f64 x y)

   1. Initial program 78.0%

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

   3. Taylor expanded in x around 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 78.0%

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

   5. Simplified 78.0%

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

      1. associate-/r* N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-/l* 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 96.7%

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

   7. Applied egg-rr 96.7%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;y \cdot \frac{\frac{x}{2}}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+191}:\\ \;\;\;\;\left(x \cdot y + \left(z \cdot t\right) \cdot -9\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{a}{x}}}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+290}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - t\_1}{2 \cdot a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -2e+290) (* z (* t (/ -4.5 a))) (/ (- (* x y) t_1) (* 2.0 a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -2e+290) {
		tmp = z * (t * (-4.5 / a));
	} else {
		tmp = ((x * y) - t_1) / (2.0 * a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * 9.0d0) * t
    if (t_1 <= (-2d+290)) then
        tmp = z * (t * ((-4.5d0) / a))
    else
        tmp = ((x * y) - t_1) / (2.0d0 * a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -2e+290) {
		tmp = z * (t * (-4.5 / a));
	} else {
		tmp = ((x * y) - t_1) / (2.0 * a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -2e+290:
		tmp = z * (t * (-4.5 / a))
	else:
		tmp = ((x * y) - t_1) / (2.0 * a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -2e+290)
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	else
		tmp = Float64(Float64(Float64(x * y) - t_1) / Float64(2.0 * a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_1 <= -2e+290)
		tmp = z * (t * (-4.5 / a));
	else
		tmp = ((x * y) - t_1) / (2.0 * a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+290], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -2.00000000000000012e290

   1. Initial program 55.4%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. flip-+ N/A

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

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

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

   4. Applied egg-rr 0.3%

      \[\leadsto \frac{\color{blue}{\frac{z \cdot \left(z \cdot \left(\left(t \cdot t\right) \cdot 81\right)\right) - x \cdot \left(y \cdot \left(x \cdot y\right)\right)}{z \cdot \left(t \cdot -9\right) - x \cdot y}}}{a \cdot 2} \]

   5. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

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

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

      6. *-lowering-*.f64 55.4%

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

   7. Simplified 55.4%

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

   8. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-*l/ N/A

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

      7. associate-/l* N/A

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

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

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

      9. /-lowering-/.f64 99.7%

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

   10. Simplified 99.7%

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

   if -2.00000000000000012e290 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 92.6%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -2 \cdot 10^{+290}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{2 \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{2} \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+32}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{a}{x}}}{2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -4e-95)
   (* (/ x 2.0) (/ y a))
   (if (<= (* x y) 1e+32) (/ (* t (* z -4.5)) a) (/ (/ y (/ a x)) 2.0))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-95) {
		tmp = (x / 2.0) * (y / a);
	} else if ((x * y) <= 1e+32) {
		tmp = (t * (z * -4.5)) / a;
	} else {
		tmp = (y / (a / x)) / 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-4d-95)) then
        tmp = (x / 2.0d0) * (y / a)
    else if ((x * y) <= 1d+32) then
        tmp = (t * (z * (-4.5d0))) / a
    else
        tmp = (y / (a / x)) / 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-95) {
		tmp = (x / 2.0) * (y / a);
	} else if ((x * y) <= 1e+32) {
		tmp = (t * (z * -4.5)) / a;
	} else {
		tmp = (y / (a / x)) / 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -4e-95:
		tmp = (x / 2.0) * (y / a)
	elif (x * y) <= 1e+32:
		tmp = (t * (z * -4.5)) / a
	else:
		tmp = (y / (a / x)) / 2.0
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -4e-95)
		tmp = Float64(Float64(x / 2.0) * Float64(y / a));
	elseif (Float64(x * y) <= 1e+32)
		tmp = Float64(Float64(t * Float64(z * -4.5)) / a);
	else
		tmp = Float64(Float64(y / Float64(a / x)) / 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -4e-95)
		tmp = (x / 2.0) * (y / a);
	elseif ((x * y) <= 1e+32)
		tmp = (t * (z * -4.5)) / a;
	else
		tmp = (y / (a / x)) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e-95], N[(N[(x / 2.0), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+32], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999996e-95

   1. Initial program 86.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 66.6%

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

   5. Simplified 66.6%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. metadata-eval N/A

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

      10. div-inv N/A

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

      11. /-lowering-/.f64 70.2%

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

   7. Applied egg-rr 70.2%

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

   if -3.99999999999999996e-95 < (*.f64 x y) < 1.00000000000000005e32

   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 78.7%

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

   5. Simplified 78.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-lowering-*.f64 78.7%

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

   7. Applied egg-rr 78.7%

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

   if 1.00000000000000005e32 < (*.f64 x y)

   1. Initial program 86.7%

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

   3. 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 79.5%

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

   5. Simplified 79.5%

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

      1. associate-/r* N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-/l* 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 85.0%

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

   7. Applied egg-rr 85.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{2} \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+32}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{a}{x}}}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{2} \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+32}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{\frac{a}{0.5}}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -4e-95)
   (* (/ x 2.0) (/ y a))
   (if (<= (* x y) 1e+32) (/ (* t (* z -4.5)) a) (/ x (/ (/ a 0.5) y)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-95) {
		tmp = (x / 2.0) * (y / a);
	} else if ((x * y) <= 1e+32) {
		tmp = (t * (z * -4.5)) / a;
	} else {
		tmp = x / ((a / 0.5) / y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-4d-95)) then
        tmp = (x / 2.0d0) * (y / a)
    else if ((x * y) <= 1d+32) then
        tmp = (t * (z * (-4.5d0))) / a
    else
        tmp = x / ((a / 0.5d0) / y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-95) {
		tmp = (x / 2.0) * (y / a);
	} else if ((x * y) <= 1e+32) {
		tmp = (t * (z * -4.5)) / a;
	} else {
		tmp = x / ((a / 0.5) / y);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -4e-95:
		tmp = (x / 2.0) * (y / a)
	elif (x * y) <= 1e+32:
		tmp = (t * (z * -4.5)) / a
	else:
		tmp = x / ((a / 0.5) / y)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -4e-95)
		tmp = Float64(Float64(x / 2.0) * Float64(y / a));
	elseif (Float64(x * y) <= 1e+32)
		tmp = Float64(Float64(t * Float64(z * -4.5)) / a);
	else
		tmp = Float64(x / Float64(Float64(a / 0.5) / y));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -4e-95)
		tmp = (x / 2.0) * (y / a);
	elseif ((x * y) <= 1e+32)
		tmp = (t * (z * -4.5)) / a;
	else
		tmp = x / ((a / 0.5) / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e-95], N[(N[(x / 2.0), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+32], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(N[(a / 0.5), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999996e-95

   1. Initial program 86.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 66.6%

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

   5. Simplified 66.6%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. metadata-eval N/A

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

      10. div-inv N/A

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

      11. /-lowering-/.f64 70.2%

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

   7. Applied egg-rr 70.2%

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

   if -3.99999999999999996e-95 < (*.f64 x y) < 1.00000000000000005e32

   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 78.7%

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

   5. Simplified 78.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-lowering-*.f64 78.7%

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

   7. Applied egg-rr 78.7%

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

   if 1.00000000000000005e32 < (*.f64 x y)

   1. Initial program 86.7%

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

   3. 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 79.5%

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

   5. Simplified 79.5%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. metadata-eval N/A

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

      7. div-inv N/A

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

      8. /-lowering-/.f64 85.3%

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

   7. Applied egg-rr 85.3%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{2} \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+32}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{\frac{a}{0.5}}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{2} \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+32}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{\frac{a}{0.5}}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -4e-95)
   (* (/ x 2.0) (/ y a))
   (if (<= (* x y) 1e+32) (* (* z t) (/ -4.5 a)) (/ x (/ (/ a 0.5) y)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-95) {
		tmp = (x / 2.0) * (y / a);
	} else if ((x * y) <= 1e+32) {
		tmp = (z * t) * (-4.5 / a);
	} else {
		tmp = x / ((a / 0.5) / y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-4d-95)) then
        tmp = (x / 2.0d0) * (y / a)
    else if ((x * y) <= 1d+32) then
        tmp = (z * t) * ((-4.5d0) / a)
    else
        tmp = x / ((a / 0.5d0) / y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-95) {
		tmp = (x / 2.0) * (y / a);
	} else if ((x * y) <= 1e+32) {
		tmp = (z * t) * (-4.5 / a);
	} else {
		tmp = x / ((a / 0.5) / y);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -4e-95:
		tmp = (x / 2.0) * (y / a)
	elif (x * y) <= 1e+32:
		tmp = (z * t) * (-4.5 / a)
	else:
		tmp = x / ((a / 0.5) / y)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -4e-95)
		tmp = Float64(Float64(x / 2.0) * Float64(y / a));
	elseif (Float64(x * y) <= 1e+32)
		tmp = Float64(Float64(z * t) * Float64(-4.5 / a));
	else
		tmp = Float64(x / Float64(Float64(a / 0.5) / y));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -4e-95)
		tmp = (x / 2.0) * (y / a);
	elseif ((x * y) <= 1e+32)
		tmp = (z * t) * (-4.5 / a);
	else
		tmp = x / ((a / 0.5) / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e-95], N[(N[(x / 2.0), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+32], N[(N[(z * t), $MachinePrecision] * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(a / 0.5), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999996e-95

   1. Initial program 86.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 66.6%

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

   5. Simplified 66.6%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. metadata-eval N/A

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

      10. div-inv N/A

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

      11. /-lowering-/.f64 70.2%

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

   7. Applied egg-rr 70.2%

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

   if -3.99999999999999996e-95 < (*.f64 x y) < 1.00000000000000005e32

   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 78.7%

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

   5. Simplified 78.7%

      \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]
   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. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 78.7%

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

   7. Applied egg-rr 78.7%

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

   if 1.00000000000000005e32 < (*.f64 x y)

   1. Initial program 86.7%

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

   3. 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 79.5%

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

   5. Simplified 79.5%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. metadata-eval N/A

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

      7. div-inv N/A

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

      8. /-lowering-/.f64 85.3%

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

   7. Applied egg-rr 85.3%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{2} \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+32}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{\frac{a}{0.5}}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{2} \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+32}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{y}}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -4e-95)
   (* (/ x 2.0) (/ y a))
   (if (<= (* x y) 1e+32) (* (* z t) (/ -4.5 a)) (/ 0.5 (/ (/ a y) x)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-95) {
		tmp = (x / 2.0) * (y / a);
	} else if ((x * y) <= 1e+32) {
		tmp = (z * t) * (-4.5 / a);
	} else {
		tmp = 0.5 / ((a / y) / x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-4d-95)) then
        tmp = (x / 2.0d0) * (y / a)
    else if ((x * y) <= 1d+32) then
        tmp = (z * t) * ((-4.5d0) / a)
    else
        tmp = 0.5d0 / ((a / y) / x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e-95) {
		tmp = (x / 2.0) * (y / a);
	} else if ((x * y) <= 1e+32) {
		tmp = (z * t) * (-4.5 / a);
	} else {
		tmp = 0.5 / ((a / y) / x);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -4e-95:
		tmp = (x / 2.0) * (y / a)
	elif (x * y) <= 1e+32:
		tmp = (z * t) * (-4.5 / a)
	else:
		tmp = 0.5 / ((a / y) / x)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -4e-95)
		tmp = Float64(Float64(x / 2.0) * Float64(y / a));
	elseif (Float64(x * y) <= 1e+32)
		tmp = Float64(Float64(z * t) * Float64(-4.5 / a));
	else
		tmp = Float64(0.5 / Float64(Float64(a / y) / x));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -4e-95)
		tmp = (x / 2.0) * (y / a);
	elseif ((x * y) <= 1e+32)
		tmp = (z * t) * (-4.5 / a);
	else
		tmp = 0.5 / ((a / y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e-95], N[(N[(x / 2.0), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+32], N[(N[(z * t), $MachinePrecision] * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(N[(a / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999996e-95

   1. Initial program 86.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 66.6%

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

   5. Simplified 66.6%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. metadata-eval N/A

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

      10. div-inv N/A

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

      11. /-lowering-/.f64 70.2%

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

   7. Applied egg-rr 70.2%

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

   if -3.99999999999999996e-95 < (*.f64 x y) < 1.00000000000000005e32

   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 78.7%

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

   5. Simplified 78.7%

      \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]
   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. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 78.7%

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

   7. Applied egg-rr 78.7%

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

   if 1.00000000000000005e32 < (*.f64 x y)

   1. Initial program 86.7%

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

      1. div-inv N/A

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

      2. flip3-- N/A

         \[\leadsto \frac{{\left(x \cdot y\right)}^{3} - {\left(\left(z \cdot 9\right) \cdot t\right)}^{3}}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(\left(z \cdot 9\right) \cdot t\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right) + \left(x \cdot y\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{\color{blue}{1}}{a \cdot 2} \]

      3. clear-num N/A

         \[\leadsto \frac{1}{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(\left(z \cdot 9\right) \cdot t\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right) + \left(x \cdot y\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)}{{\left(x \cdot y\right)}^{3} - {\left(\left(z \cdot 9\right) \cdot t\right)}^{3}}} \cdot \frac{\color{blue}{1}}{a \cdot 2} \]

      4. *-commutative N/A

         \[\leadsto \frac{1}{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(\left(z \cdot 9\right) \cdot t\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right) + \left(x \cdot y\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)}{{\left(x \cdot y\right)}^{3} - {\left(\left(z \cdot 9\right) \cdot t\right)}^{3}}} \cdot \frac{1}{2 \cdot \color{blue}{a}} \]

      5. associate-/r* N/A

         \[\leadsto \frac{1}{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(\left(z \cdot 9\right) \cdot t\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right) + \left(x \cdot y\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)}{{\left(x \cdot y\right)}^{3} - {\left(\left(z \cdot 9\right) \cdot t\right)}^{3}}} \cdot \frac{\frac{1}{2}}{\color{blue}{a}} \]

      6. frac-times N/A

         \[\leadsto \frac{1 \cdot \frac{1}{2}}{\color{blue}{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(\left(z \cdot 9\right) \cdot t\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right) + \left(x \cdot y\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)}{{\left(x \cdot y\right)}^{3} - {\left(\left(z \cdot 9\right) \cdot t\right)}^{3}} \cdot a}} \]

      7. metadata-eval N/A

         \[\leadsto \frac{1 \cdot \frac{1}{2}}{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(\left(z \cdot 9\right) \cdot t\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right) + \left(x \cdot y\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)}{\color{blue}{{\left(x \cdot y\right)}^{3} - {\left(\left(z \cdot 9\right) \cdot t\right)}^{3}}} \cdot a} \]

      8. metadata-eval N/A

         \[\leadsto \frac{\frac{1}{2}}{\color{blue}{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(\left(z \cdot 9\right) \cdot t\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right) + \left(x \cdot y\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)}{{\left(x \cdot y\right)}^{3} - {\left(\left(z \cdot 9\right) \cdot t\right)}^{3}}} \cdot a} \]

      9. metadata-eval N/A

         \[\leadsto \frac{\frac{1}{2}}{\color{blue}{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(\left(z \cdot 9\right) \cdot t\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right) + \left(x \cdot y\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)}{{\left(x \cdot y\right)}^{3} - {\left(\left(z \cdot 9\right) \cdot t\right)}^{3}}} \cdot a} \]

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

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2}\right), \color{blue}{\left(\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) + \left(\left(\left(z \cdot 9\right) \cdot t\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right) + \left(x \cdot y\right) \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)}{{\left(x \cdot y\right)}^{3} - {\left(\left(z \cdot 9\right) \cdot t\right)}^{3}} \cdot a\right)}\right) \]

   4. Applied egg-rr 86.6%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{1}{x \cdot y + z \cdot \left(t \cdot -9\right)} \cdot a}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\color{blue}{\left(\frac{1}{x \cdot y}\right)}, a\right)\right) \]
   6. Step-by-step derivation

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

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

      2. *-lowering-*.f64 79.4%

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

   7. Simplified 79.4%

      \[\leadsto \frac{0.5}{\color{blue}{\frac{1}{x \cdot y}} \cdot a} \]
   8. Step-by-step derivation

      1. *-commutative N/A

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

      2. un-div-inv N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

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

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

      6. /-lowering-/.f64 85.3%

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

   9. Applied egg-rr 85.3%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{2} \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+32}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{y}}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{2} \cdot \frac{y}{a}\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+32}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ x 2.0) (/ y a))))
   (if (<= (* x y) -4e-95)
     t_1
     (if (<= (* x y) 1e+32) (* (* z t) (/ -4.5 a)) t_1))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / 2.0) * (y / a);
	double tmp;
	if ((x * y) <= -4e-95) {
		tmp = t_1;
	} else if ((x * y) <= 1e+32) {
		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.
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 / 2.0d0) * (y / a)
    if ((x * y) <= (-4d-95)) then
        tmp = t_1
    else if ((x * y) <= 1d+32) 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;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / 2.0) * (y / a);
	double tmp;
	if ((x * y) <= -4e-95) {
		tmp = t_1;
	} else if ((x * y) <= 1e+32) {
		tmp = (z * t) * (-4.5 / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x / 2.0) * (y / a)
	tmp = 0
	if (x * y) <= -4e-95:
		tmp = t_1
	elif (x * y) <= 1e+32:
		tmp = (z * t) * (-4.5 / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / 2.0) * Float64(y / a))
	tmp = 0.0
	if (Float64(x * y) <= -4e-95)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+32)
		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])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x / 2.0) * (y / a);
	tmp = 0.0;
	if ((x * y) <= -4e-95)
		tmp = t_1;
	elseif ((x * y) <= 1e+32)
		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.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / 2.0), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e-95], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+32], 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) < -3.99999999999999996e-95 or 1.00000000000000005e32 < (*.f64 x y)

   1. Initial program 86.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 72.1%

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

   5. Simplified 72.1%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. div-inv N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. metadata-eval N/A

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

      10. div-inv N/A

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

      11. /-lowering-/.f64 76.2%

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

   7. Applied egg-rr 76.2%

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

   if -3.99999999999999996e-95 < (*.f64 x y) < 1.00000000000000005e32

   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 78.7%

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

   5. Simplified 78.7%

      \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]
   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. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 78.7%

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

   7. Applied egg-rr 78.7%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{2} \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+32}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2} \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{if}\;x \cdot y \leq -1.35 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{+33}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* x y) (/ 0.5 a))))
   (if (<= (* x y) -1.35e-59)
     t_1
     (if (<= (* x y) 7.5e+33) (* (* z t) (/ -4.5 a)) t_1))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) * (0.5 / a);
	double tmp;
	if ((x * y) <= -1.35e-59) {
		tmp = t_1;
	} else if ((x * y) <= 7.5e+33) {
		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.
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) * (0.5d0 / a)
    if ((x * y) <= (-1.35d-59)) then
        tmp = t_1
    else if ((x * y) <= 7.5d+33) 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;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) * (0.5 / a);
	double tmp;
	if ((x * y) <= -1.35e-59) {
		tmp = t_1;
	} else if ((x * y) <= 7.5e+33) {
		tmp = (z * t) * (-4.5 / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) * (0.5 / a)
	tmp = 0
	if (x * y) <= -1.35e-59:
		tmp = t_1
	elif (x * y) <= 7.5e+33:
		tmp = (z * t) * (-4.5 / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) * Float64(0.5 / a))
	tmp = 0.0
	if (Float64(x * y) <= -1.35e-59)
		tmp = t_1;
	elseif (Float64(x * y) <= 7.5e+33)
		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])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) * (0.5 / a);
	tmp = 0.0;
	if ((x * y) <= -1.35e-59)
		tmp = t_1;
	elseif ((x * y) <= 7.5e+33)
		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.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.35e-59], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 7.5e+33], 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) < -1.3499999999999999e-59 or 7.50000000000000046e33 < (*.f64 x y)

   1. Initial program 86.4%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

      5. cancel-sign-sub-inv N/A

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

      6. metadata-eval N/A

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

      12. /-lowering-/.f64 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{/.f64}\left(\frac{1}{2}, a\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 73.6%

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

   8. Simplified 73.6%

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

   if -1.3499999999999999e-59 < (*.f64 x y) < 7.50000000000000046e33

   1. Initial program 94.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   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 76.9%

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

   5. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]
   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. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 76.9%

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

   7. Applied egg-rr 76.9%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.35 \cdot 10^{-59}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{+33}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.14 \cdot 10^{-231}:\\ \;\;\;\;\left(t \cdot -4.5\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.14e-231) (* (* t -4.5) (/ z a)) (* (* z t) (/ -4.5 a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.14e-231) {
		tmp = (t * -4.5) * (z / a);
	} else {
		tmp = (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.
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 <= (-1.14d-231)) then
        tmp = (t * (-4.5d0)) * (z / a)
    else
        tmp = (z * t) * ((-4.5d0) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.14e-231) {
		tmp = (t * -4.5) * (z / a);
	} else {
		tmp = (z * t) * (-4.5 / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.14e-231:
		tmp = (t * -4.5) * (z / a)
	else:
		tmp = (z * t) * (-4.5 / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.14e-231)
		tmp = Float64(Float64(t * -4.5) * Float64(z / a));
	else
		tmp = Float64(Float64(z * t) * Float64(-4.5 / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.14e-231)
		tmp = (t * -4.5) * (z / a);
	else
		tmp = (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.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.14e-231], N[(N[(t * -4.5), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.14e-231

   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 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 48.7%

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

   5. Simplified 48.7%

      \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]
   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 51.3%

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

   7. Applied egg-rr 51.3%

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

   if -1.14e-231 < x

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   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 51.8%

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

   5. Simplified 51.8%

      \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]
   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. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 51.8%

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

   7. Applied egg-rr 51.8%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.14 \cdot 10^{-231}:\\ \;\;\;\;\left(t \cdot -4.5\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{-280}:\\ \;\;\;\;\left(t \cdot -4.5\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -8.6e-280) (* (* t -4.5) (/ z a)) (* z (* t (/ -4.5 a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8.6e-280) {
		tmp = (t * -4.5) * (z / a);
	} else {
		tmp = 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.
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 <= (-8.6d-280)) then
        tmp = (t * (-4.5d0)) * (z / a)
    else
        tmp = z * (t * ((-4.5d0) / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8.6e-280) {
		tmp = (t * -4.5) * (z / a);
	} else {
		tmp = z * (t * (-4.5 / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -8.6e-280:
		tmp = (t * -4.5) * (z / a)
	else:
		tmp = z * (t * (-4.5 / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -8.6e-280)
		tmp = Float64(Float64(t * -4.5) * Float64(z / a));
	else
		tmp = Float64(z * Float64(t * Float64(-4.5 / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -8.6e-280)
		tmp = (t * -4.5) * (z / a);
	else
		tmp = 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.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -8.6e-280], N[(N[(t * -4.5), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(z * N[(t * N[(-4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5999999999999997e-280

   1. Initial program 90.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   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 51.9%

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

   5. Simplified 51.9%

      \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]
   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 54.2%

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

   7. Applied egg-rr 54.2%

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

   if -8.5999999999999997e-280 < x

   1. Initial program 90.6%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. flip-+ N/A

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

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

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

   4. Applied egg-rr 45.0%

      \[\leadsto \frac{\color{blue}{\frac{z \cdot \left(z \cdot \left(\left(t \cdot t\right) \cdot 81\right)\right) - x \cdot \left(y \cdot \left(x \cdot y\right)\right)}{z \cdot \left(t \cdot -9\right) - x \cdot y}}}{a \cdot 2} \]

   5. Taylor expanded in z around inf

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

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

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

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

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

      3. *-commutative N/A

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

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

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

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

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

      6. *-lowering-*.f64 86.4%

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

   7. Simplified 86.4%

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

   8. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-*l/ N/A

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

      7. associate-/l* N/A

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

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

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

      9. /-lowering-/.f64 47.3%

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

   10. Simplified 47.3%

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

Alternative 13: 51.7% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.4%

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

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. flip-+ N/A

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

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

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

4. Applied egg-rr 45.8%

   \[\leadsto \frac{\color{blue}{\frac{z \cdot \left(z \cdot \left(\left(t \cdot t\right) \cdot 81\right)\right) - x \cdot \left(y \cdot \left(x \cdot y\right)\right)}{z \cdot \left(t \cdot -9\right) - x \cdot y}}}{a \cdot 2} \]

5. Taylor expanded in z around inf

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

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

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

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

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

   3. *-commutative N/A

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

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

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

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

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

   6. *-lowering-*.f64 87.1%

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

7. Simplified 87.1%

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

8. Taylor expanded in z around inf

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

   1. associate-*l/ N/A

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

   2. associate-*l* N/A

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

   3. *-commutative N/A

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

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

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

   5. *-commutative N/A

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

   6. associate-*l/ N/A

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

   7. associate-/l* N/A

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

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

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

   9. /-lowering-/.f64 50.2%

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

10. Simplified 50.2%

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

Developer Target 1: 93.5% 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 2024192 
(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)))