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

Percentage Accurate: 91.2% → 97.1%

Time: 9.2s

Alternatives: 11

Speedup: 0.7×

• 29.2% 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: 91.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+270}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x \cdot 0.5, \left(-t\right) \cdot \left(4.5 \cdot \frac{z}{a}\right)\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+255}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot t, -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, 4.5 \cdot \frac{t}{a}, \left(x \cdot \frac{0.5}{a}\right) \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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+270)
     (fma (/ y a) (* x 0.5) (* (- t) (* 4.5 (/ z a))))
     (if (<= t_1 1e+255)
       (/ (fma (* z t) -9.0 (* x y)) (* a 2.0))
       (fma (- z) (* 4.5 (/ t a)) (* (* x (/ 0.5 a)) y))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -5e+270) {
		tmp = fma((y / a), (x * 0.5), (-t * (4.5 * (z / a))));
	} else if (t_1 <= 1e+255) {
		tmp = fma((z * t), -9.0, (x * y)) / (a * 2.0);
	} else {
		tmp = fma(-z, (4.5 * (t / a)), ((x * (0.5 / a)) * y));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= -5e+270)
		tmp = fma(Float64(y / a), Float64(x * 0.5), Float64(Float64(-t) * Float64(4.5 * Float64(z / a))));
	elseif (t_1 <= 1e+255)
		tmp = Float64(fma(Float64(z * t), -9.0, Float64(x * y)) / Float64(a * 2.0));
	else
		tmp = fma(Float64(-z), Float64(4.5 * Float64(t / a)), Float64(Float64(x * Float64(0.5 / a)) * y));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+270], N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision] + N[((-t) * N[(4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+255], N[(N[(N[(z * t), $MachinePrecision] * -9.0 + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[((-z) * N[(4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -4.99999999999999976e270

   1. Initial program 74.8%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. times-frac N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. div-inv N/A

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

      12. lower-*.f64 N/A

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

      13. metadata-eval N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-/l* N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. lower-neg.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. times-frac N/A

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

      25. lower-*.f64 N/A

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

   4. Applied rewrites 94.9%

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

   if -4.99999999999999976e270 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 9.99999999999999988e254

   1. Initial program 97.2%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 97.3

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

   4. Applied rewrites 97.3%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lower-fma.f64 97.3

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 97.3

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 97.3

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

   6. Applied rewrites 97.3%

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

   if 9.99999999999999988e254 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 78.6%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. associate-/l* N/A

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

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

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. times-frac N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval N/A

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

      18. lower-/.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. associate-/l* N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

   4. Applied rewrites 93.3%

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

Alternative 2: 97.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+277} \lor \neg \left(t\_1 \leq 10^{+255}\right):\\ \;\;\;\;\mathsf{fma}\left(-z, 4.5 \cdot \frac{t}{a}, \left(x \cdot \frac{0.5}{a}\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot t, -9, x \cdot y\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 -5e+277) (not (<= t_1 1e+255)))
     (fma (- z) (* 4.5 (/ t a)) (* (* x (/ 0.5 a)) y))
     (/ (fma (* z t) -9.0 (* x y)) (* a 2.0)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -5e+277) || !(t_1 <= 1e+255)) {
		tmp = fma(-z, (4.5 * (t / a)), ((x * (0.5 / a)) * y));
	} else {
		tmp = fma((z * t), -9.0, (x * y)) / (a * 2.0);
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= -5e+277) || !(t_1 <= 1e+255))
		tmp = fma(Float64(-z), Float64(4.5 * Float64(t / a)), Float64(Float64(x * Float64(0.5 / a)) * y));
	else
		tmp = Float64(fma(Float64(z * t), -9.0, Float64(x * y)) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+277], N[Not[LessEqual[t$95$1, 1e+255]], $MachinePrecision]], N[((-z) * N[(4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] * -9.0 + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -4.99999999999999982e277 or 9.99999999999999988e254 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 76.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. associate-/l* N/A

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

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

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. times-frac N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval N/A

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

      18. lower-/.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. associate-/l* N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

   4. Applied rewrites 95.6%

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

   if -4.99999999999999982e277 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 9.99999999999999988e254

   1. Initial program 97.3%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 97.3

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

   4. Applied rewrites 97.3%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lower-fma.f64 97.3

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 97.3

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 97.3

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

   6. Applied rewrites 97.3%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+277} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+255}\right):\\ \;\;\;\;\mathsf{fma}\left(-z, 4.5 \cdot \frac{t}{a}, \left(x \cdot \frac{0.5}{a}\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot t, -9, x \cdot y\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+307} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+249}\right):\\ \;\;\;\;\frac{z}{a} \cdot \mathsf{fma}\left(0.5 \cdot y, \frac{x}{z}, -4.5 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot t, -9, x \cdot y\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 -5e+307) (not (<= t_1 5e+249)))
     (* (/ z a) (fma (* 0.5 y) (/ x z) (* -4.5 t)))
     (/ (fma (* z t) -9.0 (* x y)) (* a 2.0)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -5e+307) || !(t_1 <= 5e+249)) {
		tmp = (z / a) * fma((0.5 * y), (x / z), (-4.5 * t));
	} else {
		tmp = fma((z * t), -9.0, (x * y)) / (a * 2.0);
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= -5e+307) || !(t_1 <= 5e+249))
		tmp = Float64(Float64(z / a) * fma(Float64(0.5 * y), Float64(x / z), Float64(-4.5 * t)));
	else
		tmp = Float64(fma(Float64(z * t), -9.0, Float64(x * y)) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+307], N[Not[LessEqual[t$95$1, 5e+249]], $MachinePrecision]], N[(N[(z / a), $MachinePrecision] * N[(N[(0.5 * y), $MachinePrecision] * N[(x / z), $MachinePrecision] + N[(-4.5 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] * -9.0 + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -5e307 or 4.9999999999999996e249 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 75.5%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a}} \]

   5. Applied rewrites 86.0%

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

   7. Applied rewrites 90.1%

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

   if -5e307 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 4.9999999999999996e249

   1. Initial program 97.3%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 97.3

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

   4. Applied rewrites 97.3%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lower-fma.f64 97.3

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 97.3

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 97.3

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

   6. Applied rewrites 97.3%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+307} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+249}\right):\\ \;\;\;\;\frac{z}{a} \cdot \mathsf{fma}\left(0.5 \cdot y, \frac{x}{z}, -4.5 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot t, -9, x \cdot y\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+39} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+118}\right):\\ \;\;\;\;\left(\frac{z}{a} \cdot -4.5\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{a} \cdot 0.5\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (or (<= t_1 -4e+39) (not (<= t_1 5e+118)))
     (* (* (/ z a) -4.5) t)
     (* (* (/ x a) 0.5) y))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if ((t_1 <= -4e+39) || !(t_1 <= 5e+118)) {
		tmp = ((z / a) * -4.5) * t;
	} 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.
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 <= (-4d+39)) .or. (.not. (t_1 <= 5d+118))) then
        tmp = ((z / a) * (-4.5d0)) * t
    else
        tmp = ((x / a) * 0.5d0) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if ((t_1 <= -4e+39) || !(t_1 <= 5e+118)) {
		tmp = ((z / a) * -4.5) * t;
	} else {
		tmp = ((x / a) * 0.5) * y;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if (t_1 <= -4e+39) or not (t_1 <= 5e+118):
		tmp = ((z / a) * -4.5) * t
	else:
		tmp = ((x / a) * 0.5) * y
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if ((t_1 <= -4e+39) || !(t_1 <= 5e+118))
		tmp = Float64(Float64(Float64(z / a) * -4.5) * t);
	else
		tmp = Float64(Float64(Float64(x / a) * 0.5) * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if ((t_1 <= -4e+39) || ~((t_1 <= 5e+118)))
		tmp = ((z / a) * -4.5) * t;
	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.
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[Or[LessEqual[t$95$1, -4e+39], N[Not[LessEqual[t$95$1, 5e+118]], $MachinePrecision]], N[(N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision] * t), $MachinePrecision], N[(N[(N[(x / a), $MachinePrecision] * 0.5), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -3.99999999999999976e39 or 4.99999999999999972e118 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 89.6%

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 78.9

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

   5. Applied rewrites 78.9%

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

   if -3.99999999999999976e39 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 4.99999999999999972e118

   1. Initial program 92.6%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 71.9

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

   5. Applied rewrites 71.9%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -4 \cdot 10^{+39} \lor \neg \left(\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+118}\right):\\ \;\;\;\;\left(\frac{z}{a} \cdot -4.5\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{a} \cdot 0.5\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+39} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+118}\right):\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{a} \cdot 0.5\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (or (<= t_1 -4e+39) (not (<= t_1 5e+118)))
     (* z (/ (* -4.5 t) a))
     (* (* (/ x a) 0.5) y))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if ((t_1 <= -4e+39) || !(t_1 <= 5e+118)) {
		tmp = z * ((-4.5 * t) / 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.
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 <= (-4d+39)) .or. (.not. (t_1 <= 5d+118))) then
        tmp = z * (((-4.5d0) * t) / a)
    else
        tmp = ((x / a) * 0.5d0) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if ((t_1 <= -4e+39) || !(t_1 <= 5e+118)) {
		tmp = z * ((-4.5 * t) / a);
	} else {
		tmp = ((x / a) * 0.5) * y;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if (t_1 <= -4e+39) or not (t_1 <= 5e+118):
		tmp = z * ((-4.5 * t) / a)
	else:
		tmp = ((x / a) * 0.5) * y
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if ((t_1 <= -4e+39) || !(t_1 <= 5e+118))
		tmp = Float64(z * Float64(Float64(-4.5 * t) / a));
	else
		tmp = Float64(Float64(Float64(x / a) * 0.5) * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if ((t_1 <= -4e+39) || ~((t_1 <= 5e+118)))
		tmp = z * ((-4.5 * t) / 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.
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[Or[LessEqual[t$95$1, -4e+39], N[Not[LessEqual[t$95$1, 5e+118]], $MachinePrecision]], N[(z * N[(N[(-4.5 * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / a), $MachinePrecision] * 0.5), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -3.99999999999999976e39 or 4.99999999999999972e118 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a}} \]

   5. Applied rewrites 90.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 77.9%

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

   10. Applied rewrites 80.6%

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

   if -3.99999999999999976e39 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 4.99999999999999972e118

   1. Initial program 92.6%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 71.9

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

   5. Applied rewrites 71.9%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -4 \cdot 10^{+39} \lor \neg \left(\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+118}\right):\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{a} \cdot 0.5\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+39} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+118}\right):\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{0.5}{a}\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (or (<= t_1 -4e+39) (not (<= t_1 5e+118)))
     (* z (/ (* -4.5 t) a))
     (* (* x (/ 0.5 a)) y))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if ((t_1 <= -4e+39) || !(t_1 <= 5e+118)) {
		tmp = z * ((-4.5 * t) / a);
	} else {
		tmp = (x * (0.5 / a)) * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * 9.0d0) * t
    if ((t_1 <= (-4d+39)) .or. (.not. (t_1 <= 5d+118))) then
        tmp = z * (((-4.5d0) * t) / a)
    else
        tmp = (x * (0.5d0 / a)) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if ((t_1 <= -4e+39) || !(t_1 <= 5e+118)) {
		tmp = z * ((-4.5 * t) / a);
	} else {
		tmp = (x * (0.5 / a)) * y;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if (t_1 <= -4e+39) or not (t_1 <= 5e+118):
		tmp = z * ((-4.5 * t) / a)
	else:
		tmp = (x * (0.5 / a)) * y
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if ((t_1 <= -4e+39) || !(t_1 <= 5e+118))
		tmp = Float64(z * Float64(Float64(-4.5 * t) / a));
	else
		tmp = Float64(Float64(x * Float64(0.5 / a)) * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if ((t_1 <= -4e+39) || ~((t_1 <= 5e+118)))
		tmp = z * ((-4.5 * t) / a);
	else
		tmp = (x * (0.5 / a)) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+39], N[Not[LessEqual[t$95$1, 5e+118]], $MachinePrecision]], N[(z * N[(N[(-4.5 * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(0.5 / a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -3.99999999999999976e39 or 4.99999999999999972e118 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a}} \]

   5. Applied rewrites 90.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 77.9%

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

   10. Applied rewrites 80.6%

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

   if -3.99999999999999976e39 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 4.99999999999999972e118

   1. Initial program 92.6%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 71.9

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

   5. Applied rewrites 71.9%

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

   7. Applied rewrites 71.9%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -4 \cdot 10^{+39} \lor \neg \left(\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+118}\right):\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{0.5}{a}\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+44} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+118}\right):\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (or (<= t_1 -2e+44) (not (<= t_1 5e+118)))
     (* z (/ (* -4.5 t) a))
     (* (* x y) (/ 0.5 a)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if ((t_1 <= -2e+44) || !(t_1 <= 5e+118)) {
		tmp = z * ((-4.5 * t) / a);
	} else {
		tmp = (x * y) * (0.5 / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * 9.0d0) * t
    if ((t_1 <= (-2d+44)) .or. (.not. (t_1 <= 5d+118))) then
        tmp = z * (((-4.5d0) * t) / a)
    else
        tmp = (x * y) * (0.5d0 / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if ((t_1 <= -2e+44) || !(t_1 <= 5e+118)) {
		tmp = z * ((-4.5 * t) / a);
	} else {
		tmp = (x * y) * (0.5 / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if (t_1 <= -2e+44) or not (t_1 <= 5e+118):
		tmp = z * ((-4.5 * t) / a)
	else:
		tmp = (x * y) * (0.5 / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if ((t_1 <= -2e+44) || !(t_1 <= 5e+118))
		tmp = Float64(z * Float64(Float64(-4.5 * t) / a));
	else
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if ((t_1 <= -2e+44) || ~((t_1 <= 5e+118)))
		tmp = z * ((-4.5 * t) / a);
	else
		tmp = (x * 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.
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[Or[LessEqual[t$95$1, -2e+44], N[Not[LessEqual[t$95$1, 5e+118]], $MachinePrecision]], N[(z * N[(N[(-4.5 * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -2.0000000000000002e44 or 4.99999999999999972e118 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a}} \]

   5. Applied rewrites 91.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 78.3%

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

   10. Applied rewrites 81.1%

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

   if -2.0000000000000002e44 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 4.99999999999999972e118

   1. Initial program 92.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 71.3

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

   5. Applied rewrites 71.3%

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

   7. Applied rewrites 70.4%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -2 \cdot 10^{+44} \lor \neg \left(\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+118}\right):\\ \;\;\;\;z \cdot \frac{-4.5 \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+224}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot t, -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{a} \cdot -4.5\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* (* z 9.0) t) 2e+224)
   (/ (fma (* z t) -9.0 (* x y)) (* a 2.0))
   (* (* (/ z a) -4.5) t)))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * 9.0) * t) <= 2e+224) {
		tmp = fma((z * t), -9.0, (x * y)) / (a * 2.0);
	} else {
		tmp = ((z / a) * -4.5) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(z * 9.0) * t) <= 2e+224)
		tmp = Float64(fma(Float64(z * t), -9.0, Float64(x * y)) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(z / a) * -4.5) * t);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision], 2e+224], N[(N[(N[(z * t), $MachinePrecision] * -9.0 + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.99999999999999994e224

   1. Initial program 93.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 93.0

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

   4. Applied rewrites 93.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lower-fma.f64 93.0

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 93.0

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 93.0

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

   6. Applied rewrites 93.0%

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

   if 1.99999999999999994e224 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 75.5%

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 99.8

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

   5. Applied rewrites 99.8%

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

Alternative 9: 93.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+224}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, \left(t \cdot z\right) \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{a} \cdot -4.5\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* (* z 9.0) t) 2e+224)
   (/ (fma y x (* (* t z) -9.0)) (* a 2.0))
   (* (* (/ z a) -4.5) t)))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * 9.0) * t) <= 2e+224) {
		tmp = fma(y, x, ((t * z) * -9.0)) / (a * 2.0);
	} else {
		tmp = ((z / a) * -4.5) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(z * 9.0) * t) <= 2e+224)
		tmp = Float64(fma(y, x, Float64(Float64(t * z) * -9.0)) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(z / a) * -4.5) * t);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision], 2e+224], N[(N[(y * x + N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.99999999999999994e224

   1. Initial program 93.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r* N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 93.0

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

   4. Applied rewrites 93.0%

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

   if 1.99999999999999994e224 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 75.5%

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 99.8

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

   5. Applied rewrites 99.8%

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

Alternative 10: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+224}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, -9, y \cdot x\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{a} \cdot -4.5\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* (* z 9.0) t) 2e+224)
   (* (fma (* t z) -9.0 (* y x)) (/ 0.5 a))
   (* (* (/ z a) -4.5) t)))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * 9.0) * t) <= 2e+224) {
		tmp = fma((t * z), -9.0, (y * x)) * (0.5 / a);
	} else {
		tmp = ((z / a) * -4.5) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(z * 9.0) * t) <= 2e+224)
		tmp = Float64(fma(Float64(t * z), -9.0, Float64(y * x)) * Float64(0.5 / a));
	else
		tmp = Float64(Float64(Float64(z / a) * -4.5) * t);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision], 2e+224], N[(N[(N[(t * z), $MachinePrecision] * -9.0 + N[(y * x), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.99999999999999994e224

   1. Initial program 93.0%

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

      1. lift-/.f64 N/A

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

      2. div-inv N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*r* N/A

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

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

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. associate-/r* N/A

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

      21. lower-/.f64 N/A

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

      22. metadata-eval 92.9

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

   4. Applied rewrites 92.9%

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

   if 1.99999999999999994e224 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 75.5%

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 99.8

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

   5. Applied rewrites 99.8%

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

Alternative 11: 52.7% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.4%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a} + \frac{1}{2} \cdot \frac{x \cdot y}{a}} \]

5. Applied rewrites 81.5%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 46.8%

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

10. Applied rewrites 48.1%

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

Developer Target 1: 93.3% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024314 
(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)))