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

Percentage Accurate: 91.8% → 96.8%

Time: 10.2s

Alternatives: 12

Speedup: 0.8×

• 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: 91.8% 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: 96.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot x - t \cdot \left(9 \cdot z\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, x, \left(-4.5 \cdot \frac{z}{y}\right) \cdot t\right)}{a} \cdot y\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-9 \cdot t, z, y \cdot x\right)}{a + a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, \frac{t}{a} \cdot 4.5, \left(\frac{0.5}{a} \cdot x\right) \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* y x) (* t (* 9.0 z)))))
   (if (<= t_1 (- INFINITY))
     (* (/ (fma 0.5 x (* (* -4.5 (/ z y)) t)) a) y)
     (if (<= t_1 5e+264)
       (/ (fma (* -9.0 t) z (* y x)) (+ a a))
       (fma (- z) (* (/ t a) 4.5) (* (* (/ 0.5 a) x) y))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * x) - (t * (9.0 * z));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (fma(0.5, x, ((-4.5 * (z / y)) * t)) / a) * y;
	} else if (t_1 <= 5e+264) {
		tmp = fma((-9.0 * t), z, (y * x)) / (a + a);
	} else {
		tmp = fma(-z, ((t / a) * 4.5), (((0.5 / a) * x) * y));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * x) - Float64(t * Float64(9.0 * z)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(fma(0.5, x, Float64(Float64(-4.5 * Float64(z / y)) * t)) / a) * y);
	elseif (t_1 <= 5e+264)
		tmp = Float64(fma(Float64(-9.0 * t), z, Float64(y * x)) / Float64(a + a));
	else
		tmp = fma(Float64(-z), Float64(Float64(t / a) * 4.5), Float64(Float64(Float64(0.5 / a) * x) * y));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * x), $MachinePrecision] - N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(0.5 * x + N[(N[(-4.5 * N[(z / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 5e+264], N[(N[(N[(-9.0 * t), $MachinePrecision] * z + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(a + a), $MachinePrecision]), $MachinePrecision], N[((-z) * N[(N[(t / a), $MachinePrecision] * 4.5), $MachinePrecision] + N[(N[(N[(0.5 / a), $MachinePrecision] * x), $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)) < -inf.0

   1. Initial program 74.8%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

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

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

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

      6. distribute-neg-in N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 91.6%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 5.00000000000000033e264

   1. Initial program 99.1%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. metadata-eval 99.1

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 99.1

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

   4. Applied rewrites 99.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 99.1

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

   6. Applied rewrites 99.1%

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

   if 5.00000000000000033e264 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 71.5%

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

      1. lift-/.f64 N/A

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

      2. 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 95.1%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x - t \cdot \left(9 \cdot z\right) \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, x, \left(-4.5 \cdot \frac{z}{y}\right) \cdot t\right)}{a} \cdot y\\ \mathbf{elif}\;y \cdot x - t \cdot \left(9 \cdot z\right) \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-9 \cdot t, z, y \cdot x\right)}{a + a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, \frac{t}{a} \cdot 4.5, \left(\frac{0.5}{a} \cdot x\right) \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(0.5, x, \left(-4.5 \cdot \frac{z}{y}\right) \cdot t\right)}{a} \cdot y\\ t_2 := y \cdot x - t \cdot \left(9 \cdot z\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+264}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-9 \cdot t, z, y \cdot x\right)}{a + a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (fma 0.5 x (* (* -4.5 (/ z y)) t)) a) y))
        (t_2 (- (* y x) (* t (* 9.0 z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 2e+264) (/ (fma (* -9.0 t) z (* y x)) (+ a a)) t_1))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (fma(0.5, x, ((-4.5 * (z / y)) * t)) / a) * y;
	double t_2 = (y * x) - (t * (9.0 * z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 2e+264) {
		tmp = fma((-9.0 * t), z, (y * x)) / (a + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(fma(0.5, x, Float64(Float64(-4.5 * Float64(z / y)) * t)) / a) * y)
	t_2 = Float64(Float64(y * x) - Float64(t * Float64(9.0 * z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 2e+264)
		tmp = Float64(fma(Float64(-9.0 * t), z, Float64(y * x)) / Float64(a + 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.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(0.5 * x + N[(N[(-4.5 * N[(z / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * x), $MachinePrecision] - N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 2e+264], N[(N[(N[(-9.0 * t), $MachinePrecision] * z + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(a + 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)) < -inf.0 or 2.00000000000000009e264 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 73.3%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

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

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

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

      6. distribute-neg-in N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 92.6%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 2.00000000000000009e264

   1. Initial program 99.1%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. metadata-eval 99.1

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 99.1

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

   4. Applied rewrites 99.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 99.1

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

   6. Applied rewrites 99.1%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x - t \cdot \left(9 \cdot z\right) \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, x, \left(-4.5 \cdot \frac{z}{y}\right) \cdot t\right)}{a} \cdot y\\ \mathbf{elif}\;y \cdot x - t \cdot \left(9 \cdot z\right) \leq 2 \cdot 10^{+264}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-9 \cdot t, z, y \cdot x\right)}{a + a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, x, \left(-4.5 \cdot \frac{z}{y}\right) \cdot t\right)}{a} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -5 \cdot 10^{+83}:\\ \;\;\;\;\left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;y \cdot x \leq 5 \cdot 10^{-291}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-4.5 \cdot t\right)\\ \mathbf{elif}\;y \cdot x \leq 10^{+28}:\\ \;\;\;\;\left(\frac{t}{a} \cdot -4.5\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot y}{a} \cdot x\\ \end{array} \end{array} \]

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 (<= (* y x) -5e+83)
   (* (* 0.5 y) (/ x a))
   (if (<= (* y x) 5e-291)
     (* (/ z a) (* -4.5 t))
     (if (<= (* y x) 1e+28) (* (* (/ t a) -4.5) z) (* (/ (* 0.5 y) a) x)))))

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 ((y * x) <= -5e+83) {
		tmp = (0.5 * y) * (x / a);
	} else if ((y * x) <= 5e-291) {
		tmp = (z / a) * (-4.5 * t);
	} else if ((y * x) <= 1e+28) {
		tmp = ((t / a) * -4.5) * z;
	} else {
		tmp = ((0.5 * y) / a) * x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y * x) <= (-5d+83)) then
        tmp = (0.5d0 * y) * (x / a)
    else if ((y * x) <= 5d-291) then
        tmp = (z / a) * ((-4.5d0) * t)
    else if ((y * x) <= 1d+28) then
        tmp = ((t / a) * (-4.5d0)) * z
    else
        tmp = ((0.5d0 * y) / a) * x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -5e+83) {
		tmp = (0.5 * y) * (x / a);
	} else if ((y * x) <= 5e-291) {
		tmp = (z / a) * (-4.5 * t);
	} else if ((y * x) <= 1e+28) {
		tmp = ((t / a) * -4.5) * z;
	} else {
		tmp = ((0.5 * y) / a) * x;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (y * x) <= -5e+83:
		tmp = (0.5 * y) * (x / a)
	elif (y * x) <= 5e-291:
		tmp = (z / a) * (-4.5 * t)
	elif (y * x) <= 1e+28:
		tmp = ((t / a) * -4.5) * z
	else:
		tmp = ((0.5 * y) / a) * x
	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(y * x) <= -5e+83)
		tmp = Float64(Float64(0.5 * y) * Float64(x / a));
	elseif (Float64(y * x) <= 5e-291)
		tmp = Float64(Float64(z / a) * Float64(-4.5 * t));
	elseif (Float64(y * x) <= 1e+28)
		tmp = Float64(Float64(Float64(t / a) * -4.5) * z);
	else
		tmp = Float64(Float64(Float64(0.5 * y) / a) * x);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y * x) <= -5e+83)
		tmp = (0.5 * y) * (x / a);
	elseif ((y * x) <= 5e-291)
		tmp = (z / a) * (-4.5 * t);
	elseif ((y * x) <= 1e+28)
		tmp = ((t / a) * -4.5) * z;
	else
		tmp = ((0.5 * y) / a) * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], -5e+83], N[(N[(0.5 * y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 5e-291], N[(N[(z / a), $MachinePrecision] * N[(-4.5 * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 1e+28], N[(N[(N[(t / a), $MachinePrecision] * -4.5), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[(0.5 * y), $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -5.00000000000000029e83

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 81.7

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a} \cdot 0.5 \]

   5. Applied rewrites 81.7%

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

   7. Applied rewrites 86.4%

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

   if -5.00000000000000029e83 < (*.f64 x y) < 5.0000000000000003e-291

   1. Initial program 94.6%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 75.2

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

   5. Applied rewrites 75.2%

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

   7. Applied rewrites 76.1%

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

   if 5.0000000000000003e-291 < (*.f64 x y) < 9.99999999999999958e27

   1. Initial program 97.9%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 75.4

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

   5. Applied rewrites 75.4%

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

   7. Applied rewrites 69.7%

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

   if 9.99999999999999958e27 < (*.f64 x y)

   1. Initial program 82.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

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

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

      7. distribute-neg-in N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 92.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 83.9%

      \[\leadsto \frac{0.5 \cdot y}{a} \cdot x \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -5 \cdot 10^{+83}:\\ \;\;\;\;\left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;y \cdot x \leq 5 \cdot 10^{-291}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-4.5 \cdot t\right)\\ \mathbf{elif}\;y \cdot x \leq 10^{+28}:\\ \;\;\;\;\left(\frac{t}{a} \cdot -4.5\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot y}{a} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -5 \cdot 10^{+83}:\\ \;\;\;\;\left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;y \cdot x \leq 5 \cdot 10^{-291}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-4.5 \cdot t\right)\\ \mathbf{elif}\;y \cdot x \leq 10^{+28}:\\ \;\;\;\;\left(\frac{t}{a} \cdot -4.5\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.5}{a} \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y x) -5e+83)
   (* (* 0.5 y) (/ x a))
   (if (<= (* y x) 5e-291)
     (* (/ z a) (* -4.5 t))
     (if (<= (* y x) 1e+28) (* (* (/ t a) -4.5) z) (* (* (/ 0.5 a) y) x)))))

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 ((y * x) <= -5e+83) {
		tmp = (0.5 * y) * (x / a);
	} else if ((y * x) <= 5e-291) {
		tmp = (z / a) * (-4.5 * t);
	} else if ((y * x) <= 1e+28) {
		tmp = ((t / a) * -4.5) * z;
	} 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.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y * x) <= (-5d+83)) then
        tmp = (0.5d0 * y) * (x / a)
    else if ((y * x) <= 5d-291) then
        tmp = (z / a) * ((-4.5d0) * t)
    else if ((y * x) <= 1d+28) then
        tmp = ((t / a) * (-4.5d0)) * z
    else
        tmp = ((0.5d0 / a) * y) * x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -5e+83) {
		tmp = (0.5 * y) * (x / a);
	} else if ((y * x) <= 5e-291) {
		tmp = (z / a) * (-4.5 * t);
	} else if ((y * x) <= 1e+28) {
		tmp = ((t / a) * -4.5) * z;
	} else {
		tmp = ((0.5 / a) * y) * x;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (y * x) <= -5e+83:
		tmp = (0.5 * y) * (x / a)
	elif (y * x) <= 5e-291:
		tmp = (z / a) * (-4.5 * t)
	elif (y * x) <= 1e+28:
		tmp = ((t / a) * -4.5) * z
	else:
		tmp = ((0.5 / a) * y) * x
	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(y * x) <= -5e+83)
		tmp = Float64(Float64(0.5 * y) * Float64(x / a));
	elseif (Float64(y * x) <= 5e-291)
		tmp = Float64(Float64(z / a) * Float64(-4.5 * t));
	elseif (Float64(y * x) <= 1e+28)
		tmp = Float64(Float64(Float64(t / a) * -4.5) * z);
	else
		tmp = Float64(Float64(Float64(0.5 / a) * y) * x);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y * x) <= -5e+83)
		tmp = (0.5 * y) * (x / a);
	elseif ((y * x) <= 5e-291)
		tmp = (z / a) * (-4.5 * t);
	elseif ((y * x) <= 1e+28)
		tmp = ((t / a) * -4.5) * z;
	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.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], -5e+83], N[(N[(0.5 * y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 5e-291], N[(N[(z / a), $MachinePrecision] * N[(-4.5 * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 1e+28], N[(N[(N[(t / a), $MachinePrecision] * -4.5), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[(0.5 / a), $MachinePrecision] * y), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -5.00000000000000029e83

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 81.7

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a} \cdot 0.5 \]

   5. Applied rewrites 81.7%

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

   7. Applied rewrites 86.4%

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

   if -5.00000000000000029e83 < (*.f64 x y) < 5.0000000000000003e-291

   1. Initial program 94.6%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 75.2

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

   5. Applied rewrites 75.2%

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

   7. Applied rewrites 76.1%

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

   if 5.0000000000000003e-291 < (*.f64 x y) < 9.99999999999999958e27

   1. Initial program 97.9%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 75.4

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

   5. Applied rewrites 75.4%

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

   7. Applied rewrites 69.7%

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

   if 9.99999999999999958e27 < (*.f64 x y)

   1. Initial program 82.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 71.8

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a} \cdot 0.5 \]

   5. Applied rewrites 71.8%

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

   7. Applied rewrites 83.8%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -5 \cdot 10^{+83}:\\ \;\;\;\;\left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;y \cdot x \leq 5 \cdot 10^{-291}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-4.5 \cdot t\right)\\ \mathbf{elif}\;y \cdot x \leq 10^{+28}:\\ \;\;\;\;\left(\frac{t}{a} \cdot -4.5\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.5}{a} \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(\frac{0.5}{a} \cdot y\right) \cdot x\\ \mathbf{if}\;y \cdot x \leq -1 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot x \leq 5 \cdot 10^{-291}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-4.5 \cdot t\right)\\ \mathbf{elif}\;y \cdot x \leq 10^{+28}:\\ \;\;\;\;\left(\frac{t}{a} \cdot -4.5\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* (/ 0.5 a) y) x)))
   (if (<= (* y x) -1e-10)
     t_1
     (if (<= (* y x) 5e-291)
       (* (/ z a) (* -4.5 t))
       (if (<= (* y x) 1e+28) (* (* (/ t a) -4.5) z) t_1)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = ((0.5 / a) * y) * x;
	double tmp;
	if ((y * x) <= -1e-10) {
		tmp = t_1;
	} else if ((y * x) <= 5e-291) {
		tmp = (z / a) * (-4.5 * t);
	} else if ((y * x) <= 1e+28) {
		tmp = ((t / a) * -4.5) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((0.5d0 / a) * y) * x
    if ((y * x) <= (-1d-10)) then
        tmp = t_1
    else if ((y * x) <= 5d-291) then
        tmp = (z / a) * ((-4.5d0) * t)
    else if ((y * x) <= 1d+28) then
        tmp = ((t / a) * (-4.5d0)) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((0.5 / a) * y) * x;
	double tmp;
	if ((y * x) <= -1e-10) {
		tmp = t_1;
	} else if ((y * x) <= 5e-291) {
		tmp = (z / a) * (-4.5 * t);
	} else if ((y * x) <= 1e+28) {
		tmp = ((t / a) * -4.5) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = ((0.5 / a) * y) * x
	tmp = 0
	if (y * x) <= -1e-10:
		tmp = t_1
	elif (y * x) <= 5e-291:
		tmp = (z / a) * (-4.5 * t)
	elif (y * x) <= 1e+28:
		tmp = ((t / a) * -4.5) * z
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(0.5 / a) * y) * x)
	tmp = 0.0
	if (Float64(y * x) <= -1e-10)
		tmp = t_1;
	elseif (Float64(y * x) <= 5e-291)
		tmp = Float64(Float64(z / a) * Float64(-4.5 * t));
	elseif (Float64(y * x) <= 1e+28)
		tmp = Float64(Float64(Float64(t / a) * -4.5) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = ((0.5 / a) * y) * x;
	tmp = 0.0;
	if ((y * x) <= -1e-10)
		tmp = t_1;
	elseif ((y * x) <= 5e-291)
		tmp = (z / a) * (-4.5 * t);
	elseif ((y * x) <= 1e+28)
		tmp = ((t / a) * -4.5) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(0.5 / a), $MachinePrecision] * y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[N[(y * x), $MachinePrecision], -1e-10], t$95$1, If[LessEqual[N[(y * x), $MachinePrecision], 5e-291], N[(N[(z / a), $MachinePrecision] * N[(-4.5 * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 1e+28], N[(N[(N[(t / a), $MachinePrecision] * -4.5), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.00000000000000004e-10 or 9.99999999999999958e27 < (*.f64 x y)

   1. Initial program 87.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 75.6

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a} \cdot 0.5 \]

   5. Applied rewrites 75.6%

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

   7. Applied rewrites 79.1%

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

   if -1.00000000000000004e-10 < (*.f64 x y) < 5.0000000000000003e-291

   1. Initial program 93.8%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 81.9

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

   5. Applied rewrites 81.9%

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

   7. Applied rewrites 83.0%

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

   if 5.0000000000000003e-291 < (*.f64 x y) < 9.99999999999999958e27

   1. Initial program 97.9%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 75.4

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

   5. Applied rewrites 75.4%

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

   7. Applied rewrites 69.7%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -1 \cdot 10^{-10}:\\ \;\;\;\;\left(\frac{0.5}{a} \cdot y\right) \cdot x\\ \mathbf{elif}\;y \cdot x \leq 5 \cdot 10^{-291}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-4.5 \cdot t\right)\\ \mathbf{elif}\;y \cdot x \leq 10^{+28}:\\ \;\;\;\;\left(\frac{t}{a} \cdot -4.5\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.5}{a} \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -1 \cdot 10^{-10}:\\ \;\;\;\;\frac{y \cdot x}{a} \cdot 0.5\\ \mathbf{elif}\;y \cdot x \leq 10^{+28}:\\ \;\;\;\;\frac{t \cdot z}{a} \cdot -4.5\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot y}{a} \cdot x\\ \end{array} \end{array} \]

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 (<= (* y x) -1e-10)
   (* (/ (* y x) a) 0.5)
   (if (<= (* y x) 1e+28) (* (/ (* t z) a) -4.5) (* (/ (* 0.5 y) a) x))))

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 ((y * x) <= -1e-10) {
		tmp = ((y * x) / a) * 0.5;
	} else if ((y * x) <= 1e+28) {
		tmp = ((t * z) / a) * -4.5;
	} else {
		tmp = ((0.5 * y) / a) * x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y * x) <= (-1d-10)) then
        tmp = ((y * x) / a) * 0.5d0
    else if ((y * x) <= 1d+28) then
        tmp = ((t * z) / a) * (-4.5d0)
    else
        tmp = ((0.5d0 * y) / a) * x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -1e-10) {
		tmp = ((y * x) / a) * 0.5;
	} else if ((y * x) <= 1e+28) {
		tmp = ((t * z) / a) * -4.5;
	} else {
		tmp = ((0.5 * y) / a) * x;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (y * x) <= -1e-10:
		tmp = ((y * x) / a) * 0.5
	elif (y * x) <= 1e+28:
		tmp = ((t * z) / a) * -4.5
	else:
		tmp = ((0.5 * y) / a) * x
	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(y * x) <= -1e-10)
		tmp = Float64(Float64(Float64(y * x) / a) * 0.5);
	elseif (Float64(y * x) <= 1e+28)
		tmp = Float64(Float64(Float64(t * z) / a) * -4.5);
	else
		tmp = Float64(Float64(Float64(0.5 * y) / a) * x);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y * x) <= -1e-10)
		tmp = ((y * x) / a) * 0.5;
	elseif ((y * x) <= 1e+28)
		tmp = ((t * z) / a) * -4.5;
	else
		tmp = ((0.5 * y) / a) * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], -1e-10], N[(N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision] * 0.5), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 1e+28], N[(N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision] * -4.5), $MachinePrecision], N[(N[(N[(0.5 * y), $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.00000000000000004e-10

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 78.4

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a} \cdot 0.5 \]

   5. Applied rewrites 78.4%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a} \cdot 0.5} \]

   if -1.00000000000000004e-10 < (*.f64 x y) < 9.99999999999999958e27

   1. Initial program 95.4%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 79.4

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

   5. Applied rewrites 79.4%

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

   if 9.99999999999999958e27 < (*.f64 x y)

   1. Initial program 82.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

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

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

      7. distribute-neg-in N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 92.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 83.9%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -1 \cdot 10^{-10}:\\ \;\;\;\;\frac{y \cdot x}{a} \cdot 0.5\\ \mathbf{elif}\;y \cdot x \leq 10^{+28}:\\ \;\;\;\;\frac{t \cdot z}{a} \cdot -4.5\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot y}{a} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -5 \cdot 10^{+83}:\\ \;\;\;\;\left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;y \cdot x \leq 10^{+28}:\\ \;\;\;\;\frac{t \cdot z}{a} \cdot -4.5\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot y}{a} \cdot x\\ \end{array} \end{array} \]

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 (<= (* y x) -5e+83)
   (* (* 0.5 y) (/ x a))
   (if (<= (* y x) 1e+28) (* (/ (* t z) a) -4.5) (* (/ (* 0.5 y) a) x))))

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 ((y * x) <= -5e+83) {
		tmp = (0.5 * y) * (x / a);
	} else if ((y * x) <= 1e+28) {
		tmp = ((t * z) / a) * -4.5;
	} else {
		tmp = ((0.5 * y) / a) * x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y * x) <= (-5d+83)) then
        tmp = (0.5d0 * y) * (x / a)
    else if ((y * x) <= 1d+28) then
        tmp = ((t * z) / a) * (-4.5d0)
    else
        tmp = ((0.5d0 * y) / a) * x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -5e+83) {
		tmp = (0.5 * y) * (x / a);
	} else if ((y * x) <= 1e+28) {
		tmp = ((t * z) / a) * -4.5;
	} else {
		tmp = ((0.5 * y) / a) * x;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (y * x) <= -5e+83:
		tmp = (0.5 * y) * (x / a)
	elif (y * x) <= 1e+28:
		tmp = ((t * z) / a) * -4.5
	else:
		tmp = ((0.5 * y) / a) * x
	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(y * x) <= -5e+83)
		tmp = Float64(Float64(0.5 * y) * Float64(x / a));
	elseif (Float64(y * x) <= 1e+28)
		tmp = Float64(Float64(Float64(t * z) / a) * -4.5);
	else
		tmp = Float64(Float64(Float64(0.5 * y) / a) * x);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y * x) <= -5e+83)
		tmp = (0.5 * y) * (x / a);
	elseif ((y * x) <= 1e+28)
		tmp = ((t * z) / a) * -4.5;
	else
		tmp = ((0.5 * y) / a) * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], -5e+83], N[(N[(0.5 * y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 1e+28], N[(N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision] * -4.5), $MachinePrecision], N[(N[(N[(0.5 * y), $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.00000000000000029e83

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 81.7

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a} \cdot 0.5 \]

   5. Applied rewrites 81.7%

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

   7. Applied rewrites 86.4%

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

   if -5.00000000000000029e83 < (*.f64 x y) < 9.99999999999999958e27

   1. Initial program 95.8%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 75.3

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

   5. Applied rewrites 75.3%

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

   if 9.99999999999999958e27 < (*.f64 x y)

   1. Initial program 82.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

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

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

      7. distribute-neg-in N/A

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

      8. lower-*.f64 N/A

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

   5. Applied rewrites 92.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 83.9%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -5 \cdot 10^{+83}:\\ \;\;\;\;\left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;y \cdot x \leq 10^{+28}:\\ \;\;\;\;\frac{t \cdot z}{a} \cdot -4.5\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot y}{a} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq 2 \cdot 10^{+276}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-9 \cdot t, z, y \cdot x\right)}{a + a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.5}{a} \cdot y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y x) 2e+276)
   (/ (fma (* -9.0 t) z (* y x)) (+ a a))
   (* (* (/ 0.5 a) y) x)))

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 ((y * x) <= 2e+276) {
		tmp = fma((-9.0 * t), z, (y * x)) / (a + a);
	} else {
		tmp = ((0.5 / a) * y) * x;
	}
	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(y * x) <= 2e+276)
		tmp = Float64(fma(Float64(-9.0 * t), z, Float64(y * x)) / Float64(a + a));
	else
		tmp = Float64(Float64(Float64(0.5 / a) * y) * x);
	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[(y * x), $MachinePrecision], 2e+276], N[(N[(N[(-9.0 * t), $MachinePrecision] * z + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(a + a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(0.5 / a), $MachinePrecision] * y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 2.0000000000000001e276

   1. Initial program 94.1%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-fma.f64 N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. metadata-eval 94.1

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 94.1

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

   4. Applied rewrites 94.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 94.1

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

   6. Applied rewrites 94.1%

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

   if 2.0000000000000001e276 < (*.f64 x y)

   1. Initial program 61.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 61.8

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a} \cdot 0.5 \]

   5. Applied rewrites 61.8%

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

   7. Applied rewrites 99.8%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq 2 \cdot 10^{+276}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-9 \cdot t, z, y \cdot x\right)}{a + a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.5}{a} \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3.2 \cdot 10^{-201}:\\ \;\;\;\;\left(\frac{z}{a} \cdot -4.5\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{a} \cdot -4.5\right) \cdot z\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (<= t 3.2e-201) (* (* (/ z a) -4.5) t) (* (* (/ t a) -4.5) z)))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 3.2e-201) {
		tmp = ((z / a) * -4.5) * t;
	} else {
		tmp = ((t / a) * -4.5) * z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 3.2d-201) then
        tmp = ((z / a) * (-4.5d0)) * t
    else
        tmp = ((t / a) * (-4.5d0)) * z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 3.2e-201) {
		tmp = ((z / a) * -4.5) * t;
	} else {
		tmp = ((t / a) * -4.5) * z;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if t <= 3.2e-201:
		tmp = ((z / a) * -4.5) * t
	else:
		tmp = ((t / a) * -4.5) * z
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 3.2e-201)
		tmp = Float64(Float64(Float64(z / a) * -4.5) * t);
	else
		tmp = Float64(Float64(Float64(t / a) * -4.5) * z);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 (t <= 3.2e-201)
		tmp = ((z / a) * -4.5) * t;
	else
		tmp = ((t / a) * -4.5) * z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[t, 3.2e-201], N[(N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision] * t), $MachinePrecision], N[(N[(N[(t / a), $MachinePrecision] * -4.5), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.2000000000000001e-201

   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 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 45.2

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

   5. Applied rewrites 45.2%

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

   7. Applied rewrites 47.5%

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

   if 3.2000000000000001e-201 < 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

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 54.3

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

   5. Applied rewrites 54.3%

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

   7. Applied rewrites 56.1%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.2 \cdot 10^{-201}:\\ \;\;\;\;\left(\frac{z}{a} \cdot -4.5\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{a} \cdot -4.5\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.1% accurate, 1.6× speedup

Math

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

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 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) {
	return ((z / a) * -4.5) * t;
}

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 / a) * (-4.5d0)) * t
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 / a) * -4.5) * t;
}

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 / a) * -4.5) * t

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(Float64(Float64(z / a) * -4.5) * t)
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 / a) * -4.5) * t;
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[(N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision] * t), $MachinePrecision]

Derivation

1. Initial program 91.3%

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

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 N/A

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

   4. lower-*.f64 48.7

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

5. Applied rewrites 48.7%

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

7. Applied rewrites 50.8%

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

8. Final simplification 50.8%

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

Alternative 11: 14.2% accurate, 1.7× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* (* -2.0 a) (* (* t z) 9.0)))

C

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

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 = ((-2.0d0) * a) * ((t * z) * 9.0d0)
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 (-2.0 * a) * ((t * z) * 9.0);
}

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 (-2.0 * a) * ((t * z) * 9.0)

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(Float64(-2.0 * a) * Float64(Float64(t * z) * 9.0))
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 = (-2.0 * a) * ((t * z) * 9.0);
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[(N[(-2.0 * a), $MachinePrecision] * N[(N[(t * z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.3%

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

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 N/A

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

   4. lower-*.f64 48.7

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

5. Applied rewrites 48.7%

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

7. Applied rewrites 50.8%

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

9. Applied rewrites 13.2%

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

10. Final simplification 13.2%

    \[\leadsto \left(-2 \cdot a\right) \cdot \left(\left(t \cdot z\right) \cdot 9\right) \]
11. Add Preprocessing

Alternative 12: 4.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ 18 \cdot \left(\left(t \cdot z\right) \cdot a\right) \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* 18.0 (* (* t z) a)))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return 18.0 * ((t * z) * a);
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = 18.0d0 * ((t * z) * a)
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return 18.0 * ((t * z) * a);
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return 18.0 * ((t * z) * a)

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(18.0 * Float64(Float64(t * z) * a))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = 18.0 * ((t * z) * a);
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(18.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.3%

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

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 N/A

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

   4. lower-*.f64 48.7

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

5. Applied rewrites 48.7%

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

7. Applied rewrites 50.8%

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

9. Applied rewrites 4.1%

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

10. Taylor expanded in z around 0

    \[\leadsto 18 \cdot \color{blue}{\left(a \cdot \left(t \cdot z\right)\right)} \]
11. Step-by-step derivation

12. Applied rewrites 4.1%

    \[\leadsto \left(\left(t \cdot z\right) \cdot a\right) \cdot \color{blue}{18} \]

13. Final simplification 4.1%

    \[\leadsto 18 \cdot \left(\left(t \cdot z\right) \cdot a\right) \]
14. Add Preprocessing

Developer Target 1: 93.6% 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 2024298 
(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)))