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

Percentage Accurate: 91.2% → 96.9%

Time: 11.4s

Alternatives: 12

Speedup: 0.6×

• 28.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+272}:\\ \;\;\;\;\mathsf{fma}\left(-z, \frac{t}{a} \cdot 4.5, \frac{y}{\frac{a \cdot 2}{x}}\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+239}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a \cdot 2}, y, \frac{z}{a} \cdot \left(t \cdot -4.5\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 -2e+272)
     (fma (- z) (* (/ t a) 4.5) (/ y (/ (* a 2.0) x)))
     (if (<= t_1 4e+239)
       (/ (fma z (* t -9.0) (* x y)) (* a 2.0))
       (fma (/ x (* a 2.0)) y (* (/ z a) (* t -4.5)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -2e+272) {
		tmp = fma(-z, ((t / a) * 4.5), (y / ((a * 2.0) / x)));
	} else if (t_1 <= 4e+239) {
		tmp = fma(z, (t * -9.0), (x * y)) / (a * 2.0);
	} else {
		tmp = fma((x / (a * 2.0)), y, ((z / a) * (t * -4.5)));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= -2e+272)
		tmp = fma(Float64(-z), Float64(Float64(t / a) * 4.5), Float64(y / Float64(Float64(a * 2.0) / x)));
	elseif (t_1 <= 4e+239)
		tmp = Float64(fma(z, Float64(t * -9.0), Float64(x * y)) / Float64(a * 2.0));
	else
		tmp = fma(Float64(x / Float64(a * 2.0)), y, Float64(Float64(z / a) * Float64(t * -4.5)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+272], N[((-z) * N[(N[(t / a), $MachinePrecision] * 4.5), $MachinePrecision] + N[(y / N[(N[(a * 2.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+239], N[(N[(z * N[(t * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision] * y + N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -2.0000000000000001e272

   1. Initial program 69.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. associate-/l* N/A

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

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

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. times-frac N/A

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

      18. lower-*.f64 N/A

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

      19. lower-/.f64 N/A

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

      20. metadata-eval N/A

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

   4. Applied rewrites 95.9%

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

      1. lift-*.f64 N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r/ N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 95.9

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

   6. Applied rewrites 95.9%

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

   if -2.0000000000000001e272 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 3.99999999999999996e239

   1. Initial program 98.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. div-inv N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-/r* N/A

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

      23. lower-/.f64 N/A

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

      24. metadata-eval 98.6

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

   4. Applied rewrites 98.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. associate-/r* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. un-div-inv N/A

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

      9. lower-/.f64 98.8

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

   6. Applied rewrites 98.8%

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

   if 3.99999999999999996e239 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 56.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-/l/ N/A

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

      15. distribute-neg-frac2 N/A

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

      16. lower-/.f64 N/A

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

   4. Applied rewrites 67.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. neg-mul-1 N/A

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

      4. times-frac N/A

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

      5. metadata-eval N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r/ N/A

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

      9. lift-/.f64 N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 90.3

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

   6. Applied rewrites 90.3%

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

Alternative 2: 97.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-z, \frac{t}{a} \cdot 4.5, x \cdot \frac{y}{a \cdot 2}\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+239}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a \cdot 2}, y, \frac{z}{a} \cdot \left(t \cdot -4.5\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 (- INFINITY))
     (fma (- z) (* (/ t a) 4.5) (* x (/ y (* a 2.0))))
     (if (<= t_1 4e+239)
       (/ (fma z (* t -9.0) (* x y)) (* a 2.0))
       (fma (/ x (* a 2.0)) y (* (/ z a) (* t -4.5)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma(-z, ((t / a) * 4.5), (x * (y / (a * 2.0))));
	} else if (t_1 <= 4e+239) {
		tmp = fma(z, (t * -9.0), (x * y)) / (a * 2.0);
	} else {
		tmp = fma((x / (a * 2.0)), y, ((z / a) * (t * -4.5)));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(Float64(-z), Float64(Float64(t / a) * 4.5), Float64(x * Float64(y / Float64(a * 2.0))));
	elseif (t_1 <= 4e+239)
		tmp = Float64(fma(z, Float64(t * -9.0), Float64(x * y)) / Float64(a * 2.0));
	else
		tmp = fma(Float64(x / Float64(a * 2.0)), y, Float64(Float64(z / a) * Float64(t * -4.5)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[((-z) * N[(N[(t / a), $MachinePrecision] * 4.5), $MachinePrecision] + N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+239], N[(N[(z * N[(t * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision] * y + N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $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 62.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. associate-/l* N/A

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

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

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. times-frac N/A

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

      18. lower-*.f64 N/A

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

      19. lower-/.f64 N/A

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

      20. metadata-eval N/A

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

   4. Applied rewrites 94.9%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 3.99999999999999996e239

   1. Initial program 98.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. div-inv N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-/r* N/A

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

      23. lower-/.f64 N/A

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

      24. metadata-eval 98.6

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

   4. Applied rewrites 98.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. associate-/r* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. un-div-inv N/A

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

      9. lower-/.f64 98.8

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

   6. Applied rewrites 98.8%

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

   if 3.99999999999999996e239 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 56.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-/l/ N/A

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

      15. distribute-neg-frac2 N/A

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

      16. lower-/.f64 N/A

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

   4. Applied rewrites 67.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. neg-mul-1 N/A

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

      4. times-frac N/A

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

      5. metadata-eval N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r/ N/A

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

      9. lift-/.f64 N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 90.3

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

   6. Applied rewrites 90.3%

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

Alternative 3: 96.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{a \cdot 2}, y, \frac{z}{a} \cdot \left(t \cdot -4.5\right)\right)\\ t_2 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+239}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x (* a 2.0)) y (* (/ z a) (* t -4.5))))
        (t_2 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 4e+239) (/ (fma z (* t -9.0) (* x y)) (* a 2.0)) t_1))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / (a * 2.0)), y, ((z / a) * (t * -4.5)));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 4e+239) {
		tmp = fma(z, (t * -9.0), (x * y)) / (a * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = fma(Float64(x / Float64(a * 2.0)), y, Float64(Float64(z / a) * Float64(t * -4.5)))
	t_2 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 4e+239)
		tmp = Float64(fma(z, Float64(t * -9.0), Float64(x * y)) / Float64(a * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision] * y + N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 4e+239], N[(N[(z * N[(t * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -inf.0 or 3.99999999999999996e239 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 57.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-/l/ N/A

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

      15. distribute-neg-frac2 N/A

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

      16. lower-/.f64 N/A

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

   4. Applied rewrites 66.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. neg-mul-1 N/A

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

      4. times-frac N/A

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

      5. metadata-eval N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r/ N/A

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

      9. lift-/.f64 N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 91.5

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

   6. Applied rewrites 91.5%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 3.99999999999999996e239

   1. Initial program 98.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. div-inv N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-/r* N/A

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

      23. lower-/.f64 N/A

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

      24. metadata-eval 98.6

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

   4. Applied rewrites 98.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. associate-/r* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. un-div-inv N/A

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

      9. lower-/.f64 98.8

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

   6. Applied rewrites 98.8%

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

Alternative 4: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+302}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+247}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{a \cdot -0.2222222222222222}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -2e+302)
     (* (/ z a) (* t -4.5))
     (if (<= t_1 5e+247)
       (/ (fma z (* t -9.0) (* x y)) (* a 2.0))
       (* t (/ z (* a -0.2222222222222222)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -2e+302) {
		tmp = (z / a) * (t * -4.5);
	} else if (t_1 <= 5e+247) {
		tmp = fma(z, (t * -9.0), (x * y)) / (a * 2.0);
	} else {
		tmp = t * (z / (a * -0.2222222222222222));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -2e+302)
		tmp = Float64(Float64(z / a) * Float64(t * -4.5));
	elseif (t_1 <= 5e+247)
		tmp = Float64(fma(z, Float64(t * -9.0), Float64(x * y)) / Float64(a * 2.0));
	else
		tmp = Float64(t * Float64(z / Float64(a * -0.2222222222222222)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+302], N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+247], N[(N[(z * N[(t * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / N[(a * -0.2222222222222222), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -2.0000000000000002e302

   1. Initial program 45.2%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 96.0

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

   5. Applied rewrites 96.0%

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

      1. lift-/.f64 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 96.0

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

   7. Applied rewrites 96.0%

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

   if -2.0000000000000002e302 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 5.00000000000000023e247

   1. Initial program 94.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. div-inv N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-/r* N/A

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

      23. lower-/.f64 N/A

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

      24. metadata-eval 94.3

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

   4. Applied rewrites 94.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. associate-/r* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. un-div-inv N/A

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

      9. lower-/.f64 94.5

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

   6. Applied rewrites 94.5%

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

   if 5.00000000000000023e247 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 59.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 87.2

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

   5. Applied rewrites 87.2%

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

      1. metadata-eval N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. times-frac N/A

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

      6. *-commutative N/A

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

      7. neg-mul-1 N/A

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

      8. lift-neg.f64 N/A

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

      9. associate-/l* N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. lift-neg.f64 N/A

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

      16. frac-2neg N/A

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

      17. lower-/.f64 87.3

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

   7. Applied rewrites 87.3%

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

      1. lift-/.f64 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lift-/.f64 N/A

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

      6. div-inv N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*r* N/A

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

      9. lift-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*r* N/A

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

      13. lift-/.f64 N/A

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

      14. div-inv N/A

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

      15. clear-num N/A

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

      16. associate-*l/ N/A

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

      17. *-lft-identity N/A

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

      18. lower-/.f64 N/A

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

      19. div-inv N/A

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

      20. lower-*.f64 N/A

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

      21. metadata-eval 87.3

          \[\leadsto \frac{z}{a \cdot \color{blue}{-0.2222222222222222}} \cdot t \]

   9. Applied rewrites 87.3%

      \[\leadsto \color{blue}{\frac{z}{a \cdot -0.2222222222222222} \cdot t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -2 \cdot 10^{+302}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+247}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{a \cdot -0.2222222222222222}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+302}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+247}:\\ \;\;\;\;\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{a \cdot -0.2222222222222222}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -2e+302)
     (* (/ z a) (* t -4.5))
     (if (<= t_1 5e+247)
       (* (fma z (* t -9.0) (* x y)) (/ 0.5 a))
       (* t (/ z (* a -0.2222222222222222)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -2e+302) {
		tmp = (z / a) * (t * -4.5);
	} else if (t_1 <= 5e+247) {
		tmp = fma(z, (t * -9.0), (x * y)) * (0.5 / a);
	} else {
		tmp = t * (z / (a * -0.2222222222222222));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -2e+302)
		tmp = Float64(Float64(z / a) * Float64(t * -4.5));
	elseif (t_1 <= 5e+247)
		tmp = Float64(fma(z, Float64(t * -9.0), Float64(x * y)) * Float64(0.5 / a));
	else
		tmp = Float64(t * Float64(z / Float64(a * -0.2222222222222222)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+302], N[(N[(z / a), $MachinePrecision] * N[(t * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+247], N[(N[(z * N[(t * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / N[(a * -0.2222222222222222), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -2.0000000000000002e302

   1. Initial program 45.2%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 96.0

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

   5. Applied rewrites 96.0%

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

      1. lift-/.f64 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 96.0

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

   7. Applied rewrites 96.0%

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

   if -2.0000000000000002e302 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 5.00000000000000023e247

   1. Initial program 94.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. div-inv N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-/r* N/A

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

      23. lower-/.f64 N/A

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

      24. metadata-eval 94.3

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

   4. Applied rewrites 94.3%

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

   if 5.00000000000000023e247 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 59.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 87.2

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

   5. Applied rewrites 87.2%

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

      1. metadata-eval N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. times-frac N/A

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

      6. *-commutative N/A

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

      7. neg-mul-1 N/A

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

      8. lift-neg.f64 N/A

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

      9. associate-/l* N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. lift-neg.f64 N/A

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

      16. frac-2neg N/A

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

      17. lower-/.f64 87.3

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

   7. Applied rewrites 87.3%

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

      1. lift-/.f64 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lift-/.f64 N/A

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

      6. div-inv N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*r* N/A

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

      9. lift-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*r* N/A

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

      13. lift-/.f64 N/A

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

      14. div-inv N/A

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

      15. clear-num N/A

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

      16. associate-*l/ N/A

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

      17. *-lft-identity N/A

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

      18. lower-/.f64 N/A

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

      19. div-inv N/A

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

      20. lower-*.f64 N/A

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

      21. metadata-eval 87.3

          \[\leadsto \frac{z}{a \cdot \color{blue}{-0.2222222222222222}} \cdot t \]

   9. Applied rewrites 87.3%

      \[\leadsto \color{blue}{\frac{z}{a \cdot -0.2222222222222222} \cdot t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -2 \cdot 10^{+302}:\\ \;\;\;\;\frac{z}{a} \cdot \left(t \cdot -4.5\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+247}:\\ \;\;\;\;\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{a \cdot -0.2222222222222222}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+51}:\\ \;\;\;\;\frac{x \cdot 0.5}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -2e-62)
     (* t (* (/ z a) -4.5))
     (if (<= t_1 1e+51) (/ (* x 0.5) (/ a y)) (* -4.5 (* z (/ t a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -2e-62) {
		tmp = t * ((z / a) * -4.5);
	} else if (t_1 <= 1e+51) {
		tmp = (x * 0.5) / (a / y);
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * 9.0d0) * t
    if (t_1 <= (-2d-62)) then
        tmp = t * ((z / a) * (-4.5d0))
    else if (t_1 <= 1d+51) then
        tmp = (x * 0.5d0) / (a / y)
    else
        tmp = (-4.5d0) * (z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -2e-62) {
		tmp = t * ((z / a) * -4.5);
	} else if (t_1 <= 1e+51) {
		tmp = (x * 0.5) / (a / y);
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -2e-62:
		tmp = t * ((z / a) * -4.5)
	elif t_1 <= 1e+51:
		tmp = (x * 0.5) / (a / y)
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -2e-62)
		tmp = Float64(t * Float64(Float64(z / a) * -4.5));
	elseif (t_1 <= 1e+51)
		tmp = Float64(Float64(x * 0.5) / Float64(a / y));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_1 <= -2e-62)
		tmp = t * ((z / a) * -4.5);
	elseif (t_1 <= 1e+51)
		tmp = (x * 0.5) / (a / y);
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-62], N[(t * N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+51], N[(N[(x * 0.5), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -2.0000000000000001e-62

   1. Initial program 78.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 78.1

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

   5. Applied rewrites 78.1%

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

      1. lift-/.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 78.1

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

   7. Applied rewrites 78.1%

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

   if -2.0000000000000001e-62 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1e51

   1. Initial program 93.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. div-inv N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-/r* N/A

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

      23. lower-/.f64 N/A

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

      24. metadata-eval 93.4

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

   4. Applied rewrites 93.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-*.f64 75.8

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

   7. Applied rewrites 75.8%

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

      1. lift-/.f64 N/A

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

      2. associate-*l* N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. div-inv N/A

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

      6. metadata-eval N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 75.1

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

   9. Applied rewrites 75.1%

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

       1. associate-/r* N/A

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

       2. div-inv N/A

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

       3. metadata-eval N/A

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

       4. associate-*l* N/A

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

       5. lift-*.f64 N/A

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

       6. *-commutative N/A

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

       7. clear-num N/A

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

       8. un-div-inv N/A

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

       9. lower-/.f64 N/A

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

       10. lift-*.f64 N/A

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

       11. *-commutative N/A

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

       12. lower-*.f64 N/A

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

       13. lower-/.f64 75.2

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

   11. Applied rewrites 75.2%

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

   if 1e51 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 86.1

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

   5. Applied rewrites 86.1%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lift-/.f64 N/A

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

      5. lower-*.f64 87.6

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

   7. Applied rewrites 87.6%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -2 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 10^{+51}:\\ \;\;\;\;\frac{x \cdot 0.5}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+51}:\\ \;\;\;\;\frac{x}{\frac{a}{y \cdot 0.5}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -2e-62)
     (* t (* (/ z a) -4.5))
     (if (<= t_1 1e+51) (/ x (/ a (* y 0.5))) (* -4.5 (* z (/ t a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -2e-62) {
		tmp = t * ((z / a) * -4.5);
	} else if (t_1 <= 1e+51) {
		tmp = x / (a / (y * 0.5));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * 9.0d0) * t
    if (t_1 <= (-2d-62)) then
        tmp = t * ((z / a) * (-4.5d0))
    else if (t_1 <= 1d+51) then
        tmp = x / (a / (y * 0.5d0))
    else
        tmp = (-4.5d0) * (z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -2e-62) {
		tmp = t * ((z / a) * -4.5);
	} else if (t_1 <= 1e+51) {
		tmp = x / (a / (y * 0.5));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -2e-62:
		tmp = t * ((z / a) * -4.5)
	elif t_1 <= 1e+51:
		tmp = x / (a / (y * 0.5))
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -2e-62)
		tmp = Float64(t * Float64(Float64(z / a) * -4.5));
	elseif (t_1 <= 1e+51)
		tmp = Float64(x / Float64(a / Float64(y * 0.5)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_1 <= -2e-62)
		tmp = t * ((z / a) * -4.5);
	elseif (t_1 <= 1e+51)
		tmp = x / (a / (y * 0.5));
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-62], N[(t * N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+51], N[(x / N[(a / N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -2.0000000000000001e-62

   1. Initial program 78.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 78.1

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

   5. Applied rewrites 78.1%

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

      1. lift-/.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 78.1

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

   7. Applied rewrites 78.1%

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

   if -2.0000000000000001e-62 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1e51

   1. Initial program 93.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. div-inv N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-/r* N/A

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

      23. lower-/.f64 N/A

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

      24. metadata-eval 93.4

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

   4. Applied rewrites 93.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-*.f64 75.8

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

   7. Applied rewrites 75.8%

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

      1. lift-*.f64 N/A

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

      2. associate-*r/ N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

      7. clear-num N/A

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

      8. un-div-inv N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 75.2

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

   9. Applied rewrites 75.2%

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

   if 1e51 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 86.1

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

   5. Applied rewrites 86.1%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lift-/.f64 N/A

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

      5. lower-*.f64 87.6

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

   7. Applied rewrites 87.6%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -2 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 10^{+51}:\\ \;\;\;\;\frac{x}{\frac{a}{y \cdot 0.5}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 2 \cdot 10^{-67}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{z \cdot 4.5}{a}, x \cdot \frac{y}{a \cdot 2}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) 2e-67)
   (/ (fma z (* t -9.0) (* x y)) (* a 2.0))
   (fma (- t) (/ (* z 4.5) a) (* x (/ y (* a 2.0))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 2e-67) {
		tmp = fma(z, (t * -9.0), (x * y)) / (a * 2.0);
	} else {
		tmp = fma(-t, ((z * 4.5) / a), (x * (y / (a * 2.0))));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= 2e-67)
		tmp = Float64(fma(z, Float64(t * -9.0), Float64(x * y)) / Float64(a * 2.0));
	else
		tmp = fma(Float64(-t), Float64(Float64(z * 4.5) / a), Float64(x * Float64(y / Float64(a * 2.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 2e-67], N[(N[(z * N[(t * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[((-t) * N[(N[(z * 4.5), $MachinePrecision] / a), $MachinePrecision] + N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 1.99999999999999989e-67

   1. Initial program 90.1%

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

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. div-inv N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-/r* N/A

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

      23. lower-/.f64 N/A

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

      24. metadata-eval 90.0

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

   4. Applied rewrites 90.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. associate-/r* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. un-div-inv N/A

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

      9. lower-/.f64 90.1

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

   6. Applied rewrites 90.1%

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

   if 1.99999999999999989e-67 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 81.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

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

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

      12. lower-fma.f64 N/A

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

   4. Applied rewrites 93.3%

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

Alternative 9: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+51}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -2e-62)
     (* t (* (/ z a) -4.5))
     (if (<= t_1 1e+51) (* x (/ y (* a 2.0))) (* -4.5 (* z (/ t a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -2e-62) {
		tmp = t * ((z / a) * -4.5);
	} else if (t_1 <= 1e+51) {
		tmp = x * (y / (a * 2.0));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * 9.0d0) * t
    if (t_1 <= (-2d-62)) then
        tmp = t * ((z / a) * (-4.5d0))
    else if (t_1 <= 1d+51) then
        tmp = x * (y / (a * 2.0d0))
    else
        tmp = (-4.5d0) * (z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -2e-62) {
		tmp = t * ((z / a) * -4.5);
	} else if (t_1 <= 1e+51) {
		tmp = x * (y / (a * 2.0));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -2e-62:
		tmp = t * ((z / a) * -4.5)
	elif t_1 <= 1e+51:
		tmp = x * (y / (a * 2.0))
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -2e-62)
		tmp = Float64(t * Float64(Float64(z / a) * -4.5));
	elseif (t_1 <= 1e+51)
		tmp = Float64(x * Float64(y / Float64(a * 2.0)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_1 <= -2e-62)
		tmp = t * ((z / a) * -4.5);
	elseif (t_1 <= 1e+51)
		tmp = x * (y / (a * 2.0));
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-62], N[(t * N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+51], N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -2.0000000000000001e-62

   1. Initial program 78.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 78.1

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

   5. Applied rewrites 78.1%

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

      1. lift-/.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 78.1

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

   7. Applied rewrites 78.1%

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

   if -2.0000000000000001e-62 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1e51

   1. Initial program 93.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. div-inv N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-/r* N/A

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

      23. lower-/.f64 N/A

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

      24. metadata-eval 93.4

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

   4. Applied rewrites 93.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-*.f64 75.8

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

   7. Applied rewrites 75.8%

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

      1. lift-/.f64 N/A

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

      2. associate-*l* N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. div-inv N/A

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

      6. metadata-eval N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 75.1

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

   9. Applied rewrites 75.1%

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

   if 1e51 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 86.1

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

   5. Applied rewrites 86.1%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lift-/.f64 N/A

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

      5. lower-*.f64 87.6

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

   7. Applied rewrites 87.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -2 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 10^{+51}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+51}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -2e-62)
     (* t (* (/ z a) -4.5))
     (if (<= t_1 1e+51) (* (* x y) (/ 0.5 a)) (* -4.5 (* z (/ t a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -2e-62) {
		tmp = t * ((z / a) * -4.5);
	} else if (t_1 <= 1e+51) {
		tmp = (x * y) * (0.5 / a);
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * 9.0d0) * t
    if (t_1 <= (-2d-62)) then
        tmp = t * ((z / a) * (-4.5d0))
    else if (t_1 <= 1d+51) then
        tmp = (x * y) * (0.5d0 / a)
    else
        tmp = (-4.5d0) * (z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -2e-62) {
		tmp = t * ((z / a) * -4.5);
	} else if (t_1 <= 1e+51) {
		tmp = (x * y) * (0.5 / a);
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -2e-62:
		tmp = t * ((z / a) * -4.5)
	elif t_1 <= 1e+51:
		tmp = (x * y) * (0.5 / a)
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -2e-62)
		tmp = Float64(t * Float64(Float64(z / a) * -4.5));
	elseif (t_1 <= 1e+51)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_1 <= -2e-62)
		tmp = t * ((z / a) * -4.5);
	elseif (t_1 <= 1e+51)
		tmp = (x * y) * (0.5 / a);
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-62], N[(t * N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+51], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -2.0000000000000001e-62

   1. Initial program 78.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 78.1

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

   5. Applied rewrites 78.1%

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

      1. lift-/.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 78.1

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

   7. Applied rewrites 78.1%

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

   if -2.0000000000000001e-62 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1e51

   1. Initial program 93.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. div-inv N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-/r* N/A

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

      23. lower-/.f64 N/A

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

      24. metadata-eval 93.4

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

   4. Applied rewrites 93.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-*.f64 75.8

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

   7. Applied rewrites 75.8%

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

   if 1e51 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 86.1

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

   5. Applied rewrites 86.1%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lift-/.f64 N/A

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

      5. lower-*.f64 87.6

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

   7. Applied rewrites 87.6%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -2 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 10^{+51}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ t \cdot \left(\frac{z}{a} \cdot -4.5\right) \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* t (* (/ z a) -4.5)))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return t * ((z / a) * -4.5);
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = t * ((z / a) * (-4.5d0))
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return t * ((z / a) * -4.5);
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return t * ((z / a) * -4.5)

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(t * Float64(Float64(z / a) * -4.5))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = t * ((z / a) * -4.5);
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(t * N[(N[(z / a), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.3%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
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. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]

   2. associate-/l* N/A

      \[\leadsto \frac{-9}{2} \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   3. lower-*.f64 N/A

      \[\leadsto \frac{-9}{2} \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   4. lower-/.f64 53.0

      \[\leadsto -4.5 \cdot \left(t \cdot \color{blue}{\frac{z}{a}}\right) \]

5. Applied rewrites 53.0%

   \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
6. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \frac{-9}{2} \cdot \left(t \cdot \color{blue}{\frac{z}{a}}\right) \]

   2. *-commutative N/A

      \[\leadsto \frac{-9}{2} \cdot \color{blue}{\left(\frac{z}{a} \cdot t\right)} \]

   3. associate-*r* N/A

      \[\leadsto \color{blue}{\left(\frac{-9}{2} \cdot \frac{z}{a}\right) \cdot t} \]

   4. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(\frac{-9}{2} \cdot \frac{z}{a}\right) \cdot t} \]

   5. lower-*.f64 53.0

      \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{z}{a}\right)} \cdot t \]

7. Applied rewrites 53.0%

   \[\leadsto \color{blue}{\left(-4.5 \cdot \frac{z}{a}\right) \cdot t} \]

8. Final simplification 53.0%

   \[\leadsto t \cdot \left(\frac{z}{a} \cdot -4.5\right) \]
9. Add Preprocessing

Alternative 12: 52.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ -4.5 \cdot \left(t \cdot \frac{z}{a}\right) \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* -4.5 (* t (/ z a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t * (z / a));
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (-4.5d0) * (t * (z / a))
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t * (z / a));
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return -4.5 * (t * (z / a))

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(-4.5 * Float64(t * Float64(z / a)))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (t * (z / a));
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.3%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
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. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]

   2. associate-/l* N/A

      \[\leadsto \frac{-9}{2} \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   3. lower-*.f64 N/A

      \[\leadsto \frac{-9}{2} \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   4. lower-/.f64 53.0

      \[\leadsto -4.5 \cdot \left(t \cdot \color{blue}{\frac{z}{a}}\right) \]

5. Applied rewrites 53.0%

   \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
6. Add Preprocessing

Developer Target 1: 93.5% 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 2024216 
(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)))