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

Percentage Accurate: 95.0% → 98.1%

Time: 28.2s

Alternatives: 15

Speedup: 0.9×

• 27.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\\ \mathbf{if}\;z \leq 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-t\right) \cdot \left(z \cdot y\right), 9, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (* 27.0 b) (* x 2.0))))
   (if (<= z 1e-34)
     (fma -9.0 (* y (* z t)) t_1)
     (fma (* (- t) (* z y)) 9.0 t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, (27.0 * b), (x * 2.0));
	double tmp;
	if (z <= 1e-34) {
		tmp = fma(-9.0, (y * (z * t)), t_1);
	} else {
		tmp = fma((-t * (z * y)), 9.0, t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(a, Float64(27.0 * b), Float64(x * 2.0))
	tmp = 0.0
	if (z <= 1e-34)
		tmp = fma(-9.0, Float64(y * Float64(z * t)), t_1);
	else
		tmp = fma(Float64(Float64(-t) * Float64(z * y)), 9.0, t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 1e-34], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[((-t) * N[(z * y), $MachinePrecision]), $MachinePrecision] * 9.0 + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 9.99999999999999928e-35

   1. Initial program 97.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(9\right), y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9}, y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, \color{blue}{y \cdot \left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \color{blue}{\left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      16. *-lowering-*.f64 97.1

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 97.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]

   if 9.99999999999999928e-35 < z

   1. Initial program 94.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t\right)\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(t\right)\right) \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      7. associate-*r* N/A

         \[\leadsto \left(\mathsf{neg}\left(t\right)\right) \cdot \color{blue}{\left(\left(z \cdot y\right) \cdot 9\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(z \cdot y\right)\right) \cdot 9} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      9. +-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(z \cdot y\right)\right) \cdot 9 + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(z \cdot y\right), 9, \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(t\right)\right) \cdot \left(z \cdot y\right)}, 9, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(t\right)\right)} \cdot \left(z \cdot y\right), 9, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(\mathsf{neg}\left(t\right)\right) \cdot \color{blue}{\left(y \cdot z\right)}, 9, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(\left(\mathsf{neg}\left(t\right)\right) \cdot \color{blue}{\left(y \cdot z\right)}, 9, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      15. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(y \cdot z\right), 9, \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(y \cdot z\right), 9, \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(\left(\mathsf{neg}\left(t\right)\right) \cdot \left(y \cdot z\right), 9, \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      18. *-lowering-*.f64 93.4

          \[\leadsto \mathsf{fma}\left(\left(-t\right) \cdot \left(y \cdot z\right), 9, \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 93.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(-t\right) \cdot \left(y \cdot z\right), 9, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-t\right) \cdot \left(z \cdot y\right), 9, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 58.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+292}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+80}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_1 \leq 100:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+284}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* x 2.0) (* t (* z (* y 9.0))))))
   (if (<= t_1 -2e+292)
     (* (* z t) (* -9.0 y))
     (if (<= t_1 -2e+80)
       (* x 2.0)
       (if (<= t_1 100.0)
         (* 27.0 (* a b))
         (if (<= t_1 1e+284) (* x 2.0) (* -9.0 (* y (* z t)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (t * (z * (y * 9.0)));
	double tmp;
	if (t_1 <= -2e+292) {
		tmp = (z * t) * (-9.0 * y);
	} else if (t_1 <= -2e+80) {
		tmp = x * 2.0;
	} else if (t_1 <= 100.0) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= 1e+284) {
		tmp = x * 2.0;
	} else {
		tmp = -9.0 * (y * (z * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) - (t * (z * (y * 9.0d0)))
    if (t_1 <= (-2d+292)) then
        tmp = (z * t) * ((-9.0d0) * y)
    else if (t_1 <= (-2d+80)) then
        tmp = x * 2.0d0
    else if (t_1 <= 100.0d0) then
        tmp = 27.0d0 * (a * b)
    else if (t_1 <= 1d+284) then
        tmp = x * 2.0d0
    else
        tmp = (-9.0d0) * (y * (z * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (t * (z * (y * 9.0)));
	double tmp;
	if (t_1 <= -2e+292) {
		tmp = (z * t) * (-9.0 * y);
	} else if (t_1 <= -2e+80) {
		tmp = x * 2.0;
	} else if (t_1 <= 100.0) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= 1e+284) {
		tmp = x * 2.0;
	} else {
		tmp = -9.0 * (y * (z * t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (t * (z * (y * 9.0)))
	tmp = 0
	if t_1 <= -2e+292:
		tmp = (z * t) * (-9.0 * y)
	elif t_1 <= -2e+80:
		tmp = x * 2.0
	elif t_1 <= 100.0:
		tmp = 27.0 * (a * b)
	elif t_1 <= 1e+284:
		tmp = x * 2.0
	else:
		tmp = -9.0 * (y * (z * t))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(y * 9.0))))
	tmp = 0.0
	if (t_1 <= -2e+292)
		tmp = Float64(Float64(z * t) * Float64(-9.0 * y));
	elseif (t_1 <= -2e+80)
		tmp = Float64(x * 2.0);
	elseif (t_1 <= 100.0)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t_1 <= 1e+284)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (t * (z * (y * 9.0)));
	tmp = 0.0;
	if (t_1 <= -2e+292)
		tmp = (z * t) * (-9.0 * y);
	elseif (t_1 <= -2e+80)
		tmp = x * 2.0;
	elseif (t_1 <= 100.0)
		tmp = 27.0 * (a * b);
	elseif (t_1 <= 1e+284)
		tmp = x * 2.0;
	else
		tmp = -9.0 * (y * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+292], N[(N[(z * t), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+80], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 100.0], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+284], N[(x * 2.0), $MachinePrecision], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -2e292

   1. Initial program 78.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(9\right), y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9}, y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, \color{blue}{y \cdot \left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \color{blue}{\left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      16. *-lowering-*.f64 92.4

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 92.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-lowering-*.f64 82.6

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

   7. Simplified 82.6%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 93.0

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

   9. Applied egg-rr 93.0%

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

   if -2e292 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -2e80 or 100 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 1.00000000000000008e284

   1. Initial program 99.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 49.9

         \[\leadsto \color{blue}{2 \cdot x} \]

   5. Simplified 49.9%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if -2e80 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 100

   1. Initial program 98.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. *-lowering-*.f64 66.7

         \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if 1.00000000000000008e284 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 92.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(9\right), y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9}, y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, \color{blue}{y \cdot \left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \color{blue}{\left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      16. *-lowering-*.f64 93.3

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-lowering-*.f64 85.5

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

   7. Simplified 85.5%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. *-lowering-*.f64 78.9

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

   9. Applied egg-rr 78.9%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot t\right)\right) \cdot -9} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{+292}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{+80}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 100:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 10^{+284}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ t_2 := x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+80}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_2 \leq 100:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+284}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* y (* z t)))) (t_2 (- (* x 2.0) (* t (* z (* y 9.0))))))
   (if (<= t_2 -2e+292)
     t_1
     (if (<= t_2 -2e+80)
       (* x 2.0)
       (if (<= t_2 100.0)
         (* 27.0 (* a b))
         (if (<= t_2 1e+284) (* x 2.0) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double t_2 = (x * 2.0) - (t * (z * (y * 9.0)));
	double tmp;
	if (t_2 <= -2e+292) {
		tmp = t_1;
	} else if (t_2 <= -2e+80) {
		tmp = x * 2.0;
	} else if (t_2 <= 100.0) {
		tmp = 27.0 * (a * b);
	} else if (t_2 <= 1e+284) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-9.0d0) * (y * (z * t))
    t_2 = (x * 2.0d0) - (t * (z * (y * 9.0d0)))
    if (t_2 <= (-2d+292)) then
        tmp = t_1
    else if (t_2 <= (-2d+80)) then
        tmp = x * 2.0d0
    else if (t_2 <= 100.0d0) then
        tmp = 27.0d0 * (a * b)
    else if (t_2 <= 1d+284) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double t_2 = (x * 2.0) - (t * (z * (y * 9.0)));
	double tmp;
	if (t_2 <= -2e+292) {
		tmp = t_1;
	} else if (t_2 <= -2e+80) {
		tmp = x * 2.0;
	} else if (t_2 <= 100.0) {
		tmp = 27.0 * (a * b);
	} else if (t_2 <= 1e+284) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (y * (z * t))
	t_2 = (x * 2.0) - (t * (z * (y * 9.0)))
	tmp = 0
	if t_2 <= -2e+292:
		tmp = t_1
	elif t_2 <= -2e+80:
		tmp = x * 2.0
	elif t_2 <= 100.0:
		tmp = 27.0 * (a * b)
	elif t_2 <= 1e+284:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(y * Float64(z * t)))
	t_2 = Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(y * 9.0))))
	tmp = 0.0
	if (t_2 <= -2e+292)
		tmp = t_1;
	elseif (t_2 <= -2e+80)
		tmp = Float64(x * 2.0);
	elseif (t_2 <= 100.0)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t_2 <= 1e+284)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (y * (z * t));
	t_2 = (x * 2.0) - (t * (z * (y * 9.0)));
	tmp = 0.0;
	if (t_2 <= -2e+292)
		tmp = t_1;
	elseif (t_2 <= -2e+80)
		tmp = x * 2.0;
	elseif (t_2 <= 100.0)
		tmp = 27.0 * (a * b);
	elseif (t_2 <= 1e+284)
		tmp = x * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+292], t$95$1, If[LessEqual[t$95$2, -2e+80], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$2, 100.0], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+284], N[(x * 2.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -2e292 or 1.00000000000000008e284 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 85.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(9\right), y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9}, y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, \color{blue}{y \cdot \left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \color{blue}{\left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      16. *-lowering-*.f64 92.9

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 92.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-lowering-*.f64 84.1

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

   7. Simplified 84.1%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. *-lowering-*.f64 85.9

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

   9. Applied egg-rr 85.9%

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

   if -2e292 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -2e80 or 100 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 1.00000000000000008e284

   1. Initial program 99.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 49.9

         \[\leadsto \color{blue}{2 \cdot x} \]

   5. Simplified 49.9%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if -2e80 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 100

   1. Initial program 98.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. *-lowering-*.f64 66.7

         \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{+292}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{+80}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 100:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 10^{+284}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+285}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+80}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_1 \leq 100:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+284}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* x 2.0) (* t (* z (* y 9.0))))))
   (if (<= t_1 -2e+285)
     (* -9.0 (* t (* z y)))
     (if (<= t_1 -2e+80)
       (* x 2.0)
       (if (<= t_1 100.0)
         (* 27.0 (* a b))
         (if (<= t_1 1e+284) (* x 2.0) (* (* y t) (* z -9.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (t * (z * (y * 9.0)));
	double tmp;
	if (t_1 <= -2e+285) {
		tmp = -9.0 * (t * (z * y));
	} else if (t_1 <= -2e+80) {
		tmp = x * 2.0;
	} else if (t_1 <= 100.0) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= 1e+284) {
		tmp = x * 2.0;
	} else {
		tmp = (y * t) * (z * -9.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) - (t * (z * (y * 9.0d0)))
    if (t_1 <= (-2d+285)) then
        tmp = (-9.0d0) * (t * (z * y))
    else if (t_1 <= (-2d+80)) then
        tmp = x * 2.0d0
    else if (t_1 <= 100.0d0) then
        tmp = 27.0d0 * (a * b)
    else if (t_1 <= 1d+284) then
        tmp = x * 2.0d0
    else
        tmp = (y * t) * (z * (-9.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (t * (z * (y * 9.0)));
	double tmp;
	if (t_1 <= -2e+285) {
		tmp = -9.0 * (t * (z * y));
	} else if (t_1 <= -2e+80) {
		tmp = x * 2.0;
	} else if (t_1 <= 100.0) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= 1e+284) {
		tmp = x * 2.0;
	} else {
		tmp = (y * t) * (z * -9.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (t * (z * (y * 9.0)))
	tmp = 0
	if t_1 <= -2e+285:
		tmp = -9.0 * (t * (z * y))
	elif t_1 <= -2e+80:
		tmp = x * 2.0
	elif t_1 <= 100.0:
		tmp = 27.0 * (a * b)
	elif t_1 <= 1e+284:
		tmp = x * 2.0
	else:
		tmp = (y * t) * (z * -9.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(y * 9.0))))
	tmp = 0.0
	if (t_1 <= -2e+285)
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	elseif (t_1 <= -2e+80)
		tmp = Float64(x * 2.0);
	elseif (t_1 <= 100.0)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t_1 <= 1e+284)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(Float64(y * t) * Float64(z * -9.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (t * (z * (y * 9.0)));
	tmp = 0.0;
	if (t_1 <= -2e+285)
		tmp = -9.0 * (t * (z * y));
	elseif (t_1 <= -2e+80)
		tmp = x * 2.0;
	elseif (t_1 <= 100.0)
		tmp = 27.0 * (a * b);
	elseif (t_1 <= 1e+284)
		tmp = x * 2.0;
	else
		tmp = (y * t) * (z * -9.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+285], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+80], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 100.0], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+284], N[(x * 2.0), $MachinePrecision], N[(N[(y * t), $MachinePrecision] * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -2e285

   1. Initial program 81.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      2. metadata-eval N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{-9} \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + 27 \cdot \left(a \cdot b\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot -9} + 27 \cdot \left(a \cdot b\right) \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right)} + 27 \cdot \left(a \cdot b\right) \]

      6. *-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)} + 27 \cdot \left(a \cdot b\right) \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, -9 \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right)} \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right) \cdot -9}, 27 \cdot \left(a \cdot b\right)\right) \]

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

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right) \cdot -9}, 27 \cdot \left(a \cdot b\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right)} \cdot -9, 27 \cdot \left(a \cdot b\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]

      12. *-lowering-*.f64 74.7

          \[\leadsto \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, 27 \cdot \color{blue}{\left(a \cdot b\right)}\right) \]

   5. Simplified 74.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, 27 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + t \cdot \left(\left(y \cdot z\right) \cdot -9\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot 27} + t \cdot \left(\left(y \cdot z\right) \cdot -9\right) \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{a \cdot \left(b \cdot 27\right)} + t \cdot \left(\left(y \cdot z\right) \cdot -9\right) \]

      4. *-commutative N/A

         \[\leadsto a \cdot \color{blue}{\left(27 \cdot b\right)} + t \cdot \left(\left(y \cdot z\right) \cdot -9\right) \]

      5. *-commutative N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + t \cdot \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)} \]

      6. associate-*r* N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + t \cdot \color{blue}{\left(\left(-9 \cdot y\right) \cdot z\right)} \]

      7. *-commutative N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + t \cdot \left(\color{blue}{\left(y \cdot -9\right)} \cdot z\right) \]

      8. associate-*l* N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(t \cdot \left(y \cdot -9\right)\right) \cdot z} \]

      9. *-commutative N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(\left(y \cdot -9\right) \cdot t\right)} \cdot z \]

      10. *-commutative N/A

          \[\leadsto \color{blue}{\left(27 \cdot b\right) \cdot a} + \left(\left(y \cdot -9\right) \cdot t\right) \cdot z \]

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

          \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, \left(\left(y \cdot -9\right) \cdot t\right) \cdot z\right)} \]

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

          \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot b}, a, \left(\left(y \cdot -9\right) \cdot t\right) \cdot z\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \color{blue}{\left(y \cdot -9\right) \cdot \left(t \cdot z\right)}\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \color{blue}{\left(-9 \cdot y\right)} \cdot \left(t \cdot z\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot y\right) \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

      16. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \color{blue}{-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \color{blue}{-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      19. *-lowering-*.f64 89.9

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right)\right) \]

   7. Applied egg-rr 89.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

   8. Taylor expanded in b around 0

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

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

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

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

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

      3. *-lowering-*.f64 78.0

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

   10. Simplified 78.0%

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

   if -2e285 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -2e80 or 100 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 1.00000000000000008e284

   1. Initial program 99.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 49.9

         \[\leadsto \color{blue}{2 \cdot x} \]

   5. Simplified 49.9%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if -2e80 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 100

   1. Initial program 98.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. *-lowering-*.f64 66.7

         \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if 1.00000000000000008e284 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 92.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(9\right), y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9}, y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, \color{blue}{y \cdot \left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \color{blue}{\left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      16. *-lowering-*.f64 93.3

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-lowering-*.f64 85.5

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

   7. Simplified 85.5%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 78.8

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

   9. Applied egg-rr 78.8%

      \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-9 \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{+285}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{+80}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 100:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 10^{+284}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ t_2 := x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+285}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+80}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_2 \leq 100:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+284}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* z y)))) (t_2 (- (* x 2.0) (* t (* z (* y 9.0))))))
   (if (<= t_2 -2e+285)
     t_1
     (if (<= t_2 -2e+80)
       (* x 2.0)
       (if (<= t_2 100.0)
         (* 27.0 (* a b))
         (if (<= t_2 1e+284) (* x 2.0) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (z * y));
	double t_2 = (x * 2.0) - (t * (z * (y * 9.0)));
	double tmp;
	if (t_2 <= -2e+285) {
		tmp = t_1;
	} else if (t_2 <= -2e+80) {
		tmp = x * 2.0;
	} else if (t_2 <= 100.0) {
		tmp = 27.0 * (a * b);
	} else if (t_2 <= 1e+284) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-9.0d0) * (t * (z * y))
    t_2 = (x * 2.0d0) - (t * (z * (y * 9.0d0)))
    if (t_2 <= (-2d+285)) then
        tmp = t_1
    else if (t_2 <= (-2d+80)) then
        tmp = x * 2.0d0
    else if (t_2 <= 100.0d0) then
        tmp = 27.0d0 * (a * b)
    else if (t_2 <= 1d+284) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (z * y));
	double t_2 = (x * 2.0) - (t * (z * (y * 9.0)));
	double tmp;
	if (t_2 <= -2e+285) {
		tmp = t_1;
	} else if (t_2 <= -2e+80) {
		tmp = x * 2.0;
	} else if (t_2 <= 100.0) {
		tmp = 27.0 * (a * b);
	} else if (t_2 <= 1e+284) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (t * (z * y))
	t_2 = (x * 2.0) - (t * (z * (y * 9.0)))
	tmp = 0
	if t_2 <= -2e+285:
		tmp = t_1
	elif t_2 <= -2e+80:
		tmp = x * 2.0
	elif t_2 <= 100.0:
		tmp = 27.0 * (a * b)
	elif t_2 <= 1e+284:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(z * y)))
	t_2 = Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(y * 9.0))))
	tmp = 0.0
	if (t_2 <= -2e+285)
		tmp = t_1;
	elseif (t_2 <= -2e+80)
		tmp = Float64(x * 2.0);
	elseif (t_2 <= 100.0)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t_2 <= 1e+284)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (t * (z * y));
	t_2 = (x * 2.0) - (t * (z * (y * 9.0)));
	tmp = 0.0;
	if (t_2 <= -2e+285)
		tmp = t_1;
	elseif (t_2 <= -2e+80)
		tmp = x * 2.0;
	elseif (t_2 <= 100.0)
		tmp = 27.0 * (a * b);
	elseif (t_2 <= 1e+284)
		tmp = x * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+285], t$95$1, If[LessEqual[t$95$2, -2e+80], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$2, 100.0], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+284], N[(x * 2.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -2e285 or 1.00000000000000008e284 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 86.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      2. metadata-eval N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{-9} \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + 27 \cdot \left(a \cdot b\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot -9} + 27 \cdot \left(a \cdot b\right) \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right)} + 27 \cdot \left(a \cdot b\right) \]

      6. *-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)} + 27 \cdot \left(a \cdot b\right) \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, -9 \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right)} \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right) \cdot -9}, 27 \cdot \left(a \cdot b\right)\right) \]

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

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right) \cdot -9}, 27 \cdot \left(a \cdot b\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right)} \cdot -9, 27 \cdot \left(a \cdot b\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]

      12. *-lowering-*.f64 81.4

          \[\leadsto \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, 27 \cdot \color{blue}{\left(a \cdot b\right)}\right) \]

   5. Simplified 81.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, 27 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + t \cdot \left(\left(y \cdot z\right) \cdot -9\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot 27} + t \cdot \left(\left(y \cdot z\right) \cdot -9\right) \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{a \cdot \left(b \cdot 27\right)} + t \cdot \left(\left(y \cdot z\right) \cdot -9\right) \]

      4. *-commutative N/A

         \[\leadsto a \cdot \color{blue}{\left(27 \cdot b\right)} + t \cdot \left(\left(y \cdot z\right) \cdot -9\right) \]

      5. *-commutative N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + t \cdot \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)} \]

      6. associate-*r* N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + t \cdot \color{blue}{\left(\left(-9 \cdot y\right) \cdot z\right)} \]

      7. *-commutative N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + t \cdot \left(\color{blue}{\left(y \cdot -9\right)} \cdot z\right) \]

      8. associate-*l* N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(t \cdot \left(y \cdot -9\right)\right) \cdot z} \]

      9. *-commutative N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(\left(y \cdot -9\right) \cdot t\right)} \cdot z \]

      10. *-commutative N/A

          \[\leadsto \color{blue}{\left(27 \cdot b\right) \cdot a} + \left(\left(y \cdot -9\right) \cdot t\right) \cdot z \]

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

          \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, \left(\left(y \cdot -9\right) \cdot t\right) \cdot z\right)} \]

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

          \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot b}, a, \left(\left(y \cdot -9\right) \cdot t\right) \cdot z\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \color{blue}{\left(y \cdot -9\right) \cdot \left(t \cdot z\right)}\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \color{blue}{\left(-9 \cdot y\right)} \cdot \left(t \cdot z\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot y\right) \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

      16. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \color{blue}{-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \color{blue}{-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      19. *-lowering-*.f64 89.8

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right)\right) \]

   7. Applied egg-rr 89.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

   8. Taylor expanded in b around 0

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

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

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

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

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

      3. *-lowering-*.f64 81.5

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

   10. Simplified 81.5%

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

   if -2e285 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -2e80 or 100 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 1.00000000000000008e284

   1. Initial program 99.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 49.9

         \[\leadsto \color{blue}{2 \cdot x} \]

   5. Simplified 49.9%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if -2e80 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 100

   1. Initial program 98.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. *-lowering-*.f64 66.7

         \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{+285}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{+80}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 100:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 10^{+284}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -50:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), 27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (* 27.0 b) a (* -9.0 (* y (* z t)))))
        (t_2 (* t (* z (* y 9.0)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -50.0)
       (fma t (* -9.0 (* z y)) (* 27.0 (* a b)))
       (if (<= t_2 5e+124) (fma (* 27.0 b) a (* x 2.0)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((27.0 * b), a, (-9.0 * (y * (z * t))));
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -50.0) {
		tmp = fma(t, (-9.0 * (z * y)), (27.0 * (a * b)));
	} else if (t_2 <= 5e+124) {
		tmp = fma((27.0 * b), a, (x * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(Float64(27.0 * b), a, Float64(-9.0 * Float64(y * Float64(z * t))))
	t_2 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -50.0)
		tmp = fma(t, Float64(-9.0 * Float64(z * y)), Float64(27.0 * Float64(a * b)));
	elseif (t_2 <= 5e+124)
		tmp = fma(Float64(27.0 * b), a, Float64(x * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(27.0 * b), $MachinePrecision] * a + N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -50.0], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+124], N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -inf.0 or 4.9999999999999996e124 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 87.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      2. metadata-eval N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{-9} \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + 27 \cdot \left(a \cdot b\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot -9} + 27 \cdot \left(a \cdot b\right) \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right)} + 27 \cdot \left(a \cdot b\right) \]

      6. *-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)} + 27 \cdot \left(a \cdot b\right) \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, -9 \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right)} \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right) \cdot -9}, 27 \cdot \left(a \cdot b\right)\right) \]

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

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right) \cdot -9}, 27 \cdot \left(a \cdot b\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right)} \cdot -9, 27 \cdot \left(a \cdot b\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]

      12. *-lowering-*.f64 82.8

          \[\leadsto \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, 27 \cdot \color{blue}{\left(a \cdot b\right)}\right) \]

   5. Simplified 82.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, 27 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + t \cdot \left(\left(y \cdot z\right) \cdot -9\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot 27} + t \cdot \left(\left(y \cdot z\right) \cdot -9\right) \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{a \cdot \left(b \cdot 27\right)} + t \cdot \left(\left(y \cdot z\right) \cdot -9\right) \]

      4. *-commutative N/A

         \[\leadsto a \cdot \color{blue}{\left(27 \cdot b\right)} + t \cdot \left(\left(y \cdot z\right) \cdot -9\right) \]

      5. *-commutative N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + t \cdot \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)} \]

      6. associate-*r* N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + t \cdot \color{blue}{\left(\left(-9 \cdot y\right) \cdot z\right)} \]

      7. *-commutative N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + t \cdot \left(\color{blue}{\left(y \cdot -9\right)} \cdot z\right) \]

      8. associate-*l* N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(t \cdot \left(y \cdot -9\right)\right) \cdot z} \]

      9. *-commutative N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{\left(\left(y \cdot -9\right) \cdot t\right)} \cdot z \]

      10. *-commutative N/A

          \[\leadsto \color{blue}{\left(27 \cdot b\right) \cdot a} + \left(\left(y \cdot -9\right) \cdot t\right) \cdot z \]

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

          \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, \left(\left(y \cdot -9\right) \cdot t\right) \cdot z\right)} \]

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

          \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot b}, a, \left(\left(y \cdot -9\right) \cdot t\right) \cdot z\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \color{blue}{\left(y \cdot -9\right) \cdot \left(t \cdot z\right)}\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \color{blue}{\left(-9 \cdot y\right)} \cdot \left(t \cdot z\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \left(-9 \cdot y\right) \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

      16. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \color{blue}{-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \color{blue}{-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      19. *-lowering-*.f64 90.3

          \[\leadsto \mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right)\right) \]

   7. Applied egg-rr 90.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

   if -inf.0 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -50

   1. Initial program 99.5%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      2. metadata-eval N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{-9} \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + 27 \cdot \left(a \cdot b\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot -9} + 27 \cdot \left(a \cdot b\right) \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right)} + 27 \cdot \left(a \cdot b\right) \]

      6. *-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)} + 27 \cdot \left(a \cdot b\right) \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, -9 \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right)} \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right) \cdot -9}, 27 \cdot \left(a \cdot b\right)\right) \]

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

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right) \cdot -9}, 27 \cdot \left(a \cdot b\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right)} \cdot -9, 27 \cdot \left(a \cdot b\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]

      12. *-lowering-*.f64 87.6

          \[\leadsto \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, 27 \cdot \color{blue}{\left(a \cdot b\right)}\right) \]

   5. Simplified 87.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, 27 \cdot \left(a \cdot b\right)\right)} \]

   if -50 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 4.9999999999999996e124

   1. Initial program 99.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + 2 \cdot x} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]

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

         \[\leadsto \mathsf{fma}\left(27, \color{blue}{a \cdot b}, 2 \cdot x\right) \]

      4. *-lowering-*.f64 89.2

         \[\leadsto \mathsf{fma}\left(27, a \cdot b, \color{blue}{2 \cdot x}\right) \]

   5. Simplified 89.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 27 \cdot \color{blue}{\left(b \cdot a\right)} + 2 \cdot x \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(27 \cdot b\right) \cdot a} + 2 \cdot x \]

      3. *-commutative N/A

         \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{x \cdot 2} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)} \]

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

         \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot b}, a, x \cdot 2\right) \]

      6. *-lowering-*.f64 89.2

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \color{blue}{x \cdot 2}\right) \]

   7. Applied egg-rr 89.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -50:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), 27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 5 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), 27 \cdot \left(a \cdot b\right)\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -50:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma t (* -9.0 (* z y)) (* 27.0 (* a b))))
        (t_2 (* t (* z (* y 9.0)))))
   (if (<= t_2 -50.0)
     t_1
     (if (<= t_2 5e-29) (fma (* 27.0 b) a (* x 2.0)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(t, (-9.0 * (z * y)), (27.0 * (a * b)));
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -50.0) {
		tmp = t_1;
	} else if (t_2 <= 5e-29) {
		tmp = fma((27.0 * b), a, (x * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(t, Float64(-9.0 * Float64(z * y)), Float64(27.0 * Float64(a * b)))
	t_2 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_2 <= -50.0)
		tmp = t_1;
	elseif (t_2 <= 5e-29)
		tmp = fma(Float64(27.0 * b), a, Float64(x * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -50.0], t$95$1, If[LessEqual[t$95$2, 5e-29], N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -50 or 4.99999999999999986e-29 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 93.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      2. metadata-eval N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{-9} \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + 27 \cdot \left(a \cdot b\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot -9} + 27 \cdot \left(a \cdot b\right) \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right)} + 27 \cdot \left(a \cdot b\right) \]

      6. *-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)} + 27 \cdot \left(a \cdot b\right) \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, -9 \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right)} \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right) \cdot -9}, 27 \cdot \left(a \cdot b\right)\right) \]

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

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right) \cdot -9}, 27 \cdot \left(a \cdot b\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right)} \cdot -9, 27 \cdot \left(a \cdot b\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]

      12. *-lowering-*.f64 81.0

          \[\leadsto \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, 27 \cdot \color{blue}{\left(a \cdot b\right)}\right) \]

   5. Simplified 81.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, 27 \cdot \left(a \cdot b\right)\right)} \]

   if -50 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 4.99999999999999986e-29

   1. Initial program 99.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + 2 \cdot x} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]

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

         \[\leadsto \mathsf{fma}\left(27, \color{blue}{a \cdot b}, 2 \cdot x\right) \]

      4. *-lowering-*.f64 94.5

         \[\leadsto \mathsf{fma}\left(27, a \cdot b, \color{blue}{2 \cdot x}\right) \]

   5. Simplified 94.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 27 \cdot \color{blue}{\left(b \cdot a\right)} + 2 \cdot x \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(27 \cdot b\right) \cdot a} + 2 \cdot x \]

      3. *-commutative N/A

         \[\leadsto \left(27 \cdot b\right) \cdot a + \color{blue}{x \cdot 2} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)} \]

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

         \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot b}, a, x \cdot 2\right) \]

      6. *-lowering-*.f64 94.5

         \[\leadsto \mathsf{fma}\left(27 \cdot b, a, \color{blue}{x \cdot 2}\right) \]

   7. Applied egg-rr 94.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -50:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), 27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), 27 \cdot \left(a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), x \cdot 2\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma t (* -9.0 (* z y)) (* x 2.0))) (t_2 (* t (* z (* y 9.0)))))
   (if (<= t_2 -2e+76)
     t_1
     (if (<= t_2 2e+84) (fma 27.0 (* a b) (* x 2.0)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(t, (-9.0 * (z * y)), (x * 2.0));
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -2e+76) {
		tmp = t_1;
	} else if (t_2 <= 2e+84) {
		tmp = fma(27.0, (a * b), (x * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(t, Float64(-9.0 * Float64(z * y)), Float64(x * 2.0))
	t_2 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_2 <= -2e+76)
		tmp = t_1;
	elseif (t_2 <= 2e+84)
		tmp = fma(27.0, Float64(a * b), Float64(x * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+76], t$95$1, If[LessEqual[t$95$2, 2e+84], N[(27.0 * N[(a * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -2.0000000000000001e76 or 2.00000000000000012e84 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 92.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

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

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

      8. *-commutative N/A

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

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

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

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

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

      11. *-lowering-*.f64 83.9

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

   5. Simplified 83.9%

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

   if -2.0000000000000001e76 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.00000000000000012e84

   1. Initial program 99.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + 2 \cdot x} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]

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

         \[\leadsto \mathsf{fma}\left(27, \color{blue}{a \cdot b}, 2 \cdot x\right) \]

      4. *-lowering-*.f64 90.3

         \[\leadsto \mathsf{fma}\left(27, a \cdot b, \color{blue}{2 \cdot x}\right) \]

   5. Simplified 90.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 2 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-9, t \cdot \left(z \cdot y\right), x \cdot 2\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma -9.0 (* t (* z y)) (* x 2.0))) (t_2 (* t (* z (* y 9.0)))))
   (if (<= t_2 -2e+76)
     t_1
     (if (<= t_2 2e+84) (fma 27.0 (* a b) (* x 2.0)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-9.0, (t * (z * y)), (x * 2.0));
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -2e+76) {
		tmp = t_1;
	} else if (t_2 <= 2e+84) {
		tmp = fma(27.0, (a * b), (x * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(-9.0, Float64(t * Float64(z * y)), Float64(x * 2.0))
	t_2 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_2 <= -2e+76)
		tmp = t_1;
	elseif (t_2 <= 2e+84)
		tmp = fma(27.0, Float64(a * b), Float64(x * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+76], t$95$1, If[LessEqual[t$95$2, 2e+84], N[(27.0 * N[(a * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -2.0000000000000001e76 or 2.00000000000000012e84 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 92.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(9\right), y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9}, y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, \color{blue}{y \cdot \left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \color{blue}{\left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      16. *-lowering-*.f64 87.7

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 87.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]

   5. Taylor expanded in a around 0

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

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

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

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

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

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

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

      4. *-lowering-*.f64 83.8

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

   7. Simplified 83.8%

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

   if -2.0000000000000001e76 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.00000000000000012e84

   1. Initial program 99.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + 2 \cdot x} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]

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

         \[\leadsto \mathsf{fma}\left(27, \color{blue}{a \cdot b}, 2 \cdot x\right) \]

      4. *-lowering-*.f64 90.3

         \[\leadsto \mathsf{fma}\left(27, a \cdot b, \color{blue}{2 \cdot x}\right) \]

   5. Simplified 90.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(-9, t \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 2 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, t \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+147}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(-9 \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* z (* y 9.0)))))
   (if (<= t_1 -5e+87)
     (* t (* -9.0 (* z y)))
     (if (<= t_1 1e+147)
       (fma 27.0 (* a b) (* x 2.0))
       (* (* z y) (* -9.0 t))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * (y * 9.0));
	double tmp;
	if (t_1 <= -5e+87) {
		tmp = t * (-9.0 * (z * y));
	} else if (t_1 <= 1e+147) {
		tmp = fma(27.0, (a * b), (x * 2.0));
	} else {
		tmp = (z * y) * (-9.0 * t);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_1 <= -5e+87)
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	elseif (t_1 <= 1e+147)
		tmp = fma(27.0, Float64(a * b), Float64(x * 2.0));
	else
		tmp = Float64(Float64(z * y) * Float64(-9.0 * t));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+87], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+147], N[(27.0 * N[(a * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.9999999999999998e87

   1. Initial program 96.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 84.9

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

   5. Simplified 84.9%

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

   if -4.9999999999999998e87 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 9.9999999999999998e146

   1. Initial program 99.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + 2 \cdot x} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]

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

         \[\leadsto \mathsf{fma}\left(27, \color{blue}{a \cdot b}, 2 \cdot x\right) \]

      4. *-lowering-*.f64 88.4

         \[\leadsto \mathsf{fma}\left(27, a \cdot b, \color{blue}{2 \cdot x}\right) \]

   5. Simplified 88.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]

   if 9.9999999999999998e146 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 84.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(9\right), y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9}, y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, \color{blue}{y \cdot \left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \color{blue}{\left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      16. *-lowering-*.f64 83.7

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 83.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-lowering-*.f64 73.3

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

   7. Simplified 73.3%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -5 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 10^{+147}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(-9 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-101}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))) (t_2 (* 27.0 (* a b))))
   (if (<= t_1 -1e-63) t_2 (if (<= t_1 2e-101) (* x 2.0) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (t_1 <= -1e-63) {
		tmp = t_2;
	} else if (t_1 <= 2e-101) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    t_2 = 27.0d0 * (a * b)
    if (t_1 <= (-1d-63)) then
        tmp = t_2
    else if (t_1 <= 2d-101) then
        tmp = x * 2.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (t_1 <= -1e-63) {
		tmp = t_2;
	} else if (t_1 <= 2e-101) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	t_2 = 27.0 * (a * b)
	tmp = 0
	if t_1 <= -1e-63:
		tmp = t_2
	elif t_1 <= 2e-101:
		tmp = x * 2.0
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	t_2 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (t_1 <= -1e-63)
		tmp = t_2;
	elseif (t_1 <= 2e-101)
		tmp = Float64(x * 2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	t_2 = 27.0 * (a * b);
	tmp = 0.0;
	if (t_1 <= -1e-63)
		tmp = t_2;
	elseif (t_1 <= 2e-101)
		tmp = x * 2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-63], t$95$2, If[LessEqual[t$95$1, 2e-101], N[(x * 2.0), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.00000000000000007e-63 or 2.0000000000000001e-101 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 96.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. *-lowering-*.f64 58.1

         \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]

   5. Simplified 58.1%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if -1.00000000000000007e-63 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2.0000000000000001e-101

   1. Initial program 97.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 47.9

         \[\leadsto \color{blue}{2 \cdot x} \]

   5. Simplified 47.9%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -1 \cdot 10^{-63}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{-101}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\\ \mathbf{if}\;z \leq 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \left(-9 \cdot y\right), z, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (* 27.0 b) (* x 2.0))))
   (if (<= z 1e-34)
     (fma -9.0 (* y (* z t)) t_1)
     (fma (* t (* -9.0 y)) z t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, (27.0 * b), (x * 2.0));
	double tmp;
	if (z <= 1e-34) {
		tmp = fma(-9.0, (y * (z * t)), t_1);
	} else {
		tmp = fma((t * (-9.0 * y)), z, t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(a, Float64(27.0 * b), Float64(x * 2.0))
	tmp = 0.0
	if (z <= 1e-34)
		tmp = fma(-9.0, Float64(y * Float64(z * t)), t_1);
	else
		tmp = fma(Float64(t * Float64(-9.0 * y)), z, t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 1e-34], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(t * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision] * z + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 9.99999999999999928e-35

   1. Initial program 97.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(9\right), y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9}, y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, \color{blue}{y \cdot \left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \color{blue}{\left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      16. *-lowering-*.f64 97.1

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 97.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]

   if 9.99999999999999928e-35 < z

   1. Initial program 94.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot \left(z \cdot t\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot \color{blue}{\left(t \cdot z\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      7. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t\right) \cdot z} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t\right) \cdot z + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t, z, \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t}, z, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot \left(\mathsf{neg}\left(9\right)\right)\right)} \cdot t, z, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot \left(\mathsf{neg}\left(9\right)\right)\right)} \cdot t, z, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\left(y \cdot \color{blue}{-9}\right) \cdot t, z, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      17. *-lowering-*.f64 97.1

          \[\leadsto \mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 97.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \left(-9 \cdot y\right), z, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\\ \mathbf{if}\;z \leq 9 \cdot 10^{-107}:\\ \;\;\;\;\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot t, z \cdot -9, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (* 27.0 b) (* x 2.0))))
   (if (<= z 9e-107)
     (fma -9.0 (* y (* z t)) t_1)
     (fma (* y t) (* z -9.0) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, (27.0 * b), (x * 2.0));
	double tmp;
	if (z <= 9e-107) {
		tmp = fma(-9.0, (y * (z * t)), t_1);
	} else {
		tmp = fma((y * t), (z * -9.0), t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(a, Float64(27.0 * b), Float64(x * 2.0))
	tmp = 0.0
	if (z <= 9e-107)
		tmp = fma(-9.0, Float64(y * Float64(z * t)), t_1);
	else
		tmp = fma(Float64(y * t), Float64(z * -9.0), t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 9e-107], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(y * t), $MachinePrecision] * N[(z * -9.0), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 9.00000000000000032e-107

   1. Initial program 97.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(9\right), y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9}, y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, \color{blue}{y \cdot \left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \color{blue}{\left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      16. *-lowering-*.f64 96.9

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 96.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]

   if 9.00000000000000032e-107 < z

   1. Initial program 95.5%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      5. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(t \cdot \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*r* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t \cdot y\right) \cdot \left(9 \cdot z\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(t \cdot y\right) \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. +-commutative N/A

         \[\leadsto \left(t \cdot y\right) \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot y, \mathsf{neg}\left(9 \cdot z\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot t}, \mathsf{neg}\left(9 \cdot z\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot t}, \mathsf{neg}\left(9 \cdot z\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y \cdot t, \mathsf{neg}\left(\color{blue}{z \cdot 9}\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(y \cdot t, \color{blue}{z \cdot \left(\mathsf{neg}\left(9\right)\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(y \cdot t, \color{blue}{z \cdot \left(\mathsf{neg}\left(9\right)\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(y \cdot t, z \cdot \color{blue}{-9}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(y \cdot t, z \cdot -9, \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(y \cdot t, z \cdot -9, \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(y \cdot t, z \cdot -9, \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      19. *-lowering-*.f64 97.6

          \[\leadsto \mathsf{fma}\left(y \cdot t, z \cdot -9, \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 97.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot t, z \cdot -9, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 96.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 3.6 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, t \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 3.6e+33)
   (fma -9.0 (* y (* z t)) (fma a (* 27.0 b) (* x 2.0)))
   (fma -9.0 (* t (* z y)) (* x 2.0))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 3.6e+33) {
		tmp = fma(-9.0, (y * (z * t)), fma(a, (27.0 * b), (x * 2.0)));
	} else {
		tmp = fma(-9.0, (t * (z * y)), (x * 2.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 3.6e+33)
		tmp = fma(-9.0, Float64(y * Float64(z * t)), fma(a, Float64(27.0 * b), Float64(x * 2.0)));
	else
		tmp = fma(-9.0, Float64(t * Float64(z * y)), Float64(x * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 3.6e+33], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.6000000000000003e33

   1. Initial program 97.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(9\right), y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9}, y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, \color{blue}{y \cdot \left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \color{blue}{\left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      16. *-lowering-*.f64 97.3

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 97.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]

   if 3.6000000000000003e33 < z

   1. Initial program 93.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

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

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(9\right), y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9}, y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, \color{blue}{y \cdot \left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \color{blue}{\left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

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

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      16. *-lowering-*.f64 85.6

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 85.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]

   5. Taylor expanded in a around 0

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

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

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

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

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

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

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

      4. *-lowering-*.f64 75.8

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

   7. Simplified 75.8%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.6 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, t \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.4% accurate, 6.2× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = x * 2.0d0
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return x * 2.0

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(x * 2.0)
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = x * 2.0;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(x * 2.0), $MachinePrecision]

Derivation

1. Initial program 96.5%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

   1. *-lowering-*.f64 29.3

      \[\leadsto \color{blue}{2 \cdot x} \]

5. Simplified 29.3%

   \[\leadsto \color{blue}{2 \cdot x} \]

6. Final simplification 29.3%

   \[\leadsto x \cdot 2 \]
7. Add Preprocessing

Developer Target 1: 94.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (< y 7.590524218811189e-161)
   (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (y < 7.590524218811189d-161) then
        tmp = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + (a * (27.0d0 * b))
    else
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (t * z)))) + ((a * 27.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y < 7.590524218811189e-161:
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b))
	else:
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y < 7.590524218811189e-161)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(t * z)))) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y < 7.590524218811189e-161)
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	else
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Less[y, 7.590524218811189e-161], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024205 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y 7590524218811189/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x 2) (* (* (* y 9) z) t)) (* a (* 27 b))) (+ (- (* x 2) (* 9 (* y (* t z)))) (* (* a 27) b))))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))