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

Percentage Accurate: 95.7% → 95.7%

Time: 28.0s

Alternatives: 17

Speedup: N/A×

• 26.9% 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: 95.7% 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: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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) (* (* y (* z t)) 9.0)) (* (* a 27.0) b)))

C

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) - ((y * (z * t)) * 9.0)) + ((a * 27.0) * b);
}

Fortran

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) - ((y * (z * t)) * 9.0d0)) + ((a * 27.0d0) * b)
end function

Java

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) - ((y * (z * t)) * 9.0)) + ((a * 27.0) * b);
}

Python

[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) - ((y * (z * t)) * 9.0)) + ((a * 27.0) * b)

Julia

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

MATLAB

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) - ((y * (z * t)) * 9.0)) + ((a * 27.0) * b);
end

Wolfram

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[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.0%

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

   1. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   3. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   7. *-lowering-*.f64 96.0%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

4. Applied egg-rr 96.0%

   \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(z \cdot t\right)\right) \cdot 9}\right) + \left(a \cdot 27\right) \cdot b \]
5. Add Preprocessing

Alternative 2: 52.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-230}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-176}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+141}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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 (* (* a 27.0) b)))
   (if (<= t_1 -5e+38)
     (* a (* 27.0 b))
     (if (<= t_1 -2e-230)
       (* -9.0 (* z (* y t)))
       (if (<= t_1 1e-176)
         (* x 2.0)
         (if (<= t_1 2e+141) (* (* y (* z t)) -9.0) (* 27.0 (* a b))))))))

C

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -5e+38) {
		tmp = a * (27.0 * b);
	} else if (t_1 <= -2e-230) {
		tmp = -9.0 * (z * (y * t));
	} else if (t_1 <= 1e-176) {
		tmp = x * 2.0;
	} else if (t_1 <= 2e+141) {
		tmp = (y * (z * t)) * -9.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

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 = (a * 27.0d0) * b
    if (t_1 <= (-5d+38)) then
        tmp = a * (27.0d0 * b)
    else if (t_1 <= (-2d-230)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (t_1 <= 1d-176) then
        tmp = x * 2.0d0
    else if (t_1 <= 2d+141) then
        tmp = (y * (z * t)) * (-9.0d0)
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -5e+38) {
		tmp = a * (27.0 * b);
	} else if (t_1 <= -2e-230) {
		tmp = -9.0 * (z * (y * t));
	} else if (t_1 <= 1e-176) {
		tmp = x * 2.0;
	} else if (t_1 <= 2e+141) {
		tmp = (y * (z * t)) * -9.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -5e+38:
		tmp = a * (27.0 * b)
	elif t_1 <= -2e-230:
		tmp = -9.0 * (z * (y * t))
	elif t_1 <= 1e-176:
		tmp = x * 2.0
	elif t_1 <= 2e+141:
		tmp = (y * (z * t)) * -9.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

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(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -5e+38)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (t_1 <= -2e-230)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (t_1 <= 1e-176)
		tmp = Float64(x * 2.0);
	elseif (t_1 <= 2e+141)
		tmp = Float64(Float64(y * Float64(z * t)) * -9.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

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 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -5e+38)
		tmp = a * (27.0 * b);
	elseif (t_1 <= -2e-230)
		tmp = -9.0 * (z * (y * t));
	elseif (t_1 <= 1e-176)
		tmp = x * 2.0;
	elseif (t_1 <= 2e+141)
		tmp = (y * (z * t)) * -9.0;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

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[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+38], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-230], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-176], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+141], N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.9999999999999997e38

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 53.7%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   5. Simplified 53.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(27 \cdot b\right), \color{blue}{a}\right) \]

      4. *-lowering-*.f64 53.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(27, b\right), a\right) \]

   7. Applied egg-rr 53.7%

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

   if -4.9999999999999997e38 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2.00000000000000009e-230

   1. Initial program 95.8%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      7. *-lowering-*.f64 93.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   4. Applied egg-rr 93.8%

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

   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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

      8. *-lowering-*.f64 61.8%

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

   7. Simplified 61.8%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. metadata-eval N/A

         \[\leadsto \left(\left(t \cdot y\right) \cdot \left(\mathsf{neg}\left(9\right)\right)\right) \cdot z \]

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

         \[\leadsto \left(\mathsf{neg}\left(\left(t \cdot y\right) \cdot 9\right)\right) \cdot z \]

      6. associate-*r* N/A

         \[\leadsto \left(\mathsf{neg}\left(t \cdot \left(y \cdot 9\right)\right)\right) \cdot z \]

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

         \[\leadsto \mathsf{neg}\left(\left(t \cdot \left(y \cdot 9\right)\right) \cdot z\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(t \cdot \left(y \cdot 9\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(\left(t \cdot y\right) \cdot 9\right)\right) \]

      10. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\left(z \cdot \left(t \cdot y\right)\right) \cdot 9\right) \]

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

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

      12. metadata-eval N/A

          \[\leadsto \left(z \cdot \left(t \cdot y\right)\right) \cdot -9 \]

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

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

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

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

      15. *-lowering-*.f64 61.8%

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

   9. Applied egg-rr 61.8%

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

   if -2.00000000000000009e-230 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1e-176

   1. Initial program 94.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 60.0%

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

   5. Simplified 60.0%

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

   if 1e-176 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2.00000000000000003e141

   1. Initial program 96.1%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      7. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   4. Applied egg-rr 99.7%

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

   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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

      8. *-lowering-*.f64 58.1%

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

   7. Simplified 58.1%

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 61.7%

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

   9. Applied egg-rr 61.7%

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

   if 2.00000000000000003e141 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 95.3%

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

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 84.2%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   5. Simplified 84.2%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -5 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{-230}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 10^{-176}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+141}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-230}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-176}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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 (* (* a 27.0) b)))
   (if (<= t_1 -5e+38)
     (* a (* 27.0 b))
     (if (<= t_1 -2e-230)
       (* -9.0 (* z (* y t)))
       (if (<= t_1 1e-176)
         (* x 2.0)
         (if (<= t_1 2e+141) (* y (* t (* z -9.0))) (* 27.0 (* a b))))))))

C

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -5e+38) {
		tmp = a * (27.0 * b);
	} else if (t_1 <= -2e-230) {
		tmp = -9.0 * (z * (y * t));
	} else if (t_1 <= 1e-176) {
		tmp = x * 2.0;
	} else if (t_1 <= 2e+141) {
		tmp = y * (t * (z * -9.0));
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

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 = (a * 27.0d0) * b
    if (t_1 <= (-5d+38)) then
        tmp = a * (27.0d0 * b)
    else if (t_1 <= (-2d-230)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (t_1 <= 1d-176) then
        tmp = x * 2.0d0
    else if (t_1 <= 2d+141) then
        tmp = y * (t * (z * (-9.0d0)))
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -5e+38) {
		tmp = a * (27.0 * b);
	} else if (t_1 <= -2e-230) {
		tmp = -9.0 * (z * (y * t));
	} else if (t_1 <= 1e-176) {
		tmp = x * 2.0;
	} else if (t_1 <= 2e+141) {
		tmp = y * (t * (z * -9.0));
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -5e+38:
		tmp = a * (27.0 * b)
	elif t_1 <= -2e-230:
		tmp = -9.0 * (z * (y * t))
	elif t_1 <= 1e-176:
		tmp = x * 2.0
	elif t_1 <= 2e+141:
		tmp = y * (t * (z * -9.0))
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

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(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -5e+38)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (t_1 <= -2e-230)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (t_1 <= 1e-176)
		tmp = Float64(x * 2.0);
	elseif (t_1 <= 2e+141)
		tmp = Float64(y * Float64(t * Float64(z * -9.0)));
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

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 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -5e+38)
		tmp = a * (27.0 * b);
	elseif (t_1 <= -2e-230)
		tmp = -9.0 * (z * (y * t));
	elseif (t_1 <= 1e-176)
		tmp = x * 2.0;
	elseif (t_1 <= 2e+141)
		tmp = y * (t * (z * -9.0));
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

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[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+38], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-230], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-176], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+141], N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.9999999999999997e38

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 53.7%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   5. Simplified 53.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(27 \cdot b\right), \color{blue}{a}\right) \]

      4. *-lowering-*.f64 53.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(27, b\right), a\right) \]

   7. Applied egg-rr 53.7%

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

   if -4.9999999999999997e38 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2.00000000000000009e-230

   1. Initial program 95.8%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      7. *-lowering-*.f64 93.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   4. Applied egg-rr 93.8%

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

   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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

      8. *-lowering-*.f64 61.8%

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

   7. Simplified 61.8%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. metadata-eval N/A

         \[\leadsto \left(\left(t \cdot y\right) \cdot \left(\mathsf{neg}\left(9\right)\right)\right) \cdot z \]

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

         \[\leadsto \left(\mathsf{neg}\left(\left(t \cdot y\right) \cdot 9\right)\right) \cdot z \]

      6. associate-*r* N/A

         \[\leadsto \left(\mathsf{neg}\left(t \cdot \left(y \cdot 9\right)\right)\right) \cdot z \]

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

         \[\leadsto \mathsf{neg}\left(\left(t \cdot \left(y \cdot 9\right)\right) \cdot z\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(t \cdot \left(y \cdot 9\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(\left(t \cdot y\right) \cdot 9\right)\right) \]

      10. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\left(z \cdot \left(t \cdot y\right)\right) \cdot 9\right) \]

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

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

      12. metadata-eval N/A

          \[\leadsto \left(z \cdot \left(t \cdot y\right)\right) \cdot -9 \]

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

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

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

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

      15. *-lowering-*.f64 61.8%

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

   9. Applied egg-rr 61.8%

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

   if -2.00000000000000009e-230 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1e-176

   1. Initial program 94.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 60.0%

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

   5. Simplified 60.0%

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

   if 1e-176 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2.00000000000000003e141

   1. Initial program 96.1%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      7. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   4. Applied egg-rr 99.7%

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

   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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

      8. *-lowering-*.f64 58.1%

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

   7. Simplified 58.1%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 61.7%

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

   9. Applied egg-rr 61.7%

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

   if 2.00000000000000003e141 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 95.3%

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

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 84.2%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   5. Simplified 84.2%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -5 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{-230}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 10^{-176}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-230}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-176}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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 (* (* a 27.0) b)))
   (if (<= t_1 -5e+38)
     (* a (* 27.0 b))
     (if (<= t_1 -2e-230)
       (* (* z t) (* y -9.0))
       (if (<= t_1 1e-176)
         (* x 2.0)
         (if (<= t_1 2e+141) (* y (* t (* z -9.0))) (* 27.0 (* a b))))))))

C

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -5e+38) {
		tmp = a * (27.0 * b);
	} else if (t_1 <= -2e-230) {
		tmp = (z * t) * (y * -9.0);
	} else if (t_1 <= 1e-176) {
		tmp = x * 2.0;
	} else if (t_1 <= 2e+141) {
		tmp = y * (t * (z * -9.0));
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

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 = (a * 27.0d0) * b
    if (t_1 <= (-5d+38)) then
        tmp = a * (27.0d0 * b)
    else if (t_1 <= (-2d-230)) then
        tmp = (z * t) * (y * (-9.0d0))
    else if (t_1 <= 1d-176) then
        tmp = x * 2.0d0
    else if (t_1 <= 2d+141) then
        tmp = y * (t * (z * (-9.0d0)))
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -5e+38) {
		tmp = a * (27.0 * b);
	} else if (t_1 <= -2e-230) {
		tmp = (z * t) * (y * -9.0);
	} else if (t_1 <= 1e-176) {
		tmp = x * 2.0;
	} else if (t_1 <= 2e+141) {
		tmp = y * (t * (z * -9.0));
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -5e+38:
		tmp = a * (27.0 * b)
	elif t_1 <= -2e-230:
		tmp = (z * t) * (y * -9.0)
	elif t_1 <= 1e-176:
		tmp = x * 2.0
	elif t_1 <= 2e+141:
		tmp = y * (t * (z * -9.0))
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

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(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -5e+38)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (t_1 <= -2e-230)
		tmp = Float64(Float64(z * t) * Float64(y * -9.0));
	elseif (t_1 <= 1e-176)
		tmp = Float64(x * 2.0);
	elseif (t_1 <= 2e+141)
		tmp = Float64(y * Float64(t * Float64(z * -9.0)));
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

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 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -5e+38)
		tmp = a * (27.0 * b);
	elseif (t_1 <= -2e-230)
		tmp = (z * t) * (y * -9.0);
	elseif (t_1 <= 1e-176)
		tmp = x * 2.0;
	elseif (t_1 <= 2e+141)
		tmp = y * (t * (z * -9.0));
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

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[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+38], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-230], N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-176], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+141], N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.9999999999999997e38

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 53.7%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   5. Simplified 53.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(27 \cdot b\right), \color{blue}{a}\right) \]

      4. *-lowering-*.f64 53.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(27, b\right), a\right) \]

   7. Applied egg-rr 53.7%

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

   if -4.9999999999999997e38 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2.00000000000000009e-230

   1. Initial program 95.8%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      7. *-lowering-*.f64 93.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   4. Applied egg-rr 93.8%

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

   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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

      8. *-lowering-*.f64 61.8%

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

   7. Simplified 61.8%

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

         \[\leadsto \left(t \cdot \left(y \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(9\right)\right) \]

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

         \[\leadsto \mathsf{neg}\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 9\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(t \cdot \left(z \cdot y\right)\right) \cdot 9\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\left(\left(t \cdot z\right) \cdot y\right) \cdot 9\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(\left(z \cdot t\right) \cdot y\right) \cdot 9\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\left(z \cdot t\right) \cdot \left(y \cdot 9\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) \]

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

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

      11. *-commutative N/A

          \[\leadsto \left(\mathsf{neg}\left(9 \cdot y\right)\right) \cdot \left(z \cdot t\right) \]

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

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

      13. metadata-eval N/A

          \[\leadsto \left(-9 \cdot y\right) \cdot \left(z \cdot t\right) \]

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

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

      15. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\left(\mathsf{neg}\left(9\right)\right) \cdot y\right), \left(z \cdot t\right)\right) \]

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

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

      17. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(y \cdot 9\right)\right), \left(z \cdot t\right)\right) \]

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

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

      19. metadata-eval N/A

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

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

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

      21. *-commutative N/A

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

      22. *-lowering-*.f64 57.9%

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

   9. Applied egg-rr 57.9%

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

   if -2.00000000000000009e-230 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1e-176

   1. Initial program 94.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 60.0%

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

   5. Simplified 60.0%

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

   if 1e-176 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2.00000000000000003e141

   1. Initial program 96.1%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      7. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   4. Applied egg-rr 99.7%

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

   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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

      8. *-lowering-*.f64 58.1%

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

   7. Simplified 58.1%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 61.7%

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

   9. Applied egg-rr 61.7%

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

   if 2.00000000000000003e141 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 95.3%

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

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 84.2%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   5. Simplified 84.2%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -5 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{-230}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 10^{-176}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ t_2 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-176}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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 (* y (* t (* z -9.0)))) (t_2 (* (* a 27.0) b)))
   (if (<= t_2 -5e+38)
     (* a (* 27.0 b))
     (if (<= t_2 -2e-230)
       t_1
       (if (<= t_2 1e-176)
         (* x 2.0)
         (if (<= t_2 2e+141) t_1 (* 27.0 (* a b))))))))

C

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 = y * (t * (z * -9.0));
	double t_2 = (a * 27.0) * b;
	double tmp;
	if (t_2 <= -5e+38) {
		tmp = a * (27.0 * b);
	} else if (t_2 <= -2e-230) {
		tmp = t_1;
	} else if (t_2 <= 1e-176) {
		tmp = x * 2.0;
	} else if (t_2 <= 2e+141) {
		tmp = t_1;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

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 = y * (t * (z * (-9.0d0)))
    t_2 = (a * 27.0d0) * b
    if (t_2 <= (-5d+38)) then
        tmp = a * (27.0d0 * b)
    else if (t_2 <= (-2d-230)) then
        tmp = t_1
    else if (t_2 <= 1d-176) then
        tmp = x * 2.0d0
    else if (t_2 <= 2d+141) then
        tmp = t_1
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

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 = y * (t * (z * -9.0));
	double t_2 = (a * 27.0) * b;
	double tmp;
	if (t_2 <= -5e+38) {
		tmp = a * (27.0 * b);
	} else if (t_2 <= -2e-230) {
		tmp = t_1;
	} else if (t_2 <= 1e-176) {
		tmp = x * 2.0;
	} else if (t_2 <= 2e+141) {
		tmp = t_1;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = y * (t * (z * -9.0))
	t_2 = (a * 27.0) * b
	tmp = 0
	if t_2 <= -5e+38:
		tmp = a * (27.0 * b)
	elif t_2 <= -2e-230:
		tmp = t_1
	elif t_2 <= 1e-176:
		tmp = x * 2.0
	elif t_2 <= 2e+141:
		tmp = t_1
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(t * Float64(z * -9.0)))
	t_2 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_2 <= -5e+38)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (t_2 <= -2e-230)
		tmp = t_1;
	elseif (t_2 <= 1e-176)
		tmp = Float64(x * 2.0);
	elseif (t_2 <= 2e+141)
		tmp = t_1;
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

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 = y * (t * (z * -9.0));
	t_2 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_2 <= -5e+38)
		tmp = a * (27.0 * b);
	elseif (t_2 <= -2e-230)
		tmp = t_1;
	elseif (t_2 <= 1e-176)
		tmp = x * 2.0;
	elseif (t_2 <= 2e+141)
		tmp = t_1;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

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[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+38], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-230], t$95$1, If[LessEqual[t$95$2, 1e-176], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$2, 2e+141], t$95$1, N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.9999999999999997e38

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 53.7%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   5. Simplified 53.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(27 \cdot b\right), \color{blue}{a}\right) \]

      4. *-lowering-*.f64 53.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(27, b\right), a\right) \]

   7. Applied egg-rr 53.7%

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

   if -4.9999999999999997e38 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2.00000000000000009e-230 or 1e-176 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2.00000000000000003e141

   1. Initial program 95.9%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      7. *-lowering-*.f64 96.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   4. Applied egg-rr 96.8%

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

   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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

      8. *-lowering-*.f64 59.9%

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

   7. Simplified 59.9%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 59.8%

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

   9. Applied egg-rr 59.8%

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

   if -2.00000000000000009e-230 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1e-176

   1. Initial program 94.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 60.0%

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

   5. Simplified 60.0%

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

   if 2.00000000000000003e141 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 95.3%

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

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 84.2%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   5. Simplified 84.2%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -5 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 10^{-176}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ t_2 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-176}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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 (* -9.0 (* y z)))) (t_2 (* (* a 27.0) b)))
   (if (<= t_2 -2e+36)
     (* a (* 27.0 b))
     (if (<= t_2 -2e-230)
       t_1
       (if (<= t_2 1e-176)
         (* x 2.0)
         (if (<= t_2 5e+170) t_1 (* 27.0 (* a b))))))))

C

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 * (-9.0 * (y * z));
	double t_2 = (a * 27.0) * b;
	double tmp;
	if (t_2 <= -2e+36) {
		tmp = a * (27.0 * b);
	} else if (t_2 <= -2e-230) {
		tmp = t_1;
	} else if (t_2 <= 1e-176) {
		tmp = x * 2.0;
	} else if (t_2 <= 5e+170) {
		tmp = t_1;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

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 = t * ((-9.0d0) * (y * z))
    t_2 = (a * 27.0d0) * b
    if (t_2 <= (-2d+36)) then
        tmp = a * (27.0d0 * b)
    else if (t_2 <= (-2d-230)) then
        tmp = t_1
    else if (t_2 <= 1d-176) then
        tmp = x * 2.0d0
    else if (t_2 <= 5d+170) then
        tmp = t_1
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

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 = t * (-9.0 * (y * z));
	double t_2 = (a * 27.0) * b;
	double tmp;
	if (t_2 <= -2e+36) {
		tmp = a * (27.0 * b);
	} else if (t_2 <= -2e-230) {
		tmp = t_1;
	} else if (t_2 <= 1e-176) {
		tmp = x * 2.0;
	} else if (t_2 <= 5e+170) {
		tmp = t_1;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = t * (-9.0 * (y * z))
	t_2 = (a * 27.0) * b
	tmp = 0
	if t_2 <= -2e+36:
		tmp = a * (27.0 * b)
	elif t_2 <= -2e-230:
		tmp = t_1
	elif t_2 <= 1e-176:
		tmp = x * 2.0
	elif t_2 <= 5e+170:
		tmp = t_1
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

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(-9.0 * Float64(y * z)))
	t_2 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_2 <= -2e+36)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (t_2 <= -2e-230)
		tmp = t_1;
	elseif (t_2 <= 1e-176)
		tmp = Float64(x * 2.0);
	elseif (t_2 <= 5e+170)
		tmp = t_1;
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

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 = t * (-9.0 * (y * z));
	t_2 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_2 <= -2e+36)
		tmp = a * (27.0 * b);
	elseif (t_2 <= -2e-230)
		tmp = t_1;
	elseif (t_2 <= 1e-176)
		tmp = x * 2.0;
	elseif (t_2 <= 5e+170)
		tmp = t_1;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

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[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+36], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-230], t$95$1, If[LessEqual[t$95$2, 1e-176], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$2, 5e+170], t$95$1, N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2.00000000000000008e36

   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 inf

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

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

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 52.8%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   5. Simplified 52.8%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(27 \cdot b\right), \color{blue}{a}\right) \]

      4. *-lowering-*.f64 52.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(27, b\right), a\right) \]

   7. Applied egg-rr 52.8%

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

   if -2.00000000000000008e36 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2.00000000000000009e-230 or 1e-176 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 4.99999999999999977e170

   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

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 59.1%

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

   5. Simplified 59.1%

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

   if -2.00000000000000009e-230 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1e-176

   1. Initial program 94.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 60.0%

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

   5. Simplified 60.0%

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

   if 4.99999999999999977e170 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   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. 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

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 90.2%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   5. Simplified 90.2%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{-230}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 10^{-176}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 5 \cdot 10^{+170}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ t_2 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-176}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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 (* y (* z -9.0)))) (t_2 (* (* a 27.0) b)))
   (if (<= t_2 -2e+36)
     (* a (* 27.0 b))
     (if (<= t_2 -2e-230)
       t_1
       (if (<= t_2 1e-176)
         (* x 2.0)
         (if (<= t_2 5e+170) t_1 (* 27.0 (* a b))))))))

C

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 * (y * (z * -9.0));
	double t_2 = (a * 27.0) * b;
	double tmp;
	if (t_2 <= -2e+36) {
		tmp = a * (27.0 * b);
	} else if (t_2 <= -2e-230) {
		tmp = t_1;
	} else if (t_2 <= 1e-176) {
		tmp = x * 2.0;
	} else if (t_2 <= 5e+170) {
		tmp = t_1;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

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 = t * (y * (z * (-9.0d0)))
    t_2 = (a * 27.0d0) * b
    if (t_2 <= (-2d+36)) then
        tmp = a * (27.0d0 * b)
    else if (t_2 <= (-2d-230)) then
        tmp = t_1
    else if (t_2 <= 1d-176) then
        tmp = x * 2.0d0
    else if (t_2 <= 5d+170) then
        tmp = t_1
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

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 = t * (y * (z * -9.0));
	double t_2 = (a * 27.0) * b;
	double tmp;
	if (t_2 <= -2e+36) {
		tmp = a * (27.0 * b);
	} else if (t_2 <= -2e-230) {
		tmp = t_1;
	} else if (t_2 <= 1e-176) {
		tmp = x * 2.0;
	} else if (t_2 <= 5e+170) {
		tmp = t_1;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = t * (y * (z * -9.0))
	t_2 = (a * 27.0) * b
	tmp = 0
	if t_2 <= -2e+36:
		tmp = a * (27.0 * b)
	elif t_2 <= -2e-230:
		tmp = t_1
	elif t_2 <= 1e-176:
		tmp = x * 2.0
	elif t_2 <= 5e+170:
		tmp = t_1
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

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(y * Float64(z * -9.0)))
	t_2 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_2 <= -2e+36)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (t_2 <= -2e-230)
		tmp = t_1;
	elseif (t_2 <= 1e-176)
		tmp = Float64(x * 2.0);
	elseif (t_2 <= 5e+170)
		tmp = t_1;
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

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 = t * (y * (z * -9.0));
	t_2 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_2 <= -2e+36)
		tmp = a * (27.0 * b);
	elseif (t_2 <= -2e-230)
		tmp = t_1;
	elseif (t_2 <= 1e-176)
		tmp = x * 2.0;
	elseif (t_2 <= 5e+170)
		tmp = t_1;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

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[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+36], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-230], t$95$1, If[LessEqual[t$95$2, 1e-176], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$2, 5e+170], t$95$1, N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2.00000000000000008e36

   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 inf

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

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

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 52.8%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   5. Simplified 52.8%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(27 \cdot b\right), \color{blue}{a}\right) \]

      4. *-lowering-*.f64 52.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(27, b\right), a\right) \]

   7. Applied egg-rr 52.8%

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

   if -2.00000000000000008e36 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2.00000000000000009e-230 or 1e-176 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 4.99999999999999977e170

   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. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      7. *-lowering-*.f64 96.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   4. Applied egg-rr 96.9%

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

   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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

      8. *-lowering-*.f64 59.1%

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

   7. Simplified 59.1%

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

   if -2.00000000000000009e-230 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1e-176

   1. Initial program 94.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 60.0%

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

   5. Simplified 60.0%

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

   if 4.99999999999999977e170 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   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. 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

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 90.2%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   5. Simplified 90.2%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{-230}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 10^{-176}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 5 \cdot 10^{+170}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-21}:\\ \;\;\;\;t\_1 + \left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \end{array} \end{array} \]

FPCore

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 (* (* a 27.0) b)))
   (if (<= t_1 -2e-21)
     (+ t_1 (* (* y t) (* z -9.0)))
     (if (<= t_1 2e+21)
       (+ (* y (* t (* z -9.0))) (* x 2.0))
       (+ t_1 (* (* y (* z t)) -9.0))))))

C

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -2e-21) {
		tmp = t_1 + ((y * t) * (z * -9.0));
	} else if (t_1 <= 2e+21) {
		tmp = (y * (t * (z * -9.0))) + (x * 2.0);
	} else {
		tmp = t_1 + ((y * (z * t)) * -9.0);
	}
	return tmp;
}

Fortran

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 = (a * 27.0d0) * b
    if (t_1 <= (-2d-21)) then
        tmp = t_1 + ((y * t) * (z * (-9.0d0)))
    else if (t_1 <= 2d+21) then
        tmp = (y * (t * (z * (-9.0d0)))) + (x * 2.0d0)
    else
        tmp = t_1 + ((y * (z * t)) * (-9.0d0))
    end if
    code = tmp
end function

Java

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -2e-21) {
		tmp = t_1 + ((y * t) * (z * -9.0));
	} else if (t_1 <= 2e+21) {
		tmp = (y * (t * (z * -9.0))) + (x * 2.0);
	} else {
		tmp = t_1 + ((y * (z * t)) * -9.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -2e-21:
		tmp = t_1 + ((y * t) * (z * -9.0))
	elif t_1 <= 2e+21:
		tmp = (y * (t * (z * -9.0))) + (x * 2.0)
	else:
		tmp = t_1 + ((y * (z * t)) * -9.0)
	return tmp

Julia

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(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -2e-21)
		tmp = Float64(t_1 + Float64(Float64(y * t) * Float64(z * -9.0)));
	elseif (t_1 <= 2e+21)
		tmp = Float64(Float64(y * Float64(t * Float64(z * -9.0))) + Float64(x * 2.0));
	else
		tmp = Float64(t_1 + Float64(Float64(y * Float64(z * t)) * -9.0));
	end
	return tmp
end

MATLAB

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 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -2e-21)
		tmp = t_1 + ((y * t) * (z * -9.0));
	elseif (t_1 <= 2e+21)
		tmp = (y * (t * (z * -9.0))) + (x * 2.0);
	else
		tmp = t_1 + ((y * (z * t)) * -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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-21], N[(t$95$1 + N[(N[(y * t), $MachinePrecision] * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+21], N[(N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.99999999999999982e-21

   1. Initial program 93.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot -9\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-9 \cdot \left(y \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(y \cdot z\right) \cdot -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\left(y \cdot z\right), -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      7. *-lowering-*.f64 83.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   5. Simplified 83.0%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot y\right) \cdot \left(z \cdot -9\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(t \cdot y\right), \left(z \cdot -9\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y\right), \left(z \cdot -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{a}, 27\right), b\right)\right) \]

      5. *-lowering-*.f64 83.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y\right), \mathsf{*.f64}\left(z, -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

   7. Applied egg-rr 83.1%

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

   if -1.99999999999999982e-21 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2e21

   1. Initial program 95.6%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      7. *-lowering-*.f64 97.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   4. Applied egg-rr 97.0%

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

   5. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

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

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

      12. *-lowering-*.f64 91.6%

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

   7. Simplified 91.6%

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

      1. +-commutative N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 92.9%

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

   9. Applied egg-rr 92.9%

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

   if 2e21 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot -9\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-9 \cdot \left(y \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(y \cdot z\right) \cdot -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\left(y \cdot z\right), -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      7. *-lowering-*.f64 89.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   5. Simplified 89.1%

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

      1. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot -9\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(y \cdot z\right) \cdot t\right) \cdot -9\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{a}, 27\right), b\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{a}, 27\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), -9\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), -9\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{a}, 27\right), b\right)\right) \]

      6. *-lowering-*.f64 90.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), -9\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   7. Applied egg-rr 90.5%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{-21}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-21}:\\ \;\;\;\;t\_1 + \left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= t_1 -2e-21)
     (+ t_1 (* (* y t) (* z -9.0)))
     (if (<= t_1 2e+21)
       (+ (* y (* t (* z -9.0))) (* x 2.0))
       (+ t_1 (* t (* -9.0 (* y z))))))))

C

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -2e-21) {
		tmp = t_1 + ((y * t) * (z * -9.0));
	} else if (t_1 <= 2e+21) {
		tmp = (y * (t * (z * -9.0))) + (x * 2.0);
	} else {
		tmp = t_1 + (t * (-9.0 * (y * z)));
	}
	return tmp;
}

Fortran

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 = (a * 27.0d0) * b
    if (t_1 <= (-2d-21)) then
        tmp = t_1 + ((y * t) * (z * (-9.0d0)))
    else if (t_1 <= 2d+21) then
        tmp = (y * (t * (z * (-9.0d0)))) + (x * 2.0d0)
    else
        tmp = t_1 + (t * ((-9.0d0) * (y * z)))
    end if
    code = tmp
end function

Java

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -2e-21) {
		tmp = t_1 + ((y * t) * (z * -9.0));
	} else if (t_1 <= 2e+21) {
		tmp = (y * (t * (z * -9.0))) + (x * 2.0);
	} else {
		tmp = t_1 + (t * (-9.0 * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -2e-21:
		tmp = t_1 + ((y * t) * (z * -9.0))
	elif t_1 <= 2e+21:
		tmp = (y * (t * (z * -9.0))) + (x * 2.0)
	else:
		tmp = t_1 + (t * (-9.0 * (y * z)))
	return tmp

Julia

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(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -2e-21)
		tmp = Float64(t_1 + Float64(Float64(y * t) * Float64(z * -9.0)));
	elseif (t_1 <= 2e+21)
		tmp = Float64(Float64(y * Float64(t * Float64(z * -9.0))) + Float64(x * 2.0));
	else
		tmp = Float64(t_1 + Float64(t * Float64(-9.0 * Float64(y * z))));
	end
	return tmp
end

MATLAB

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 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -2e-21)
		tmp = t_1 + ((y * t) * (z * -9.0));
	elseif (t_1 <= 2e+21)
		tmp = (y * (t * (z * -9.0))) + (x * 2.0);
	else
		tmp = t_1 + (t * (-9.0 * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

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[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-21], N[(t$95$1 + N[(N[(y * t), $MachinePrecision] * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+21], N[(N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t * N[(-9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.99999999999999982e-21

   1. Initial program 93.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot -9\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-9 \cdot \left(y \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(y \cdot z\right) \cdot -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\left(y \cdot z\right), -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      7. *-lowering-*.f64 83.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   5. Simplified 83.0%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot y\right) \cdot \left(z \cdot -9\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(t \cdot y\right), \left(z \cdot -9\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y\right), \left(z \cdot -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{a}, 27\right), b\right)\right) \]

      5. *-lowering-*.f64 83.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(t, y\right), \mathsf{*.f64}\left(z, -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

   7. Applied egg-rr 83.1%

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

   if -1.99999999999999982e-21 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2e21

   1. Initial program 95.6%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      7. *-lowering-*.f64 97.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   4. Applied egg-rr 97.0%

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

   5. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

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

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

      12. *-lowering-*.f64 91.6%

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

   7. Simplified 91.6%

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

      1. +-commutative N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 92.9%

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

   9. Applied egg-rr 92.9%

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

   if 2e21 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot -9\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-9 \cdot \left(y \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(y \cdot z\right) \cdot -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\left(y \cdot z\right), -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      7. *-lowering-*.f64 89.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   5. Simplified 89.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{-21}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := t\_1 + t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)) (t_2 (+ t_1 (* t (* -9.0 (* y z))))))
   (if (<= t_1 -2e-21)
     t_2
     (if (<= t_1 2e+21) (+ (* y (* t (* z -9.0))) (* x 2.0)) t_2))))

C

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 = (a * 27.0) * b;
	double t_2 = t_1 + (t * (-9.0 * (y * z)));
	double tmp;
	if (t_1 <= -2e-21) {
		tmp = t_2;
	} else if (t_1 <= 2e+21) {
		tmp = (y * (t * (z * -9.0))) + (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.
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 = (a * 27.0d0) * b
    t_2 = t_1 + (t * ((-9.0d0) * (y * z)))
    if (t_1 <= (-2d-21)) then
        tmp = t_2
    else if (t_1 <= 2d+21) then
        tmp = (y * (t * (z * (-9.0d0)))) + (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;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = t_1 + (t * (-9.0 * (y * z)));
	double tmp;
	if (t_1 <= -2e-21) {
		tmp = t_2;
	} else if (t_1 <= 2e+21) {
		tmp = (y * (t * (z * -9.0))) + (x * 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	t_2 = t_1 + (t * (-9.0 * (y * z)))
	tmp = 0
	if t_1 <= -2e-21:
		tmp = t_2
	elif t_1 <= 2e+21:
		tmp = (y * (t * (z * -9.0))) + (x * 2.0)
	else:
		tmp = t_2
	return tmp

Julia

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(a * 27.0) * b)
	t_2 = Float64(t_1 + Float64(t * Float64(-9.0 * Float64(y * z))))
	tmp = 0.0
	if (t_1 <= -2e-21)
		tmp = t_2;
	elseif (t_1 <= 2e+21)
		tmp = Float64(Float64(y * Float64(t * Float64(z * -9.0))) + 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])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	t_2 = t_1 + (t * (-9.0 * (y * z)));
	tmp = 0.0;
	if (t_1 <= -2e-21)
		tmp = t_2;
	elseif (t_1 <= 2e+21)
		tmp = (y * (t * (z * -9.0))) + (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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(t * N[(-9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-21], t$95$2, If[LessEqual[t$95$1, 2e+21], N[(N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.99999999999999982e-21 or 2e21 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 94.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot -9\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(-9 \cdot \left(y \cdot z\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(y \cdot z\right) \cdot -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\left(y \cdot z\right), -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      7. *-lowering-*.f64 85.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), -9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   5. Simplified 85.9%

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

   if -1.99999999999999982e-21 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2e21

   1. Initial program 95.6%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      7. *-lowering-*.f64 97.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   4. Applied egg-rr 97.0%

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

   5. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

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

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

      12. *-lowering-*.f64 91.6%

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

   7. Simplified 91.6%

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

      1. +-commutative N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 92.9%

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

   9. Applied egg-rr 92.9%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{-21}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+168}:\\ \;\;\;\;t\_1 + x \cdot 2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+170}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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 (* (* a 27.0) b)))
   (if (<= t_1 -5e+168)
     (+ t_1 (* x 2.0))
     (if (<= t_1 5e+170)
       (+ (* y (* t (* z -9.0))) (* x 2.0))
       (+ (* x 2.0) (* 27.0 (* a b)))))))

C

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -5e+168) {
		tmp = t_1 + (x * 2.0);
	} else if (t_1 <= 5e+170) {
		tmp = (y * (t * (z * -9.0))) + (x * 2.0);
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Fortran

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 = (a * 27.0d0) * b
    if (t_1 <= (-5d+168)) then
        tmp = t_1 + (x * 2.0d0)
    else if (t_1 <= 5d+170) then
        tmp = (y * (t * (z * (-9.0d0)))) + (x * 2.0d0)
    else
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    end if
    code = tmp
end function

Java

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -5e+168) {
		tmp = t_1 + (x * 2.0);
	} else if (t_1 <= 5e+170) {
		tmp = (y * (t * (z * -9.0))) + (x * 2.0);
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -5e+168:
		tmp = t_1 + (x * 2.0)
	elif t_1 <= 5e+170:
		tmp = (y * (t * (z * -9.0))) + (x * 2.0)
	else:
		tmp = (x * 2.0) + (27.0 * (a * b))
	return tmp

Julia

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(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -5e+168)
		tmp = Float64(t_1 + Float64(x * 2.0));
	elseif (t_1 <= 5e+170)
		tmp = Float64(Float64(y * Float64(t * Float64(z * -9.0))) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	end
	return tmp
end

MATLAB

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 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -5e+168)
		tmp = t_1 + (x * 2.0);
	elseif (t_1 <= 5e+170)
		tmp = (y * (t * (z * -9.0))) + (x * 2.0);
	else
		tmp = (x * 2.0) + (27.0 * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

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[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+168], N[(t$95$1 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+170], N[(N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.99999999999999967e168

   1. Initial program 91.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(2 \cdot x\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 73.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

   5. Simplified 73.3%

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

   if -4.99999999999999967e168 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 4.99999999999999977e170

   1. Initial program 95.1%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      7. *-lowering-*.f64 97.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   4. Applied egg-rr 97.2%

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

   5. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

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

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

      12. *-lowering-*.f64 84.6%

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

   7. Simplified 84.6%

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

      1. +-commutative N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

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

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

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

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

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

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 86.6%

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

   9. Applied egg-rr 86.6%

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

   if 4.99999999999999977e170 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   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. 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

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(27 \cdot \left(a \cdot b\right)\right), \color{blue}{\left(2 \cdot x\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(27, \left(a \cdot b\right)\right), \left(\color{blue}{2} \cdot x\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, b\right)\right), \left(2 \cdot x\right)\right) \]

      5. *-lowering-*.f64 94.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, b\right)\right), \mathsf{*.f64}\left(2, \color{blue}{x}\right)\right) \]

   5. Simplified 94.8%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -5 \cdot 10^{+168}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + x \cdot 2\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 5 \cdot 10^{+170}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 81.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+36}:\\ \;\;\;\;x \cdot 2 + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+170}:\\ \;\;\;\;x \cdot 2 + t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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 (* (* a 27.0) b)))
   (if (<= t_1 -2e+36)
     (+ (* x 2.0) (* a (* 27.0 b)))
     (if (<= t_1 5e+170)
       (+ (* x 2.0) (* t (* y (* z -9.0))))
       (+ (* x 2.0) (* 27.0 (* a b)))))))

C

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -2e+36) {
		tmp = (x * 2.0) + (a * (27.0 * b));
	} else if (t_1 <= 5e+170) {
		tmp = (x * 2.0) + (t * (y * (z * -9.0)));
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Fortran

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 = (a * 27.0d0) * b
    if (t_1 <= (-2d+36)) then
        tmp = (x * 2.0d0) + (a * (27.0d0 * b))
    else if (t_1 <= 5d+170) then
        tmp = (x * 2.0d0) + (t * (y * (z * (-9.0d0))))
    else
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    end if
    code = tmp
end function

Java

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -2e+36) {
		tmp = (x * 2.0) + (a * (27.0 * b));
	} else if (t_1 <= 5e+170) {
		tmp = (x * 2.0) + (t * (y * (z * -9.0)));
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -2e+36:
		tmp = (x * 2.0) + (a * (27.0 * b))
	elif t_1 <= 5e+170:
		tmp = (x * 2.0) + (t * (y * (z * -9.0)))
	else:
		tmp = (x * 2.0) + (27.0 * (a * b))
	return tmp

Julia

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(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -2e+36)
		tmp = Float64(Float64(x * 2.0) + Float64(a * Float64(27.0 * b)));
	elseif (t_1 <= 5e+170)
		tmp = Float64(Float64(x * 2.0) + Float64(t * Float64(y * Float64(z * -9.0))));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	end
	return tmp
end

MATLAB

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 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -2e+36)
		tmp = (x * 2.0) + (a * (27.0 * b));
	elseif (t_1 <= 5e+170)
		tmp = (x * 2.0) + (t * (y * (z * -9.0)));
	else
		tmp = (x * 2.0) + (27.0 * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

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[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+36], N[(N[(x * 2.0), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+170], N[(N[(x * 2.0), $MachinePrecision] + N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2.00000000000000008e36

   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 x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(2 \cdot x\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 67.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

   5. Simplified 67.5%

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

      1. *-commutative N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{\left(\left(a \cdot 27\right) \cdot b\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\color{blue}{\left(a \cdot 27\right)} \cdot b\right)\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(a \cdot \color{blue}{\left(27 \cdot b\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(a, \color{blue}{\left(27 \cdot b\right)}\right)\right) \]

      6. *-lowering-*.f64 65.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, \color{blue}{b}\right)\right)\right) \]

   7. Applied egg-rr 65.6%

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

   if -2.00000000000000008e36 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 4.99999999999999977e170

   1. Initial program 95.2%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      7. *-lowering-*.f64 96.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   4. Applied egg-rr 96.9%

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

   5. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

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

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

      12. *-lowering-*.f64 87.6%

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

   7. Simplified 87.6%

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

   if 4.99999999999999977e170 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   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. 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

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(27 \cdot \left(a \cdot b\right)\right), \color{blue}{\left(2 \cdot x\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(27, \left(a \cdot b\right)\right), \left(\color{blue}{2} \cdot x\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, b\right)\right), \left(2 \cdot x\right)\right) \]

      5. *-lowering-*.f64 94.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, b\right)\right), \mathsf{*.f64}\left(2, \color{blue}{x}\right)\right) \]

   5. Simplified 94.8%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{+36}:\\ \;\;\;\;x \cdot 2 + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 5 \cdot 10^{+170}:\\ \;\;\;\;x \cdot 2 + t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -10:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+21}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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 (* (* a 27.0) b)))
   (if (<= t_1 -10.0)
     (* a (* 27.0 b))
     (if (<= t_1 2e+21) (* x 2.0) (* 27.0 (* a b))))))

C

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -10.0) {
		tmp = a * (27.0 * b);
	} else if (t_1 <= 2e+21) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

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 = (a * 27.0d0) * b
    if (t_1 <= (-10.0d0)) then
        tmp = a * (27.0d0 * b)
    else if (t_1 <= 2d+21) then
        tmp = x * 2.0d0
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -10.0) {
		tmp = a * (27.0 * b);
	} else if (t_1 <= 2e+21) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -10.0:
		tmp = a * (27.0 * b)
	elif t_1 <= 2e+21:
		tmp = x * 2.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

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(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -10.0)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (t_1 <= 2e+21)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

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 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -10.0)
		tmp = a * (27.0 * b);
	elseif (t_1 <= 2e+21)
		tmp = x * 2.0;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

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[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -10.0], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+21], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -10

   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. 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

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 49.1%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   5. Simplified 49.1%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(27 \cdot b\right), \color{blue}{a}\right) \]

      4. *-lowering-*.f64 49.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(27, b\right), a\right) \]

   7. Applied egg-rr 49.1%

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

   if -10 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2e21

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 47.2%

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

   5. Simplified 47.2%

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

   if 2e21 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 95.0%

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

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 67.9%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   5. Simplified 67.9%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -10:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+21}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 73.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* z (* y t)))))
   (if (<= z -1.6e-91)
     t_1
     (if (<= z 4.6e+17) (+ (* (* a 27.0) b) (* x 2.0)) t_1))))

C

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 * (z * (y * t));
	double tmp;
	if (z <= -1.6e-91) {
		tmp = t_1;
	} else if (z <= 4.6e+17) {
		tmp = ((a * 27.0) * b) + (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.
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 = (-9.0d0) * (z * (y * t))
    if (z <= (-1.6d-91)) then
        tmp = t_1
    else if (z <= 4.6d+17) then
        tmp = ((a * 27.0d0) * b) + (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;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (z * (y * t));
	double tmp;
	if (z <= -1.6e-91) {
		tmp = t_1;
	} else if (z <= 4.6e+17) {
		tmp = ((a * 27.0) * b) + (x * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[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 * (z * (y * t))
	tmp = 0
	if z <= -1.6e-91:
		tmp = t_1
	elif z <= 4.6e+17:
		tmp = ((a * 27.0) * b) + (x * 2.0)
	else:
		tmp = t_1
	return tmp

Julia

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(z * Float64(y * t)))
	tmp = 0.0
	if (z <= -1.6e-91)
		tmp = t_1;
	elseif (z <= 4.6e+17)
		tmp = Float64(Float64(Float64(a * 27.0) * b) + 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])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (z * (y * t));
	tmp = 0.0;
	if (z <= -1.6e-91)
		tmp = t_1;
	elseif (z <= 4.6e+17)
		tmp = ((a * 27.0) * b) + (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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e-91], t$95$1, If[LessEqual[z, 4.6e+17], N[(N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999998e-91 or 4.6e17 < z

   1. Initial program 91.3%

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

      1. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(y \cdot \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

      7. *-lowering-*.f64 93.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right), 9\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   4. Applied egg-rr 93.1%

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

   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. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

      8. *-lowering-*.f64 53.8%

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

   7. Simplified 53.8%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. metadata-eval N/A

         \[\leadsto \left(\left(t \cdot y\right) \cdot \left(\mathsf{neg}\left(9\right)\right)\right) \cdot z \]

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

         \[\leadsto \left(\mathsf{neg}\left(\left(t \cdot y\right) \cdot 9\right)\right) \cdot z \]

      6. associate-*r* N/A

         \[\leadsto \left(\mathsf{neg}\left(t \cdot \left(y \cdot 9\right)\right)\right) \cdot z \]

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

         \[\leadsto \mathsf{neg}\left(\left(t \cdot \left(y \cdot 9\right)\right) \cdot z\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(t \cdot \left(y \cdot 9\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(\left(t \cdot y\right) \cdot 9\right)\right) \]

      10. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\left(z \cdot \left(t \cdot y\right)\right) \cdot 9\right) \]

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

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

      12. metadata-eval N/A

          \[\leadsto \left(z \cdot \left(t \cdot y\right)\right) \cdot -9 \]

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

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

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

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

      15. *-lowering-*.f64 58.9%

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

   9. Applied egg-rr 58.9%

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

   if -1.59999999999999998e-91 < z < 4.6e17

   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

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(2 \cdot x\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 75.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

   5. Simplified 75.6%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-91}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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
 (+ (* (* a 27.0) b) (- (* x 2.0) (* z (* 9.0 (* y t))))))

C

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 ((a * 27.0) * b) + ((x * 2.0) - (z * (9.0 * (y * t))));
}

Fortran

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 = ((a * 27.0d0) * b) + ((x * 2.0d0) - (z * (9.0d0 * (y * t))))
end function

Java

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 ((a * 27.0) * b) + ((x * 2.0) - (z * (9.0 * (y * t))));
}

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((a * 27.0) * b) + ((x * 2.0) - (z * (9.0 * (y * t))));
end

Wolfram

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[(N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(z * N[(9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.0%

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

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(t \cdot \left(\left(y \cdot 9\right) \cdot z\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

   2. associate-*r* N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(t \cdot \left(y \cdot 9\right)\right) \cdot z\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot 9\right)\right), z\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{27}\right), b\right)\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(\left(y \cdot 9\right) \cdot t\right), z\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   5. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(\left(9 \cdot y\right) \cdot t\right), z\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   6. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(9 \cdot \left(y \cdot t\right)\right), z\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\left(9 \cdot \left(t \cdot y\right)\right), z\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(9, \left(t \cdot y\right)\right), z\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   9. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(9, \left(y \cdot t\right)\right), z\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

   10. *-lowering-*.f64 95.4%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, t\right)\right), z\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]

4. Applied egg-rr 95.4%

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

5. Final simplification 95.4%

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

Alternative 16: 46.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+20}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= b -2.5e-108) t_1 (if (<= b 1.6e+20) (* x 2.0) t_1))))

C

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 = 27.0 * (a * b);
	double tmp;
	if (b <= -2.5e-108) {
		tmp = t_1;
	} else if (b <= 1.6e+20) {
		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.
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 = 27.0d0 * (a * b)
    if (b <= (-2.5d-108)) then
        tmp = t_1
    else if (b <= 1.6d+20) 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;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (b <= -2.5e-108) {
		tmp = t_1;
	} else if (b <= 1.6e+20) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if b <= -2.5e-108:
		tmp = t_1
	elif b <= 1.6e+20:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (b <= -2.5e-108)
		tmp = t_1;
	elseif (b <= 1.6e+20)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (b <= -2.5e-108)
		tmp = t_1;
	elseif (b <= 1.6e+20)
		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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.5e-108], t$95$1, If[LessEqual[b, 1.6e+20], N[(x * 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.5e-108 or 1.6e20 < b

   1. Initial program 95.2%

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

   3. Taylor expanded in a around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 46.1%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   5. Simplified 46.1%

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

   if -2.5e-108 < b < 1.6e20

   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. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 44.2%

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

   5. Simplified 44.2%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-108}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+20}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 31.2% accurate, 5.7× speedup

Math

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

FPCore

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

C

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.
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;
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])
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])
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])){:}
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.
code[x_, y_, z_, t_, a_, b_] := N[(x * 2.0), $MachinePrecision]

Derivation

1. Initial program 95.0%

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

3. Taylor expanded in x around inf

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

   1. *-lowering-*.f64 30.1%

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

5. Simplified 30.1%

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

6. Final simplification 30.1%

   \[\leadsto x \cdot 2 \]
7. Add Preprocessing

Developer Target 1: 95.3% accurate, 0.8× 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 2024192 
(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)))