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

Percentage Accurate: 95.2% → 95.7%

Time: 17.5s

Alternatives: 12

Speedup: 1.0×

• 26.5% 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: 95.2% 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

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((a * (27.0d0 * b)) + (y * (t * (z * (-9.0d0))))) + (x * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((a * (27.0 * b)) + (y * (t * (z * -9.0)))) + (x * 2.0);
end

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. sub-neg N/A

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

   2. associate-+l+ N/A

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

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

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

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

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

   5. +-commutative N/A

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

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

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

   7. associate-*l* N/A

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

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

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

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

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

   10. associate-*l* N/A

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

   11. associate-*l* N/A

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

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

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

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

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

   14. associate-*r* N/A

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

   15. *-commutative N/A

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

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

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

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

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

   18. *-commutative N/A

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

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

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

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

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

   21. metadata-eval 96.8%

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

3. Simplified 96.8%

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

5. Final simplification 96.8%

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

Alternative 2: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := b \cdot \left(a \cdot 27\right)\\ t_3 := -9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+25}:\\ \;\;\;\;t\_3 + t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+34}:\\ \;\;\;\;t\_3 + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b)))
        (t_2 (* b (* a 27.0)))
        (t_3 (* -9.0 (* y (* t z)))))
   (if (<= t_2 -1e+25)
     (+ t_3 t_1)
     (if (<= t_2 2e+34) (+ t_3 (* x 2.0)) (+ t_1 (* x 2.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = b * (a * 27.0);
	double t_3 = -9.0 * (y * (t * z));
	double tmp;
	if (t_2 <= -1e+25) {
		tmp = t_3 + t_1;
	} else if (t_2 <= 2e+34) {
		tmp = t_3 + (x * 2.0);
	} else {
		tmp = t_1 + (x * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = b * (a * 27.0d0)
    t_3 = (-9.0d0) * (y * (t * z))
    if (t_2 <= (-1d+25)) then
        tmp = t_3 + t_1
    else if (t_2 <= 2d+34) then
        tmp = t_3 + (x * 2.0d0)
    else
        tmp = t_1 + (x * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = b * (a * 27.0);
	double t_3 = -9.0 * (y * (t * z));
	double tmp;
	if (t_2 <= -1e+25) {
		tmp = t_3 + t_1;
	} else if (t_2 <= 2e+34) {
		tmp = t_3 + (x * 2.0);
	} else {
		tmp = t_1 + (x * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = b * (a * 27.0)
	t_3 = -9.0 * (y * (t * z))
	tmp = 0
	if t_2 <= -1e+25:
		tmp = t_3 + t_1
	elif t_2 <= 2e+34:
		tmp = t_3 + (x * 2.0)
	else:
		tmp = t_1 + (x * 2.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(b * Float64(a * 27.0))
	t_3 = Float64(-9.0 * Float64(y * Float64(t * z)))
	tmp = 0.0
	if (t_2 <= -1e+25)
		tmp = Float64(t_3 + t_1);
	elseif (t_2 <= 2e+34)
		tmp = Float64(t_3 + Float64(x * 2.0));
	else
		tmp = Float64(t_1 + Float64(x * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = b * (a * 27.0);
	t_3 = -9.0 * (y * (t * z));
	tmp = 0.0;
	if (t_2 <= -1e+25)
		tmp = t_3 + t_1;
	elseif (t_2 <= 2e+34)
		tmp = t_3 + (x * 2.0);
	else
		tmp = t_1 + (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+25], N[(t$95$3 + t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 2e+34], N[(t$95$3 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.00000000000000009e25

   1. Initial program 92.0%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in x around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

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

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

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

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

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

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

      9. *-lowering-*.f64 90.3%

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

   7. Simplified 90.3%

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

   if -1.00000000000000009e25 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.99999999999999989e34

   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. Step-by-step derivation

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in a around 0

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

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 89.1%

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

   7. Simplified 89.1%

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

   if 1.99999999999999989e34 < (*.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. Step-by-step derivation

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 84.7%

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

   7. Simplified 84.7%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -1 \cdot 10^{+25}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right) + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{+34}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := 27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+34}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))) (t_2 (+ (* 27.0 (* a b)) (* x 2.0))))
   (if (<= t_1 -1e+25)
     t_2
     (if (<= t_1 2e+34) (+ (* -9.0 (* y (* t z))) (* x 2.0)) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = (27.0 * (a * b)) + (x * 2.0);
	double tmp;
	if (t_1 <= -1e+25) {
		tmp = t_2;
	} else if (t_1 <= 2e+34) {
		tmp = (-9.0 * (y * (t * z))) + (x * 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    t_2 = (27.0d0 * (a * b)) + (x * 2.0d0)
    if (t_1 <= (-1d+25)) then
        tmp = t_2
    else if (t_1 <= 2d+34) then
        tmp = ((-9.0d0) * (y * (t * z))) + (x * 2.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = (27.0 * (a * b)) + (x * 2.0);
	double tmp;
	if (t_1 <= -1e+25) {
		tmp = t_2;
	} else if (t_1 <= 2e+34) {
		tmp = (-9.0 * (y * (t * z))) + (x * 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	t_2 = (27.0 * (a * b)) + (x * 2.0)
	tmp = 0
	if t_1 <= -1e+25:
		tmp = t_2
	elif t_1 <= 2e+34:
		tmp = (-9.0 * (y * (t * z))) + (x * 2.0)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	t_2 = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0))
	tmp = 0.0
	if (t_1 <= -1e+25)
		tmp = t_2;
	elseif (t_1 <= 2e+34)
		tmp = Float64(Float64(-9.0 * Float64(y * Float64(t * z))) + Float64(x * 2.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	t_2 = (27.0 * (a * b)) + (x * 2.0);
	tmp = 0.0;
	if (t_1 <= -1e+25)
		tmp = t_2;
	elseif (t_1 <= 2e+34)
		tmp = (-9.0 * (y * (t * z))) + (x * 2.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+25], t$95$2, If[LessEqual[t$95$1, 2e+34], N[(N[(-9.0 * N[(y * N[(t * z), $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) < -1.00000000000000009e25 or 1.99999999999999989e34 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   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. Step-by-step derivation

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 81.6%

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

   7. Simplified 81.6%

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

   if -1.00000000000000009e25 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.99999999999999989e34

   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. Step-by-step derivation

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in a around 0

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

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 89.1%

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

   7. Simplified 89.1%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -1 \cdot 10^{+25}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{+34}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := 27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+34}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))) (t_2 (+ (* 27.0 (* a b)) (* x 2.0))))
   (if (<= t_1 -1e+17)
     t_2
     (if (<= t_1 2e+34) (+ (* -9.0 (* t (* y z))) (* x 2.0)) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = (27.0 * (a * b)) + (x * 2.0);
	double tmp;
	if (t_1 <= -1e+17) {
		tmp = t_2;
	} else if (t_1 <= 2e+34) {
		tmp = (-9.0 * (t * (y * z))) + (x * 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    t_2 = (27.0d0 * (a * b)) + (x * 2.0d0)
    if (t_1 <= (-1d+17)) then
        tmp = t_2
    else if (t_1 <= 2d+34) then
        tmp = ((-9.0d0) * (t * (y * z))) + (x * 2.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = (27.0 * (a * b)) + (x * 2.0);
	double tmp;
	if (t_1 <= -1e+17) {
		tmp = t_2;
	} else if (t_1 <= 2e+34) {
		tmp = (-9.0 * (t * (y * z))) + (x * 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	t_2 = (27.0 * (a * b)) + (x * 2.0)
	tmp = 0
	if t_1 <= -1e+17:
		tmp = t_2
	elif t_1 <= 2e+34:
		tmp = (-9.0 * (t * (y * z))) + (x * 2.0)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	t_2 = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0))
	tmp = 0.0
	if (t_1 <= -1e+17)
		tmp = t_2;
	elseif (t_1 <= 2e+34)
		tmp = Float64(Float64(-9.0 * Float64(t * Float64(y * z))) + Float64(x * 2.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	t_2 = (27.0 * (a * b)) + (x * 2.0);
	tmp = 0.0;
	if (t_1 <= -1e+17)
		tmp = t_2;
	elseif (t_1 <= 2e+34)
		tmp = (-9.0 * (t * (y * z))) + (x * 2.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+17], t$95$2, If[LessEqual[t$95$1, 2e+34], N[(N[(-9.0 * N[(t * N[(y * z), $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) < -1e17 or 1.99999999999999989e34 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 92.5%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 80.9%

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

   7. Simplified 80.9%

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

   if -1e17 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.99999999999999989e34

   1. Initial program 94.9%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 96.6%

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

   3. Simplified 96.6%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-lowering-*.f64 98.1%

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

   6. Applied egg-rr 98.1%

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

   7. Taylor expanded in a around 0

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

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

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

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

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

      3. *-lowering-*.f64 87.3%

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

   9. Simplified 87.3%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -1 \cdot 10^{+17}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{+34}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-231}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-50}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.4e-58)
   (* y (* t (* z -9.0)))
   (if (<= z 4.8e-231)
     (* 27.0 (* a b))
     (if (<= z 5.9e-50) (* x 2.0) (* (* z -9.0) (* y t))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.4e-58) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 4.8e-231) {
		tmp = 27.0 * (a * b);
	} else if (z <= 5.9e-50) {
		tmp = x * 2.0;
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.4d-58)) then
        tmp = y * (t * (z * (-9.0d0)))
    else if (z <= 4.8d-231) then
        tmp = 27.0d0 * (a * b)
    else if (z <= 5.9d-50) then
        tmp = x * 2.0d0
    else
        tmp = (z * (-9.0d0)) * (y * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.4e-58) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 4.8e-231) {
		tmp = 27.0 * (a * b);
	} else if (z <= 5.9e-50) {
		tmp = x * 2.0;
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.4e-58:
		tmp = y * (t * (z * -9.0))
	elif z <= 4.8e-231:
		tmp = 27.0 * (a * b)
	elif z <= 5.9e-50:
		tmp = x * 2.0
	else:
		tmp = (z * -9.0) * (y * t)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.4e-58)
		tmp = Float64(y * Float64(t * Float64(z * -9.0)));
	elseif (z <= 4.8e-231)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (z <= 5.9e-50)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(Float64(z * -9.0) * Float64(y * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.4e-58)
		tmp = y * (t * (z * -9.0));
	elseif (z <= 4.8e-231)
		tmp = 27.0 * (a * b);
	elseif (z <= 5.9e-50)
		tmp = x * 2.0;
	else
		tmp = (z * -9.0) * (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.4e-58], N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-231], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.9e-50], N[(x * 2.0), $MachinePrecision], N[(N[(z * -9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4000000000000001e-58

   1. Initial program 83.8%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 94.7%

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

   3. Simplified 94.7%

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

   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. *-lowering-*.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 61.8%

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

   7. Simplified 61.8%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

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

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

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

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

      9. *-lowering-*.f64 61.8%

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

   9. Applied egg-rr 61.8%

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

   if -2.4000000000000001e-58 < z < 4.79999999999999983e-231

   1. Initial program 98.4%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   6. 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 43.6%

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

   7. Simplified 43.6%

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

   if 4.79999999999999983e-231 < z < 5.9e-50

   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. Step-by-step derivation

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 55.2%

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

   7. Simplified 55.2%

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

   if 5.9e-50 < z

   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. Step-by-step derivation

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 94.4%

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

   3. Simplified 94.4%

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

   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. *-lowering-*.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 56.3%

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

   7. Simplified 56.3%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

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

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

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

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

      7. *-lowering-*.f64 58.1%

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

   9. Applied egg-rr 58.1%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-231}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-50}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-57}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-233}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-48}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.9e-57)
   (* -9.0 (* y (* t z)))
   (if (<= z 2.3e-233)
     (* 27.0 (* a b))
     (if (<= z 6.2e-48) (* x 2.0) (* (* z -9.0) (* y t))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.9e-57) {
		tmp = -9.0 * (y * (t * z));
	} else if (z <= 2.3e-233) {
		tmp = 27.0 * (a * b);
	} else if (z <= 6.2e-48) {
		tmp = x * 2.0;
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.9d-57)) then
        tmp = (-9.0d0) * (y * (t * z))
    else if (z <= 2.3d-233) then
        tmp = 27.0d0 * (a * b)
    else if (z <= 6.2d-48) then
        tmp = x * 2.0d0
    else
        tmp = (z * (-9.0d0)) * (y * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.9e-57) {
		tmp = -9.0 * (y * (t * z));
	} else if (z <= 2.3e-233) {
		tmp = 27.0 * (a * b);
	} else if (z <= 6.2e-48) {
		tmp = x * 2.0;
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.9e-57:
		tmp = -9.0 * (y * (t * z))
	elif z <= 2.3e-233:
		tmp = 27.0 * (a * b)
	elif z <= 6.2e-48:
		tmp = x * 2.0
	else:
		tmp = (z * -9.0) * (y * t)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.9e-57)
		tmp = Float64(-9.0 * Float64(y * Float64(t * z)));
	elseif (z <= 2.3e-233)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (z <= 6.2e-48)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(Float64(z * -9.0) * Float64(y * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.9e-57)
		tmp = -9.0 * (y * (t * z));
	elseif (z <= 2.3e-233)
		tmp = 27.0 * (a * b);
	elseif (z <= 6.2e-48)
		tmp = x * 2.0;
	else
		tmp = (z * -9.0) * (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.9e-57], N[(-9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e-233], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e-48], N[(x * 2.0), $MachinePrecision], N[(N[(z * -9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.90000000000000025e-57

   1. Initial program 83.8%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 94.7%

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

   3. Simplified 94.7%

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

   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. *-lowering-*.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 61.8%

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

   7. Simplified 61.8%

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

   if -2.90000000000000025e-57 < z < 2.3000000000000002e-233

   1. Initial program 98.4%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   6. 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 43.6%

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

   7. Simplified 43.6%

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

   if 2.3000000000000002e-233 < z < 6.20000000000000033e-48

   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. Step-by-step derivation

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 56.3%

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

   7. Simplified 56.3%

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

   if 6.20000000000000033e-48 < z

   1. Initial program 97.3%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 94.4%

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

   3. Simplified 94.4%

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

   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. *-lowering-*.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 57.0%

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

   7. Simplified 57.0%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

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

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

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

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

      7. *-lowering-*.f64 58.8%

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

   9. Applied egg-rr 58.8%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-57}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-233}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-48}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-229}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* y (* t z)))))
   (if (<= z -1.25e-57)
     t_1
     (if (<= z 4.4e-229) (* 27.0 (* a b)) (if (<= z 2.7e-45) (* x 2.0) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (t * z));
	double tmp;
	if (z <= -1.25e-57) {
		tmp = t_1;
	} else if (z <= 4.4e-229) {
		tmp = 27.0 * (a * b);
	} else if (z <= 2.7e-45) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-9.0d0) * (y * (t * z))
    if (z <= (-1.25d-57)) then
        tmp = t_1
    else if (z <= 4.4d-229) then
        tmp = 27.0d0 * (a * b)
    else if (z <= 2.7d-45) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (t * z));
	double tmp;
	if (z <= -1.25e-57) {
		tmp = t_1;
	} else if (z <= 4.4e-229) {
		tmp = 27.0 * (a * b);
	} else if (z <= 2.7e-45) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (y * (t * z))
	tmp = 0
	if z <= -1.25e-57:
		tmp = t_1
	elif z <= 4.4e-229:
		tmp = 27.0 * (a * b)
	elif z <= 2.7e-45:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(y * Float64(t * z)))
	tmp = 0.0
	if (z <= -1.25e-57)
		tmp = t_1;
	elseif (z <= 4.4e-229)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (z <= 2.7e-45)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (y * (t * z));
	tmp = 0.0;
	if (z <= -1.25e-57)
		tmp = t_1;
	elseif (z <= 4.4e-229)
		tmp = 27.0 * (a * b);
	elseif (z <= 2.7e-45)
		tmp = x * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e-57], t$95$1, If[LessEqual[z, 4.4e-229], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-45], N[(x * 2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25e-57 or 2.69999999999999985e-45 < z

   1. Initial program 90.4%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 94.6%

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

   3. Simplified 94.6%

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

   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. *-lowering-*.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 59.5%

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

   7. Simplified 59.5%

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

   if -1.25e-57 < z < 4.3999999999999998e-229

   1. Initial program 98.4%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   6. 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 43.6%

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

   7. Simplified 43.6%

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

   if 4.3999999999999998e-229 < z < 2.69999999999999985e-45

   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. Step-by-step derivation

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 56.3%

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

   7. Simplified 56.3%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-57}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-229}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-26}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.8e-43)
   (* y (* t (* z -9.0)))
   (if (<= z 1.7e-26) (+ (* 27.0 (* a b)) (* x 2.0)) (* (* z -9.0) (* y t)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.8e-43) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 1.7e-26) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-5.8d-43)) then
        tmp = y * (t * (z * (-9.0d0)))
    else if (z <= 1.7d-26) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (z * (-9.0d0)) * (y * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.8e-43) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 1.7e-26) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.8e-43:
		tmp = y * (t * (z * -9.0))
	elif z <= 1.7e-26:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = (z * -9.0) * (y * t)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.8e-43)
		tmp = Float64(y * Float64(t * Float64(z * -9.0)));
	elseif (z <= 1.7e-26)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(z * -9.0) * Float64(y * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.8e-43)
		tmp = y * (t * (z * -9.0));
	elseif (z <= 1.7e-26)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = (z * -9.0) * (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.8e-43], N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-26], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z * -9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8000000000000003e-43

   1. Initial program 82.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto x \cdot 2 + \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(\left(a \cdot 27\right) \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(a \cdot \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot \color{blue}{t}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(9 \cdot z\right) \cdot t\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(t \cdot \left(9 \cdot z\right)\right)\right)\right)\right)\right) \]

      16. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval 94.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, -9\right)\right)\right)\right)\right) \]

   3. Simplified 94.4%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   4. Add Preprocessing

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \left(\left(y \cdot z\right) \cdot \color{blue}{t}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \left(y \cdot \left(t \cdot \color{blue}{z}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \mathsf{*.f64}\left(y, \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 62.4%

         \[\leadsto \mathsf{*.f64}\left(-9, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 62.4%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(y \cdot \left(t \cdot z\right)\right) \cdot \color{blue}{-9} \]

      2. associate-*r* N/A

         \[\leadsto \left(\left(y \cdot t\right) \cdot z\right) \cdot -9 \]

      3. associate-*r* N/A

         \[\leadsto \left(y \cdot t\right) \cdot \color{blue}{\left(z \cdot -9\right)} \]

      4. *-commutative N/A

         \[\leadsto \left(z \cdot -9\right) \cdot \color{blue}{\left(y \cdot t\right)} \]

      5. *-commutative N/A

         \[\leadsto \left(z \cdot -9\right) \cdot \left(t \cdot \color{blue}{y}\right) \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(z \cdot -9\right) \cdot t\right) \cdot \color{blue}{y} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(z \cdot -9\right) \cdot t\right), \color{blue}{y}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(z \cdot -9\right), t\right), y\right) \]

      9. *-lowering-*.f64 62.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -9\right), t\right), y\right) \]

   9. Applied egg-rr 62.4%

      \[\leadsto \color{blue}{\left(\left(z \cdot -9\right) \cdot t\right) \cdot y} \]

   if -5.8000000000000003e-43 < z < 1.70000000000000007e-26

   1. Initial program 99.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto x \cdot 2 + \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(\left(a \cdot 27\right) \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(a \cdot \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot \color{blue}{t}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(9 \cdot z\right) \cdot t\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(t \cdot \left(9 \cdot z\right)\right)\right)\right)\right)\right) \]

      16. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, -9\right)\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \color{blue}{\left(27 \cdot \left(a \cdot b\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      2. *-lowering-*.f64 89.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   7. Simplified 89.9%

      \[\leadsto x \cdot 2 + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if 1.70000000000000007e-26 < z

   1. Initial program 97.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto x \cdot 2 + \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(\left(a \cdot 27\right) \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(a \cdot \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot \color{blue}{t}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(9 \cdot z\right) \cdot t\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(t \cdot \left(9 \cdot z\right)\right)\right)\right)\right)\right) \]

      16. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval 93.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, -9\right)\right)\right)\right)\right) \]

   3. Simplified 93.9%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   4. Add Preprocessing

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \left(\left(y \cdot z\right) \cdot \color{blue}{t}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \left(y \cdot \left(t \cdot \color{blue}{z}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \mathsf{*.f64}\left(y, \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 60.4%

         \[\leadsto \mathsf{*.f64}\left(-9, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 60.4%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(y \cdot \left(t \cdot z\right)\right) \cdot \color{blue}{-9} \]

      2. associate-*r* N/A

         \[\leadsto \left(\left(y \cdot t\right) \cdot z\right) \cdot -9 \]

      3. associate-*r* N/A

         \[\leadsto \left(y \cdot t\right) \cdot \color{blue}{\left(z \cdot -9\right)} \]

      4. *-commutative N/A

         \[\leadsto \left(z \cdot -9\right) \cdot \color{blue}{\left(y \cdot t\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot -9\right), \color{blue}{\left(y \cdot t\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -9\right), \left(\color{blue}{y} \cdot t\right)\right) \]

      7. *-lowering-*.f64 62.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -9\right), \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right) \]

   9. Applied egg-rr 62.3%

      \[\leadsto \color{blue}{\left(z \cdot -9\right) \cdot \left(y \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-26}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-21}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.48e-40)
   (* y (* t (* z -9.0)))
   (if (<= z 1.55e-21) (+ (* b (* a 27.0)) (* x 2.0)) (* (* z -9.0) (* y t)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.48e-40) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 1.55e-21) {
		tmp = (b * (a * 27.0)) + (x * 2.0);
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.48d-40)) then
        tmp = y * (t * (z * (-9.0d0)))
    else if (z <= 1.55d-21) then
        tmp = (b * (a * 27.0d0)) + (x * 2.0d0)
    else
        tmp = (z * (-9.0d0)) * (y * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.48e-40) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 1.55e-21) {
		tmp = (b * (a * 27.0)) + (x * 2.0);
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.48e-40:
		tmp = y * (t * (z * -9.0))
	elif z <= 1.55e-21:
		tmp = (b * (a * 27.0)) + (x * 2.0)
	else:
		tmp = (z * -9.0) * (y * t)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.48e-40)
		tmp = Float64(y * Float64(t * Float64(z * -9.0)));
	elseif (z <= 1.55e-21)
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(z * -9.0) * Float64(y * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.48e-40)
		tmp = y * (t * (z * -9.0));
	elseif (z <= 1.55e-21)
		tmp = (b * (a * 27.0)) + (x * 2.0);
	else
		tmp = (z * -9.0) * (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.48e-40], N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-21], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z * -9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4800000000000001e-40

   1. Initial program 82.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto x \cdot 2 + \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(\left(a \cdot 27\right) \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(a \cdot \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot \color{blue}{t}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(9 \cdot z\right) \cdot t\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(t \cdot \left(9 \cdot z\right)\right)\right)\right)\right)\right) \]

      16. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval 94.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, -9\right)\right)\right)\right)\right) \]

   3. Simplified 94.4%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   4. Add Preprocessing

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \left(\left(y \cdot z\right) \cdot \color{blue}{t}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \left(y \cdot \left(t \cdot \color{blue}{z}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \mathsf{*.f64}\left(y, \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 62.4%

         \[\leadsto \mathsf{*.f64}\left(-9, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 62.4%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(y \cdot \left(t \cdot z\right)\right) \cdot \color{blue}{-9} \]

      2. associate-*r* N/A

         \[\leadsto \left(\left(y \cdot t\right) \cdot z\right) \cdot -9 \]

      3. associate-*r* N/A

         \[\leadsto \left(y \cdot t\right) \cdot \color{blue}{\left(z \cdot -9\right)} \]

      4. *-commutative N/A

         \[\leadsto \left(z \cdot -9\right) \cdot \color{blue}{\left(y \cdot t\right)} \]

      5. *-commutative N/A

         \[\leadsto \left(z \cdot -9\right) \cdot \left(t \cdot \color{blue}{y}\right) \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(z \cdot -9\right) \cdot t\right) \cdot \color{blue}{y} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(z \cdot -9\right) \cdot t\right), \color{blue}{y}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(z \cdot -9\right), t\right), y\right) \]

      9. *-lowering-*.f64 62.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -9\right), t\right), y\right) \]

   9. Applied egg-rr 62.4%

      \[\leadsto \color{blue}{\left(\left(z \cdot -9\right) \cdot t\right) \cdot y} \]

   if -1.4800000000000001e-40 < z < 1.5499999999999999e-21

   1. Initial program 99.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(2 \cdot x\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 88.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, x\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

   5. Simplified 88.4%

      \[\leadsto \color{blue}{2 \cdot x} + \left(a \cdot 27\right) \cdot b \]

   if 1.5499999999999999e-21 < z

   1. Initial program 97.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto x \cdot 2 + \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(\left(a \cdot 27\right) \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(a \cdot \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot \color{blue}{t}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(9 \cdot z\right) \cdot t\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(t \cdot \left(9 \cdot z\right)\right)\right)\right)\right)\right) \]

      16. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval 93.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, -9\right)\right)\right)\right)\right) \]

   3. Simplified 93.8%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   4. Add Preprocessing

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \left(\left(y \cdot z\right) \cdot \color{blue}{t}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \left(y \cdot \left(t \cdot \color{blue}{z}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-9, \mathsf{*.f64}\left(y, \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      6. *-lowering-*.f64 60.7%

         \[\leadsto \mathsf{*.f64}\left(-9, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 60.7%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(y \cdot \left(t \cdot z\right)\right) \cdot \color{blue}{-9} \]

      2. associate-*r* N/A

         \[\leadsto \left(\left(y \cdot t\right) \cdot z\right) \cdot -9 \]

      3. associate-*r* N/A

         \[\leadsto \left(y \cdot t\right) \cdot \color{blue}{\left(z \cdot -9\right)} \]

      4. *-commutative N/A

         \[\leadsto \left(z \cdot -9\right) \cdot \color{blue}{\left(y \cdot t\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot -9\right), \color{blue}{\left(y \cdot t\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -9\right), \left(\color{blue}{y} \cdot t\right)\right) \]

      7. *-lowering-*.f64 62.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -9\right), \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right) \]

   9. Applied egg-rr 62.7%

      \[\leadsto \color{blue}{\left(z \cdot -9\right) \cdot \left(y \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-21}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+103}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 10^{-137}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4e+103)
   (* 27.0 (* a b))
   (if (<= a 1e-137) (* x 2.0) (* b (* a 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4e+103) {
		tmp = 27.0 * (a * b);
	} else if (a <= 1e-137) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-4d+103)) then
        tmp = 27.0d0 * (a * b)
    else if (a <= 1d-137) then
        tmp = x * 2.0d0
    else
        tmp = b * (a * 27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4e+103) {
		tmp = 27.0 * (a * b);
	} else if (a <= 1e-137) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4e+103:
		tmp = 27.0 * (a * b)
	elif a <= 1e-137:
		tmp = x * 2.0
	else:
		tmp = b * (a * 27.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4e+103)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (a <= 1e-137)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(b * Float64(a * 27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4e+103)
		tmp = 27.0 * (a * b);
	elseif (a <= 1e-137)
		tmp = x * 2.0;
	else
		tmp = b * (a * 27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4e+103], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-137], N[(x * 2.0), $MachinePrecision], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4e103

   1. Initial program 97.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto x \cdot 2 + \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(\left(a \cdot 27\right) \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(a \cdot \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot \color{blue}{t}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(9 \cdot z\right) \cdot t\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(t \cdot \left(9 \cdot z\right)\right)\right)\right)\right)\right) \]

      16. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, -9\right)\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   6. 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 64.4%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 64.4%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if -4e103 < a < 9.99999999999999978e-138

   1. Initial program 96.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto x \cdot 2 + \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(\left(a \cdot 27\right) \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(a \cdot \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot \color{blue}{t}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(9 \cdot z\right) \cdot t\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(t \cdot \left(9 \cdot z\right)\right)\right)\right)\right)\right) \]

      16. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval 96.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, -9\right)\right)\right)\right)\right) \]

   3. Simplified 96.9%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 38.1%

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{x}\right) \]

   7. Simplified 38.1%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if 9.99999999999999978e-138 < a

   1. Initial program 88.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto x \cdot 2 + \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(\left(a \cdot 27\right) \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(a \cdot \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot \color{blue}{t}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(9 \cdot z\right) \cdot t\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(t \cdot \left(9 \cdot z\right)\right)\right)\right)\right)\right) \]

      16. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval 95.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, -9\right)\right)\right)\right)\right) \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   6. 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 37.0%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 37.0%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(27 \cdot a\right) \cdot \color{blue}{b} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(27 \cdot a\right), \color{blue}{b}\right) \]

      3. *-lowering-*.f64 37.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(27, a\right), b\right) \]

   9. Applied egg-rr 37.0%

      \[\leadsto \color{blue}{\left(27 \cdot a\right) \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+103}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 10^{-137}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \leq -4 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 10^{-137}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= a -4e+103) t_1 (if (<= a 1e-137) (* x 2.0) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (a <= -4e+103) {
		tmp = t_1;
	} else if (a <= 1e-137) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (a <= (-4d+103)) then
        tmp = t_1
    else if (a <= 1d-137) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (a <= -4e+103) {
		tmp = t_1;
	} else if (a <= 1e-137) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if a <= -4e+103:
		tmp = t_1
	elif a <= 1e-137:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (a <= -4e+103)
		tmp = t_1;
	elseif (a <= 1e-137)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (a <= -4e+103)
		tmp = t_1;
	elseif (a <= 1e-137)
		tmp = x * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+103], t$95$1, If[LessEqual[a, 1e-137], N[(x * 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -4e103 or 9.99999999999999978e-138 < a

   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. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto x \cdot 2 + \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(\left(a \cdot 27\right) \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(a \cdot \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot \color{blue}{t}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(9 \cdot z\right) \cdot t\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(t \cdot \left(9 \cdot z\right)\right)\right)\right)\right)\right) \]

      16. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval 96.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, -9\right)\right)\right)\right)\right) \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   6. 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 45.1%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 45.1%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if -4e103 < a < 9.99999999999999978e-138

   1. Initial program 96.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto x \cdot 2 + \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(\left(a \cdot 27\right) \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(a \cdot \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot \color{blue}{t}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(9 \cdot z\right) \cdot t\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(t \cdot \left(9 \cdot z\right)\right)\right)\right)\right)\right) \]

      16. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval 96.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, -9\right)\right)\right)\right)\right) \]

   3. Simplified 96.9%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 38.1%

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{x}\right) \]

   7. Simplified 38.1%

      \[\leadsto \color{blue}{2 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+103}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 10^{-137}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 32.1% accurate, 5.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ x \cdot 2 \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* x 2.0))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * 2.0d0
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return x * 2.0

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(x * 2.0)
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = x * 2.0;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(x * 2.0), $MachinePrecision]

Derivation

1. Initial program 93.9%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto \left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

   2. associate-+l+ N/A

      \[\leadsto x \cdot 2 + \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)} \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)}\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right)\right) \]

   5. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

   6. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(\left(a \cdot 27\right) \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

   7. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(a \cdot \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot \color{blue}{t}\right)\right)\right)\right) \]

   10. associate-*l* N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)\right)\right) \]

   11. associate-*l* N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\right)\right)\right) \]

   12. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

   13. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

   14. associate-*r* N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(9 \cdot z\right) \cdot t\right)\right)\right)\right)\right) \]

   15. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(t \cdot \left(9 \cdot z\right)\right)\right)\right)\right)\right) \]

   16. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

   17. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

   18. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right)\right)\right)\right) \]

   19. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

   20. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

   21. metadata-eval 96.8%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, -9\right)\right)\right)\right)\right) \]

3. Simplified 96.8%

   \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{2 \cdot x} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 30.2%

      \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{x}\right) \]

7. Simplified 30.2%

   \[\leadsto \color{blue}{2 \cdot x} \]

8. Final simplification 30.2%

   \[\leadsto x \cdot 2 \]
9. Add Preprocessing

Developer Target 1: 94.7% 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 2024158 
(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)))