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

Percentage Accurate: 95.7% → 96.2%

Time: 18.5s

Alternatives: 12

Speedup: 0.8×

• 27.5% 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: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 3.4 \cdot 10^{+14}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(t \cdot -9\right) + x \cdot 2\\ \end{array} \end{array} \]

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
 (if (<= z 3.4e+14)
   (+ (+ (* a (* 27.0 b)) (* y (* t (* z -9.0)))) (* x 2.0))
   (+ (* (* z y) (* t -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) {
	double tmp;
	if (z <= 3.4e+14) {
		tmp = ((a * (27.0 * b)) + (y * (t * (z * -9.0)))) + (x * 2.0);
	} else {
		tmp = ((z * y) * (t * -9.0)) + (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) :: tmp
    if (z <= 3.4d+14) then
        tmp = ((a * (27.0d0 * b)) + (y * (t * (z * (-9.0d0))))) + (x * 2.0d0)
    else
        tmp = ((z * y) * (t * (-9.0d0))) + (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 tmp;
	if (z <= 3.4e+14) {
		tmp = ((a * (27.0 * b)) + (y * (t * (z * -9.0)))) + (x * 2.0);
	} else {
		tmp = ((z * y) * (t * -9.0)) + (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):
	tmp = 0
	if z <= 3.4e+14:
		tmp = ((a * (27.0 * b)) + (y * (t * (z * -9.0)))) + (x * 2.0)
	else:
		tmp = ((z * y) * (t * -9.0)) + (x * 2.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 3.4e+14)
		tmp = Float64(Float64(Float64(a * Float64(27.0 * b)) + Float64(y * Float64(t * Float64(z * -9.0)))) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(Float64(z * y) * Float64(t * -9.0)) + 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)
	tmp = 0.0;
	if (z <= 3.4e+14)
		tmp = ((a * (27.0 * b)) + (y * (t * (z * -9.0)))) + (x * 2.0);
	else
		tmp = ((z * y) * (t * -9.0)) + (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_] := If[LessEqual[z, 3.4e+14], 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], N[(N[(N[(z * y), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.4e14

   1. Initial program 96.5%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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 95.9%

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

   3. Simplified 95.9%

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

   if 3.4e14 < z

   1. Initial program 81.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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 89.3%

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

   3. Simplified 89.3%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   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 79.4%

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

   7. Simplified 79.4%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*l* N/A

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

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

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

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

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

      11. *-lowering-*.f64 73.4%

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

   9. Applied egg-rr 73.4%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.4 \cdot 10^{+14}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(t \cdot -9\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := t\_1 + -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+115}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(t \cdot -9\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (+ t_1 (* -9.0 (* y (* z t))))))
   (if (<= t_1 -2e+93)
     t_2
     (if (<= t_1 1e+115) (+ (* (* z y) (* t -9.0)) (* 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 = t_1 + (-9.0 * (y * (z * t)));
	double tmp;
	if (t_1 <= -2e+93) {
		tmp = t_2;
	} else if (t_1 <= 1e+115) {
		tmp = ((z * y) * (t * -9.0)) + (x * 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 = t_1 + ((-9.0d0) * (y * (z * t)))
    if (t_1 <= (-2d+93)) then
        tmp = t_2
    else if (t_1 <= 1d+115) then
        tmp = ((z * y) * (t * (-9.0d0))) + (x * 2.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
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 = t_1 + (-9.0 * (y * (z * t)));
	double tmp;
	if (t_1 <= -2e+93) {
		tmp = t_2;
	} else if (t_1 <= 1e+115) {
		tmp = ((z * y) * (t * -9.0)) + (x * 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[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 = t_1 + (-9.0 * (y * (z * t)))
	tmp = 0
	if t_1 <= -2e+93:
		tmp = t_2
	elif t_1 <= 1e+115:
		tmp = ((z * y) * (t * -9.0)) + (x * 2.0)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
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(t_1 + Float64(-9.0 * Float64(y * Float64(z * t))))
	tmp = 0.0
	if (t_1 <= -2e+93)
		tmp = t_2;
	elseif (t_1 <= 1e+115)
		tmp = Float64(Float64(Float64(z * y) * Float64(t * -9.0)) + Float64(x * 2.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
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 = t_1 + (-9.0 * (y * (z * t)));
	tmp = 0.0;
	if (t_1 <= -2e+93)
		tmp = t_2;
	elseif (t_1 <= 1e+115)
		tmp = ((z * y) * (t * -9.0)) + (x * 2.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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[(t$95$1 + N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+93], t$95$2, If[LessEqual[t$95$1, 1e+115], N[(N[(N[(z * y), $MachinePrecision] * N[(t * -9.0), $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) < -2.00000000000000009e93 or 1e115 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 85.2%

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

   5. Simplified 85.2%

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

   if -2.00000000000000009e93 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1e115

   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 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in a around 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 87.7%

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

   7. Simplified 87.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*l* N/A

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

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

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

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

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

      11. *-lowering-*.f64 85.9%

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

   9. Applied egg-rr 85.9%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -2 \cdot 10^{+93}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 10^{+115}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(t \cdot -9\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -10500:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-220}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-143}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -10500.0)
   (* (* z -9.0) (* y t))
   (if (<= z -2.2e-148)
     (* x 2.0)
     (if (<= z -6.8e-220)
       (* 27.0 (* a b))
       (if (<= z 8.5e-143) (* x 2.0) (* t (* y (* z -9.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -10500.0) {
		tmp = (z * -9.0) * (y * t);
	} else if (z <= -2.2e-148) {
		tmp = x * 2.0;
	} else if (z <= -6.8e-220) {
		tmp = 27.0 * (a * b);
	} else if (z <= 8.5e-143) {
		tmp = x * 2.0;
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-10500.0d0)) then
        tmp = (z * (-9.0d0)) * (y * t)
    else if (z <= (-2.2d-148)) then
        tmp = x * 2.0d0
    else if (z <= (-6.8d-220)) then
        tmp = 27.0d0 * (a * b)
    else if (z <= 8.5d-143) then
        tmp = x * 2.0d0
    else
        tmp = t * (y * (z * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -10500.0) {
		tmp = (z * -9.0) * (y * t);
	} else if (z <= -2.2e-148) {
		tmp = x * 2.0;
	} else if (z <= -6.8e-220) {
		tmp = 27.0 * (a * b);
	} else if (z <= 8.5e-143) {
		tmp = x * 2.0;
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -10500.0:
		tmp = (z * -9.0) * (y * t)
	elif z <= -2.2e-148:
		tmp = x * 2.0
	elif z <= -6.8e-220:
		tmp = 27.0 * (a * b)
	elif z <= 8.5e-143:
		tmp = x * 2.0
	else:
		tmp = t * (y * (z * -9.0))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -10500.0)
		tmp = Float64(Float64(z * -9.0) * Float64(y * t));
	elseif (z <= -2.2e-148)
		tmp = Float64(x * 2.0);
	elseif (z <= -6.8e-220)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (z <= 8.5e-143)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -10500.0)
		tmp = (z * -9.0) * (y * t);
	elseif (z <= -2.2e-148)
		tmp = x * 2.0;
	elseif (z <= -6.8e-220)
		tmp = 27.0 * (a * b);
	elseif (z <= 8.5e-143)
		tmp = x * 2.0;
	else
		tmp = t * (y * (z * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -10500.0], N[(N[(z * -9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.2e-148], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -6.8e-220], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-143], N[(x * 2.0), $MachinePrecision], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -10500

   1. Initial program 91.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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 92.3%

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

   3. Simplified 92.3%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   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 50.6%

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

   7. Simplified 50.6%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   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-*l* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

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

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 52.0%

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

   9. Applied egg-rr 52.0%

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

   if -10500 < z < -2.20000000000000017e-148 or -6.79999999999999987e-220 < z < 8.50000000000000072e-143

   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 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 46.5%

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

   7. Simplified 46.5%

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

   if -2.20000000000000017e-148 < z < -6.79999999999999987e-220

   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 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 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 46.6%

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

   7. Simplified 46.6%

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

   if 8.50000000000000072e-143 < z

   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 93.0%

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

   3. Simplified 93.0%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   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 50.4%

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

   7. Simplified 50.4%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   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-*l* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

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

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

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

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

      9. *-lowering-*.f64 48.2%

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

   9. Applied egg-rr 48.2%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10500:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-220}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-143}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7200:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-150}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-219}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-141}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7200.0)
   (* -9.0 (* y (* z t)))
   (if (<= z -8.5e-150)
     (* x 2.0)
     (if (<= z -1.5e-219)
       (* 27.0 (* a b))
       (if (<= z 2.05e-141) (* x 2.0) (* t (* y (* z -9.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7200.0) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= -8.5e-150) {
		tmp = x * 2.0;
	} else if (z <= -1.5e-219) {
		tmp = 27.0 * (a * b);
	} else if (z <= 2.05e-141) {
		tmp = x * 2.0;
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-7200.0d0)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= (-8.5d-150)) then
        tmp = x * 2.0d0
    else if (z <= (-1.5d-219)) then
        tmp = 27.0d0 * (a * b)
    else if (z <= 2.05d-141) then
        tmp = x * 2.0d0
    else
        tmp = t * (y * (z * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7200.0) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= -8.5e-150) {
		tmp = x * 2.0;
	} else if (z <= -1.5e-219) {
		tmp = 27.0 * (a * b);
	} else if (z <= 2.05e-141) {
		tmp = x * 2.0;
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7200.0:
		tmp = -9.0 * (y * (z * t))
	elif z <= -8.5e-150:
		tmp = x * 2.0
	elif z <= -1.5e-219:
		tmp = 27.0 * (a * b)
	elif z <= 2.05e-141:
		tmp = x * 2.0
	else:
		tmp = t * (y * (z * -9.0))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7200.0)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= -8.5e-150)
		tmp = Float64(x * 2.0);
	elseif (z <= -1.5e-219)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (z <= 2.05e-141)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -7200.0)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= -8.5e-150)
		tmp = x * 2.0;
	elseif (z <= -1.5e-219)
		tmp = 27.0 * (a * b);
	elseif (z <= 2.05e-141)
		tmp = x * 2.0;
	else
		tmp = t * (y * (z * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7200.0], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.5e-150], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -1.5e-219], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e-141], N[(x * 2.0), $MachinePrecision], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7200

   1. Initial program 91.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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 92.3%

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

   3. Simplified 92.3%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   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 50.6%

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

   7. Simplified 50.6%

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

   if -7200 < z < -8.4999999999999997e-150 or -1.5e-219 < z < 2.05000000000000001e-141

   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 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 46.5%

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

   7. Simplified 46.5%

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

   if -8.4999999999999997e-150 < z < -1.5e-219

   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 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 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 46.6%

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

   7. Simplified 46.6%

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

   if 2.05000000000000001e-141 < z

   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 93.0%

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

   3. Simplified 93.0%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   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 50.4%

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

   7. Simplified 50.4%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   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-*l* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

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

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

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

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

      9. *-lowering-*.f64 48.2%

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

   9. Applied egg-rr 48.2%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7200:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-150}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-219}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-141}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -980:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-146}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-220}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-140}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -980.0)
   (* -9.0 (* y (* z t)))
   (if (<= z -1.65e-146)
     (* x 2.0)
     (if (<= z -5.6e-220)
       (* 27.0 (* a b))
       (if (<= z 1.75e-140) (* x 2.0) (* -9.0 (* t (* z y))))))))

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 <= -980.0) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= -1.65e-146) {
		tmp = x * 2.0;
	} else if (z <= -5.6e-220) {
		tmp = 27.0 * (a * b);
	} else if (z <= 1.75e-140) {
		tmp = x * 2.0;
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	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 <= (-980.0d0)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= (-1.65d-146)) then
        tmp = x * 2.0d0
    else if (z <= (-5.6d-220)) then
        tmp = 27.0d0 * (a * b)
    else if (z <= 1.75d-140) then
        tmp = x * 2.0d0
    else
        tmp = (-9.0d0) * (t * (z * y))
    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 <= -980.0) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= -1.65e-146) {
		tmp = x * 2.0;
	} else if (z <= -5.6e-220) {
		tmp = 27.0 * (a * b);
	} else if (z <= 1.75e-140) {
		tmp = x * 2.0;
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	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 <= -980.0:
		tmp = -9.0 * (y * (z * t))
	elif z <= -1.65e-146:
		tmp = x * 2.0
	elif z <= -5.6e-220:
		tmp = 27.0 * (a * b)
	elif z <= 1.75e-140:
		tmp = x * 2.0
	else:
		tmp = -9.0 * (t * (z * y))
	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 <= -980.0)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= -1.65e-146)
		tmp = Float64(x * 2.0);
	elseif (z <= -5.6e-220)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (z <= 1.75e-140)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	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 <= -980.0)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= -1.65e-146)
		tmp = x * 2.0;
	elseif (z <= -5.6e-220)
		tmp = 27.0 * (a * b);
	elseif (z <= 1.75e-140)
		tmp = x * 2.0;
	else
		tmp = -9.0 * (t * (z * y));
	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, -980.0], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.65e-146], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -5.6e-220], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-140], N[(x * 2.0), $MachinePrecision], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -980

   1. Initial program 91.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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 92.3%

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

   3. Simplified 92.3%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   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 50.6%

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

   7. Simplified 50.6%

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

   if -980 < z < -1.65e-146 or -5.5999999999999998e-220 < z < 1.7499999999999999e-140

   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 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 46.5%

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

   7. Simplified 46.5%

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

   if -1.65e-146 < z < -5.5999999999999998e-220

   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 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 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 46.6%

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

   7. Simplified 46.6%

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

   if 1.7499999999999999e-140 < z

   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 93.0%

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

   3. Simplified 93.0%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   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 50.4%

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

   7. Simplified 50.4%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-lowering-*.f64 48.2%

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

   9. Applied egg-rr 48.2%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -980:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-146}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-220}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-140}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;z \leq -620:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-219}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-139}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* y (* z t)))))
   (if (<= z -620.0)
     t_1
     (if (<= z -5.5e-148)
       (* x 2.0)
       (if (<= z -1.16e-219)
         (* 27.0 (* a b))
         (if (<= z 2.8e-139) (* x 2.0) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double tmp;
	if (z <= -620.0) {
		tmp = t_1;
	} else if (z <= -5.5e-148) {
		tmp = x * 2.0;
	} else if (z <= -1.16e-219) {
		tmp = 27.0 * (a * b);
	} else if (z <= 2.8e-139) {
		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 * (z * t))
    if (z <= (-620.0d0)) then
        tmp = t_1
    else if (z <= (-5.5d-148)) then
        tmp = x * 2.0d0
    else if (z <= (-1.16d-219)) then
        tmp = 27.0d0 * (a * b)
    else if (z <= 2.8d-139) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double tmp;
	if (z <= -620.0) {
		tmp = t_1;
	} else if (z <= -5.5e-148) {
		tmp = x * 2.0;
	} else if (z <= -1.16e-219) {
		tmp = 27.0 * (a * b);
	} else if (z <= 2.8e-139) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (y * (z * t))
	tmp = 0
	if z <= -620.0:
		tmp = t_1
	elif z <= -5.5e-148:
		tmp = x * 2.0
	elif z <= -1.16e-219:
		tmp = 27.0 * (a * b)
	elif z <= 2.8e-139:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(y * Float64(z * t)))
	tmp = 0.0
	if (z <= -620.0)
		tmp = t_1;
	elseif (z <= -5.5e-148)
		tmp = Float64(x * 2.0);
	elseif (z <= -1.16e-219)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (z <= 2.8e-139)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (y * (z * t));
	tmp = 0.0;
	if (z <= -620.0)
		tmp = t_1;
	elseif (z <= -5.5e-148)
		tmp = x * 2.0;
	elseif (z <= -1.16e-219)
		tmp = 27.0 * (a * b);
	elseif (z <= 2.8e-139)
		tmp = x * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -620.0], t$95$1, If[LessEqual[z, -5.5e-148], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -1.16e-219], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-139], N[(x * 2.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -620 or 2.7999999999999999e-139 < z

   1. Initial program 89.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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 92.7%

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

   3. Simplified 92.7%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   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 50.5%

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

   7. Simplified 50.5%

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

   if -620 < z < -5.5000000000000003e-148 or -1.1599999999999999e-219 < z < 2.7999999999999999e-139

   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 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 46.5%

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

   7. Simplified 46.5%

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

   if -5.5000000000000003e-148 < z < -1.1599999999999999e-219

   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 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 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 46.6%

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

   7. Simplified 46.6%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -620:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-219}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-139}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right) + x \cdot 2\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-143}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + x \cdot 2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* -9.0 (* y (* z t))) (* x 2.0))))
   (if (<= z -1.1e-25)
     t_1
     (if (<= z 1.15e-143)
       (+ (* b (* a 27.0)) (* x 2.0))
       (if (<= z 5.8e+88) t_1 (* -9.0 (* t (* z y))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-9.0 * (y * (z * t))) + (x * 2.0);
	double tmp;
	if (z <= -1.1e-25) {
		tmp = t_1;
	} else if (z <= 1.15e-143) {
		tmp = (b * (a * 27.0)) + (x * 2.0);
	} else if (z <= 5.8e+88) {
		tmp = t_1;
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	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 * (z * t))) + (x * 2.0d0)
    if (z <= (-1.1d-25)) then
        tmp = t_1
    else if (z <= 1.15d-143) then
        tmp = (b * (a * 27.0d0)) + (x * 2.0d0)
    else if (z <= 5.8d+88) then
        tmp = t_1
    else
        tmp = (-9.0d0) * (t * (z * y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-9.0 * (y * (z * t))) + (x * 2.0);
	double tmp;
	if (z <= -1.1e-25) {
		tmp = t_1;
	} else if (z <= 1.15e-143) {
		tmp = (b * (a * 27.0)) + (x * 2.0);
	} else if (z <= 5.8e+88) {
		tmp = t_1;
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (-9.0 * (y * (z * t))) + (x * 2.0)
	tmp = 0
	if z <= -1.1e-25:
		tmp = t_1
	elif z <= 1.15e-143:
		tmp = (b * (a * 27.0)) + (x * 2.0)
	elif z <= 5.8e+88:
		tmp = t_1
	else:
		tmp = -9.0 * (t * (z * y))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-9.0 * Float64(y * Float64(z * t))) + Float64(x * 2.0))
	tmp = 0.0
	if (z <= -1.1e-25)
		tmp = t_1;
	elseif (z <= 1.15e-143)
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(x * 2.0));
	elseif (z <= 5.8e+88)
		tmp = t_1;
	else
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (-9.0 * (y * (z * t))) + (x * 2.0);
	tmp = 0.0;
	if (z <= -1.1e-25)
		tmp = t_1;
	elseif (z <= 1.15e-143)
		tmp = (b * (a * 27.0)) + (x * 2.0);
	elseif (z <= 5.8e+88)
		tmp = t_1;
	else
		tmp = -9.0 * (t * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e-25], t$95$1, If[LessEqual[z, 1.15e-143], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+88], t$95$1, N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1000000000000001e-25 or 1.15000000000000006e-143 < z < 5.7999999999999999e88

   1. Initial program 92.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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 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 72.8%

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

   7. Simplified 72.8%

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

   if -1.1000000000000001e-25 < z < 1.15000000000000006e-143

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 83.2%

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

   5. Simplified 83.2%

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

   if 5.7999999999999999e88 < z

   1. Initial program 82.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in 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 62.7%

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

   7. Simplified 62.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-lowering-*.f64 62.8%

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

   9. Applied egg-rr 62.8%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-25}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right) + x \cdot 2\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-143}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + x \cdot 2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+88}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-28}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right) + x \cdot 2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-145}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(t \cdot -9\right) + x \cdot 2\\ \end{array} \end{array} \]

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
 (if (<= z -3.1e-28)
   (+ (* -9.0 (* y (* z t))) (* x 2.0))
   (if (<= z 1.1e-145)
     (+ (* b (* a 27.0)) (* x 2.0))
     (+ (* (* z y) (* t -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) {
	double tmp;
	if (z <= -3.1e-28) {
		tmp = (-9.0 * (y * (z * t))) + (x * 2.0);
	} else if (z <= 1.1e-145) {
		tmp = (b * (a * 27.0)) + (x * 2.0);
	} else {
		tmp = ((z * y) * (t * -9.0)) + (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) :: tmp
    if (z <= (-3.1d-28)) then
        tmp = ((-9.0d0) * (y * (z * t))) + (x * 2.0d0)
    else if (z <= 1.1d-145) then
        tmp = (b * (a * 27.0d0)) + (x * 2.0d0)
    else
        tmp = ((z * y) * (t * (-9.0d0))) + (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 tmp;
	if (z <= -3.1e-28) {
		tmp = (-9.0 * (y * (z * t))) + (x * 2.0);
	} else if (z <= 1.1e-145) {
		tmp = (b * (a * 27.0)) + (x * 2.0);
	} else {
		tmp = ((z * y) * (t * -9.0)) + (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):
	tmp = 0
	if z <= -3.1e-28:
		tmp = (-9.0 * (y * (z * t))) + (x * 2.0)
	elif z <= 1.1e-145:
		tmp = (b * (a * 27.0)) + (x * 2.0)
	else:
		tmp = ((z * y) * (t * -9.0)) + (x * 2.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.1e-28)
		tmp = Float64(Float64(-9.0 * Float64(y * Float64(z * t))) + Float64(x * 2.0));
	elseif (z <= 1.1e-145)
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(Float64(z * y) * Float64(t * -9.0)) + 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)
	tmp = 0.0;
	if (z <= -3.1e-28)
		tmp = (-9.0 * (y * (z * t))) + (x * 2.0);
	elseif (z <= 1.1e-145)
		tmp = (b * (a * 27.0)) + (x * 2.0);
	else
		tmp = ((z * y) * (t * -9.0)) + (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_] := If[LessEqual[z, -3.1e-28], N[(N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-145], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * y), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.09999999999999992e-28

   1. Initial program 91.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in a around 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 75.0%

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

   7. Simplified 75.0%

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

   if -3.09999999999999992e-28 < z < 1.1e-145

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 84.1%

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

   5. Simplified 84.1%

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

   if 1.1e-145 < z

   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 93.0%

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

   3. Simplified 93.0%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   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 74.7%

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

   7. Simplified 74.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*l* N/A

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

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

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

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

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

      11. *-lowering-*.f64 71.5%

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

   9. Applied egg-rr 71.5%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-28}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right) + x \cdot 2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-145}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(t \cdot -9\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+53}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{+91}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.2e+53)
   (* (* z -9.0) (* y t))
   (if (<= z 6.1e+91) (+ (* b (* a 27.0)) (* x 2.0)) (* -9.0 (* t (* z y))))))

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 <= -1.2e+53) {
		tmp = (z * -9.0) * (y * t);
	} else if (z <= 6.1e+91) {
		tmp = (b * (a * 27.0)) + (x * 2.0);
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	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 <= (-1.2d+53)) then
        tmp = (z * (-9.0d0)) * (y * t)
    else if (z <= 6.1d+91) then
        tmp = (b * (a * 27.0d0)) + (x * 2.0d0)
    else
        tmp = (-9.0d0) * (t * (z * y))
    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 <= -1.2e+53) {
		tmp = (z * -9.0) * (y * t);
	} else if (z <= 6.1e+91) {
		tmp = (b * (a * 27.0)) + (x * 2.0);
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	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 <= -1.2e+53:
		tmp = (z * -9.0) * (y * t)
	elif z <= 6.1e+91:
		tmp = (b * (a * 27.0)) + (x * 2.0)
	else:
		tmp = -9.0 * (t * (z * y))
	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 <= -1.2e+53)
		tmp = Float64(Float64(z * -9.0) * Float64(y * t));
	elseif (z <= 6.1e+91)
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(x * 2.0));
	else
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	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 <= -1.2e+53)
		tmp = (z * -9.0) * (y * t);
	elseif (z <= 6.1e+91)
		tmp = (b * (a * 27.0)) + (x * 2.0);
	else
		tmp = -9.0 * (t * (z * y));
	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, -1.2e+53], N[(N[(z * -9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.1e+91], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e53

   1. Initial program 89.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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 90.7%

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

   3. Simplified 90.7%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   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 49.5%

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

   7. Simplified 49.5%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   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-*l* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

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

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 51.1%

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

   9. Applied egg-rr 51.1%

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

   if -1.2e53 < z < 6.1e91

   1. Initial program 98.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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 73.7%

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

   5. Simplified 73.7%

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

   if 6.1e91 < z

   1. Initial program 82.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in 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 62.7%

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

   7. Simplified 62.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-lowering-*.f64 62.8%

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

   9. Applied egg-rr 62.8%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+53}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{+91}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 (<= b -3.8e-59)
   (* b (* a 27.0))
   (if (<= b 3.2e+23) (* x 2.0) (* 27.0 (* a b)))))

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 (b <= -3.8e-59) {
		tmp = b * (a * 27.0);
	} else if (b <= 3.2e+23) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 (b <= (-3.8d-59)) then
        tmp = b * (a * 27.0d0)
    else if (b <= 3.2d+23) then
        tmp = x * 2.0d0
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
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 (b <= -3.8e-59) {
		tmp = b * (a * 27.0);
	} else if (b <= 3.2e+23) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.8e-59:
		tmp = b * (a * 27.0)
	elif b <= 3.2e+23:
		tmp = x * 2.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
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 (b <= -3.8e-59)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (b <= 3.2e+23)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
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 (b <= -3.8e-59)
		tmp = b * (a * 27.0);
	elseif (b <= 3.2e+23)
		tmp = x * 2.0;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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[b, -3.8e-59], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+23], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.79999999999999983e-59

   1. Initial program 94.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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 94.2%

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

   3. Simplified 94.2%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   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 41.6%

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

   7. Simplified 41.6%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   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 41.6%

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

   9. Applied egg-rr 41.6%

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

   if -3.79999999999999983e-59 < b < 3.2e23

   1. Initial program 95.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 43.7%

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

   7. Simplified 43.7%

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

   if 3.2e23 < b

   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 91.6%

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

   3. Simplified 91.6%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   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 51.9%

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

   7. Simplified 51.9%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+23}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (<= b -6e-59) t_1 (if (<= b 2.9e+23) (* 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 (b <= -6e-59) {
		tmp = t_1;
	} else if (b <= 2.9e+23) {
		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 (b <= (-6d-59)) then
        tmp = t_1
    else if (b <= 2.9d+23) 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 (b <= -6e-59) {
		tmp = t_1;
	} else if (b <= 2.9e+23) {
		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 b <= -6e-59:
		tmp = t_1
	elif b <= 2.9e+23:
		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 (b <= -6e-59)
		tmp = t_1;
	elseif (b <= 2.9e+23)
		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 (b <= -6e-59)
		tmp = t_1;
	elseif (b <= 2.9e+23)
		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[b, -6e-59], t$95$1, If[LessEqual[b, 2.9e+23], N[(x * 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.0000000000000002e-59 or 2.90000000000000013e23 < b

   1. Initial program 92.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   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 46.8%

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

   7. Simplified 46.8%

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

   if -6.0000000000000002e-59 < b < 2.90000000000000013e23

   1. Initial program 95.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 43.7%

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

   7. Simplified 43.7%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{-59}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+23}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.5% 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 93.7%

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

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

   1. *-lowering-*.f64 33.7%

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

7. Simplified 33.7%

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

8. Final simplification 33.7%

   \[\leadsto x \cdot 2 \]
9. Add Preprocessing

Developer Target 1: 95.1% 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 2024160 
(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)))