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

Percentage Accurate: 95.6% → 98.5%

Time: 23.6s

Alternatives: 20

Speedup: 0.9×

• 27.8% 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: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-223}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, y \cdot -9, \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4e-223)
   (fma (* t z) (* y -9.0) (fma (* 27.0 b) a (* x 2.0)))
   (+ (* (* a 27.0) b) (- (* x 2.0) (* (* (* 9.0 y) z) t)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4e-223) {
		tmp = fma((t * z), (y * -9.0), fma((27.0 * b), a, (x * 2.0)));
	} else {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (((9.0 * y) * z) * t));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4e-223)
		tmp = fma(Float64(t * z), Float64(y * -9.0), fma(Float64(27.0 * b), a, Float64(x * 2.0)));
	else
		tmp = Float64(Float64(Float64(a * 27.0) * b) + Float64(Float64(x * 2.0) - Float64(Float64(Float64(9.0 * y) * z) * t)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4e-223], N[(N[(t * z), $MachinePrecision] * N[(y * -9.0), $MachinePrecision] + N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9999999999999999e-223

   1. Initial program 91.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 89.3%

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

   if -3.9999999999999999e-223 < z

   1. Initial program 94.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-223}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, y \cdot -9, \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 57.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+264}:\\ \;\;\;\;\left(\left(y \cdot -9\right) \cdot t\right) \cdot z\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+204}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;t\_1 \leq 10^{+307}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot -9\right) \cdot \left(t \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* x 2.0) (* (* (* 9.0 y) z) t))))
   (if (<= t_1 -5e+264)
     (* (* (* y -9.0) t) z)
     (if (<= t_1 -5e+90)
       (* x 2.0)
       (if (<= t_1 5e+204)
         (* (* a b) 27.0)
         (if (<= t_1 1e+307) (* x 2.0) (* (* y -9.0) (* t z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (((9.0 * y) * z) * t);
	double tmp;
	if (t_1 <= -5e+264) {
		tmp = ((y * -9.0) * t) * z;
	} else if (t_1 <= -5e+90) {
		tmp = x * 2.0;
	} else if (t_1 <= 5e+204) {
		tmp = (a * b) * 27.0;
	} else if (t_1 <= 1e+307) {
		tmp = x * 2.0;
	} else {
		tmp = (y * -9.0) * (t * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) - (((9.0d0 * y) * z) * t)
    if (t_1 <= (-5d+264)) then
        tmp = ((y * (-9.0d0)) * t) * z
    else if (t_1 <= (-5d+90)) then
        tmp = x * 2.0d0
    else if (t_1 <= 5d+204) then
        tmp = (a * b) * 27.0d0
    else if (t_1 <= 1d+307) then
        tmp = x * 2.0d0
    else
        tmp = (y * (-9.0d0)) * (t * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (((9.0 * y) * z) * t);
	double tmp;
	if (t_1 <= -5e+264) {
		tmp = ((y * -9.0) * t) * z;
	} else if (t_1 <= -5e+90) {
		tmp = x * 2.0;
	} else if (t_1 <= 5e+204) {
		tmp = (a * b) * 27.0;
	} else if (t_1 <= 1e+307) {
		tmp = x * 2.0;
	} else {
		tmp = (y * -9.0) * (t * z);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (((9.0 * y) * z) * t)
	tmp = 0
	if t_1 <= -5e+264:
		tmp = ((y * -9.0) * t) * z
	elif t_1 <= -5e+90:
		tmp = x * 2.0
	elif t_1 <= 5e+204:
		tmp = (a * b) * 27.0
	elif t_1 <= 1e+307:
		tmp = x * 2.0
	else:
		tmp = (y * -9.0) * (t * z)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(Float64(Float64(9.0 * y) * z) * t))
	tmp = 0.0
	if (t_1 <= -5e+264)
		tmp = Float64(Float64(Float64(y * -9.0) * t) * z);
	elseif (t_1 <= -5e+90)
		tmp = Float64(x * 2.0);
	elseif (t_1 <= 5e+204)
		tmp = Float64(Float64(a * b) * 27.0);
	elseif (t_1 <= 1e+307)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(Float64(y * -9.0) * Float64(t * z));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (((9.0 * y) * z) * t);
	tmp = 0.0;
	if (t_1 <= -5e+264)
		tmp = ((y * -9.0) * t) * z;
	elseif (t_1 <= -5e+90)
		tmp = x * 2.0;
	elseif (t_1 <= 5e+204)
		tmp = (a * b) * 27.0;
	elseif (t_1 <= 1e+307)
		tmp = x * 2.0;
	else
		tmp = (y * -9.0) * (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+264], N[(N[(N[(y * -9.0), $MachinePrecision] * t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, -5e+90], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+204], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+307], N[(x * 2.0), $MachinePrecision], N[(N[(y * -9.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -5.00000000000000033e264

   1. Initial program 82.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 10.7

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

   5. Applied rewrites 10.7%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 77.2

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

   8. Applied rewrites 77.2%

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

   10. Applied rewrites 84.6%

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

   if -5.00000000000000033e264 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -5.0000000000000004e90 or 5.00000000000000008e204 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 9.99999999999999986e306

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 56.8

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

   5. Applied rewrites 56.8%

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

   if -5.0000000000000004e90 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 5.00000000000000008e204

   1. Initial program 98.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 66.5

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

   5. Applied rewrites 66.5%

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

   if 9.99999999999999986e306 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 67.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 1.8

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

   5. Applied rewrites 1.8%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 70.9

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

   8. Applied rewrites 70.9%

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

   10. Applied rewrites 96.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+264}:\\ \;\;\;\;\left(\left(y \cdot -9\right) \cdot t\right) \cdot z\\ \mathbf{elif}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+204}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 10^{+307}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot -9\right) \cdot \left(t \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+264}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-9 \cdot z\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+204}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;t\_1 \leq 10^{+307}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot -9\right) \cdot \left(t \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* x 2.0) (* (* (* 9.0 y) z) t))))
   (if (<= t_1 -5e+264)
     (* (* y t) (* -9.0 z))
     (if (<= t_1 -5e+90)
       (* x 2.0)
       (if (<= t_1 5e+204)
         (* (* a b) 27.0)
         (if (<= t_1 1e+307) (* x 2.0) (* (* y -9.0) (* t z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (((9.0 * y) * z) * t);
	double tmp;
	if (t_1 <= -5e+264) {
		tmp = (y * t) * (-9.0 * z);
	} else if (t_1 <= -5e+90) {
		tmp = x * 2.0;
	} else if (t_1 <= 5e+204) {
		tmp = (a * b) * 27.0;
	} else if (t_1 <= 1e+307) {
		tmp = x * 2.0;
	} else {
		tmp = (y * -9.0) * (t * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) - (((9.0d0 * y) * z) * t)
    if (t_1 <= (-5d+264)) then
        tmp = (y * t) * ((-9.0d0) * z)
    else if (t_1 <= (-5d+90)) then
        tmp = x * 2.0d0
    else if (t_1 <= 5d+204) then
        tmp = (a * b) * 27.0d0
    else if (t_1 <= 1d+307) then
        tmp = x * 2.0d0
    else
        tmp = (y * (-9.0d0)) * (t * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (((9.0 * y) * z) * t);
	double tmp;
	if (t_1 <= -5e+264) {
		tmp = (y * t) * (-9.0 * z);
	} else if (t_1 <= -5e+90) {
		tmp = x * 2.0;
	} else if (t_1 <= 5e+204) {
		tmp = (a * b) * 27.0;
	} else if (t_1 <= 1e+307) {
		tmp = x * 2.0;
	} else {
		tmp = (y * -9.0) * (t * z);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (((9.0 * y) * z) * t)
	tmp = 0
	if t_1 <= -5e+264:
		tmp = (y * t) * (-9.0 * z)
	elif t_1 <= -5e+90:
		tmp = x * 2.0
	elif t_1 <= 5e+204:
		tmp = (a * b) * 27.0
	elif t_1 <= 1e+307:
		tmp = x * 2.0
	else:
		tmp = (y * -9.0) * (t * z)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(Float64(Float64(9.0 * y) * z) * t))
	tmp = 0.0
	if (t_1 <= -5e+264)
		tmp = Float64(Float64(y * t) * Float64(-9.0 * z));
	elseif (t_1 <= -5e+90)
		tmp = Float64(x * 2.0);
	elseif (t_1 <= 5e+204)
		tmp = Float64(Float64(a * b) * 27.0);
	elseif (t_1 <= 1e+307)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(Float64(y * -9.0) * Float64(t * z));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (((9.0 * y) * z) * t);
	tmp = 0.0;
	if (t_1 <= -5e+264)
		tmp = (y * t) * (-9.0 * z);
	elseif (t_1 <= -5e+90)
		tmp = x * 2.0;
	elseif (t_1 <= 5e+204)
		tmp = (a * b) * 27.0;
	elseif (t_1 <= 1e+307)
		tmp = x * 2.0;
	else
		tmp = (y * -9.0) * (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+264], N[(N[(y * t), $MachinePrecision] * N[(-9.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+90], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+204], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+307], N[(x * 2.0), $MachinePrecision], N[(N[(y * -9.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -5.00000000000000033e264

   1. Initial program 82.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 10.7

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

   5. Applied rewrites 10.7%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 77.2

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

   8. Applied rewrites 77.2%

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

   10. Applied rewrites 84.6%

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

   if -5.00000000000000033e264 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -5.0000000000000004e90 or 5.00000000000000008e204 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 9.99999999999999986e306

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 56.8

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

   5. Applied rewrites 56.8%

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

   if -5.0000000000000004e90 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 5.00000000000000008e204

   1. Initial program 98.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 66.5

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

   5. Applied rewrites 66.5%

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

   if 9.99999999999999986e306 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 67.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 1.8

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

   5. Applied rewrites 1.8%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 70.9

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

   8. Applied rewrites 70.9%

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

   10. Applied rewrites 96.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+264}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-9 \cdot z\right)\\ \mathbf{elif}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+204}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 10^{+307}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot -9\right) \cdot \left(t \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+204}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;t\_1 \leq 10^{+307}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot -9\right) \cdot \left(t \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* x 2.0) (* (* (* 9.0 y) z) t))))
   (if (<= t_1 (- INFINITY))
     (* (* -9.0 (* t z)) y)
     (if (<= t_1 -5e+90)
       (* x 2.0)
       (if (<= t_1 5e+204)
         (* (* a b) 27.0)
         (if (<= t_1 1e+307) (* x 2.0) (* (* y -9.0) (* t z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (((9.0 * y) * z) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (-9.0 * (t * z)) * y;
	} else if (t_1 <= -5e+90) {
		tmp = x * 2.0;
	} else if (t_1 <= 5e+204) {
		tmp = (a * b) * 27.0;
	} else if (t_1 <= 1e+307) {
		tmp = x * 2.0;
	} else {
		tmp = (y * -9.0) * (t * z);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (((9.0 * y) * z) * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (-9.0 * (t * z)) * y;
	} else if (t_1 <= -5e+90) {
		tmp = x * 2.0;
	} else if (t_1 <= 5e+204) {
		tmp = (a * b) * 27.0;
	} else if (t_1 <= 1e+307) {
		tmp = x * 2.0;
	} else {
		tmp = (y * -9.0) * (t * z);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (((9.0 * y) * z) * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (-9.0 * (t * z)) * y
	elif t_1 <= -5e+90:
		tmp = x * 2.0
	elif t_1 <= 5e+204:
		tmp = (a * b) * 27.0
	elif t_1 <= 1e+307:
		tmp = x * 2.0
	else:
		tmp = (y * -9.0) * (t * z)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(Float64(Float64(9.0 * y) * z) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(-9.0 * Float64(t * z)) * y);
	elseif (t_1 <= -5e+90)
		tmp = Float64(x * 2.0);
	elseif (t_1 <= 5e+204)
		tmp = Float64(Float64(a * b) * 27.0);
	elseif (t_1 <= 1e+307)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(Float64(y * -9.0) * Float64(t * z));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (((9.0 * y) * z) * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (-9.0 * (t * z)) * y;
	elseif (t_1 <= -5e+90)
		tmp = x * 2.0;
	elseif (t_1 <= 5e+204)
		tmp = (a * b) * 27.0;
	elseif (t_1 <= 1e+307)
		tmp = x * 2.0;
	else
		tmp = (y * -9.0) * (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(-9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, -5e+90], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+204], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+307], N[(x * 2.0), $MachinePrecision], N[(N[(y * -9.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 78.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 3.3

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

   5. Applied rewrites 3.3%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 84.8

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

   8. Applied rewrites 84.8%

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

   10. Applied rewrites 96.7%

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

   if -inf.0 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -5.0000000000000004e90 or 5.00000000000000008e204 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 9.99999999999999986e306

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 55.7

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

   5. Applied rewrites 55.7%

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

   if -5.0000000000000004e90 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 5.00000000000000008e204

   1. Initial program 98.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 66.5

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

   5. Applied rewrites 66.5%

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

   if 9.99999999999999986e306 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 67.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 1.8

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

   5. Applied rewrites 1.8%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 70.9

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

   8. Applied rewrites 70.9%

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

   10. Applied rewrites 96.1%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -\infty:\\ \;\;\;\;\left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\\ \mathbf{elif}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+204}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 10^{+307}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot -9\right) \cdot \left(t \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\\ t_2 := x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+204}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;t\_2 \leq 10^{+307}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* -9.0 (* t z)) y)) (t_2 (- (* x 2.0) (* (* (* 9.0 y) z) t))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e+90)
       (* x 2.0)
       (if (<= t_2 5e+204)
         (* (* a b) 27.0)
         (if (<= t_2 1e+307) (* x 2.0) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-9.0 * (t * z)) * y;
	double t_2 = (x * 2.0) - (((9.0 * y) * z) * t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e+90) {
		tmp = x * 2.0;
	} else if (t_2 <= 5e+204) {
		tmp = (a * b) * 27.0;
	} else if (t_2 <= 1e+307) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-9.0 * (t * z)) * y;
	double t_2 = (x * 2.0) - (((9.0 * y) * z) * t);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e+90) {
		tmp = x * 2.0;
	} else if (t_2 <= 5e+204) {
		tmp = (a * b) * 27.0;
	} else if (t_2 <= 1e+307) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (-9.0 * (t * z)) * y
	t_2 = (x * 2.0) - (((9.0 * y) * z) * t)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e+90:
		tmp = x * 2.0
	elif t_2 <= 5e+204:
		tmp = (a * b) * 27.0
	elif t_2 <= 1e+307:
		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(Float64(-9.0 * Float64(t * z)) * y)
	t_2 = Float64(Float64(x * 2.0) - Float64(Float64(Float64(9.0 * y) * z) * t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e+90)
		tmp = Float64(x * 2.0);
	elseif (t_2 <= 5e+204)
		tmp = Float64(Float64(a * b) * 27.0);
	elseif (t_2 <= 1e+307)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (-9.0 * (t * z)) * y;
	t_2 = (x * 2.0) - (((9.0 * y) * z) * t);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e+90)
		tmp = x * 2.0;
	elseif (t_2 <= 5e+204)
		tmp = (a * b) * 27.0;
	elseif (t_2 <= 1e+307)
		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[(N[(-9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e+90], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$2, 5e+204], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], If[LessEqual[t$95$2, 1e+307], N[(x * 2.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -inf.0 or 9.99999999999999986e306 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 73.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 2.6

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

   5. Applied rewrites 2.6%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 78.4

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

   8. Applied rewrites 78.4%

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

   10. Applied rewrites 96.4%

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

   if -inf.0 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -5.0000000000000004e90 or 5.00000000000000008e204 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 9.99999999999999986e306

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 55.7

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

   5. Applied rewrites 55.7%

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

   if -5.0000000000000004e90 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 5.00000000000000008e204

   1. Initial program 98.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 66.5

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

   5. Applied rewrites 66.5%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -\infty:\\ \;\;\;\;\left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\\ \mathbf{elif}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+204}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 10^{+307}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(-9 \cdot \left(t \cdot z\right)\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot z\right) \cdot t\right) \cdot -9\\ t_2 := x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+204}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;t\_2 \leq 10^{+307}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* (* y z) t) -9.0)) (t_2 (- (* x 2.0) (* (* (* 9.0 y) z) t))))
   (if (<= t_2 -5e+269)
     t_1
     (if (<= t_2 -5e+90)
       (* x 2.0)
       (if (<= t_2 5e+204)
         (* (* a b) 27.0)
         (if (<= t_2 1e+307) (* 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 = ((y * z) * t) * -9.0;
	double t_2 = (x * 2.0) - (((9.0 * y) * z) * t);
	double tmp;
	if (t_2 <= -5e+269) {
		tmp = t_1;
	} else if (t_2 <= -5e+90) {
		tmp = x * 2.0;
	} else if (t_2 <= 5e+204) {
		tmp = (a * b) * 27.0;
	} else if (t_2 <= 1e+307) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((y * z) * t) * (-9.0d0)
    t_2 = (x * 2.0d0) - (((9.0d0 * y) * z) * t)
    if (t_2 <= (-5d+269)) then
        tmp = t_1
    else if (t_2 <= (-5d+90)) then
        tmp = x * 2.0d0
    else if (t_2 <= 5d+204) then
        tmp = (a * b) * 27.0d0
    else if (t_2 <= 1d+307) 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 = ((y * z) * t) * -9.0;
	double t_2 = (x * 2.0) - (((9.0 * y) * z) * t);
	double tmp;
	if (t_2 <= -5e+269) {
		tmp = t_1;
	} else if (t_2 <= -5e+90) {
		tmp = x * 2.0;
	} else if (t_2 <= 5e+204) {
		tmp = (a * b) * 27.0;
	} else if (t_2 <= 1e+307) {
		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 = ((y * z) * t) * -9.0
	t_2 = (x * 2.0) - (((9.0 * y) * z) * t)
	tmp = 0
	if t_2 <= -5e+269:
		tmp = t_1
	elif t_2 <= -5e+90:
		tmp = x * 2.0
	elif t_2 <= 5e+204:
		tmp = (a * b) * 27.0
	elif t_2 <= 1e+307:
		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(Float64(Float64(y * z) * t) * -9.0)
	t_2 = Float64(Float64(x * 2.0) - Float64(Float64(Float64(9.0 * y) * z) * t))
	tmp = 0.0
	if (t_2 <= -5e+269)
		tmp = t_1;
	elseif (t_2 <= -5e+90)
		tmp = Float64(x * 2.0);
	elseif (t_2 <= 5e+204)
		tmp = Float64(Float64(a * b) * 27.0);
	elseif (t_2 <= 1e+307)
		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 = ((y * z) * t) * -9.0;
	t_2 = (x * 2.0) - (((9.0 * y) * z) * t);
	tmp = 0.0;
	if (t_2 <= -5e+269)
		tmp = t_1;
	elseif (t_2 <= -5e+90)
		tmp = x * 2.0;
	elseif (t_2 <= 5e+204)
		tmp = (a * b) * 27.0;
	elseif (t_2 <= 1e+307)
		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[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * -9.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+269], t$95$1, If[LessEqual[t$95$2, -5e+90], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$2, 5e+204], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], If[LessEqual[t$95$2, 1e+307], N[(x * 2.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -5.0000000000000002e269 or 9.99999999999999986e306 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 75.3%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 75.4

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

   5. Applied rewrites 75.4%

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

   if -5.0000000000000002e269 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -5.0000000000000004e90 or 5.00000000000000008e204 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 9.99999999999999986e306

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 56.6

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

   5. Applied rewrites 56.6%

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

   if -5.0000000000000004e90 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 5.00000000000000008e204

   1. Initial program 98.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 66.5

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

   5. Applied rewrites 66.5%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+269}:\\ \;\;\;\;\left(\left(y \cdot z\right) \cdot t\right) \cdot -9\\ \mathbf{elif}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+204}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;x \cdot 2 - \left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 10^{+307}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot z\right) \cdot t\right) \cdot -9\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+289}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot t\right) \cdot -9, z, x \cdot 2\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+155}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, -9 \cdot t, \left(a \cdot b\right) \cdot 27\right)\\ \mathbf{elif}\;t\_1 \leq 6 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, -9 \cdot t, x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* 9.0 y) z) t)))
   (if (<= t_1 -5e+289)
     (fma (* (* y t) -9.0) z (* x 2.0))
     (if (<= t_1 -5e+155)
       (fma (* y z) (* -9.0 t) (* (* a b) 27.0))
       (if (<= t_1 6e+58)
         (fma (* a 27.0) b (* x 2.0))
         (fma (* y z) (* -9.0 t) (* x 2.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_1 <= -5e+289) {
		tmp = fma(((y * t) * -9.0), z, (x * 2.0));
	} else if (t_1 <= -5e+155) {
		tmp = fma((y * z), (-9.0 * t), ((a * b) * 27.0));
	} else if (t_1 <= 6e+58) {
		tmp = fma((a * 27.0), b, (x * 2.0));
	} else {
		tmp = fma((y * z), (-9.0 * t), (x * 2.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_1 <= -5e+289)
		tmp = fma(Float64(Float64(y * t) * -9.0), z, Float64(x * 2.0));
	elseif (t_1 <= -5e+155)
		tmp = fma(Float64(y * z), Float64(-9.0 * t), Float64(Float64(a * b) * 27.0));
	elseif (t_1 <= 6e+58)
		tmp = fma(Float64(a * 27.0), b, Float64(x * 2.0));
	else
		tmp = fma(Float64(y * z), Float64(-9.0 * t), Float64(x * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+289], N[(N[(N[(y * t), $MachinePrecision] * -9.0), $MachinePrecision] * z + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+155], N[(N[(y * z), $MachinePrecision] * N[(-9.0 * t), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 6e+58], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * N[(-9.0 * t), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.00000000000000031e289

   1. Initial program 68.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

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

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 92.7%

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

   5. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 92.8

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

   7. Applied rewrites 92.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 92.7

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

   9. Applied rewrites 92.7%

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

   if -5.00000000000000031e289 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.9999999999999999e155

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 75.0

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

   5. Applied rewrites 75.0%

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

   7. Applied rewrites 89.4%

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

   if -4.9999999999999999e155 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 6.0000000000000005e58

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 93.8

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

   5. Applied rewrites 93.8%

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

   7. Applied rewrites 93.8%

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

   if 6.0000000000000005e58 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 84.1

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

   7. Applied rewrites 84.1%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 82.8

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

   9. Applied rewrites 82.8%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+289}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot t\right) \cdot -9, z, x \cdot 2\right)\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+155}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, -9 \cdot t, \left(a \cdot b\right) \cdot 27\right)\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 6 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, -9 \cdot t, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 27\\ t_2 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+155}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, t\_1\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot t, -9 \cdot z, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a b) 27.0)) (t_2 (* (* (* 9.0 y) z) t)))
   (if (<= t_2 -5e+155)
     (fma (* -9.0 (* t z)) y t_1)
     (if (<= t_2 2e+106)
       (fma (* a 27.0) b (* x 2.0))
       (fma (* y t) (* -9.0 z) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) * 27.0;
	double t_2 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_2 <= -5e+155) {
		tmp = fma((-9.0 * (t * z)), y, t_1);
	} else if (t_2 <= 2e+106) {
		tmp = fma((a * 27.0), b, (x * 2.0));
	} else {
		tmp = fma((y * t), (-9.0 * z), t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * b) * 27.0)
	t_2 = Float64(Float64(Float64(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_2 <= -5e+155)
		tmp = fma(Float64(-9.0 * Float64(t * z)), y, t_1);
	elseif (t_2 <= 2e+106)
		tmp = fma(Float64(a * 27.0), b, Float64(x * 2.0));
	else
		tmp = fma(Float64(y * t), Float64(-9.0 * z), t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+155], N[(N[(-9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision] * y + t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 2e+106], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * t), $MachinePrecision] * N[(-9.0 * z), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.9999999999999999e155

   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. Add Preprocessing

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 86.3

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

   5. Applied rewrites 86.3%

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

   if -4.9999999999999999e155 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.00000000000000018e106

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 92.8

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

   5. Applied rewrites 92.8%

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

   7. Applied rewrites 92.9%

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

   if 2.00000000000000018e106 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 86.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. associate-*r* N/A

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

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

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

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

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

      17. lower-*.f64 N/A

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

      18. metadata-eval N/A

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

   4. Applied rewrites 86.3%

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

   5. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 86.5

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

   7. Applied rewrites 86.5%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+155}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, \left(a \cdot b\right) \cdot 27\right)\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 2 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot t, -9 \cdot z, \left(a \cdot b\right) \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+155}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, \left(a \cdot b\right) \cdot 27\right)\\ \mathbf{elif}\;t\_1 \leq 6 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, -9 \cdot t, x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* 9.0 y) z) t)))
   (if (<= t_1 -5e+155)
     (fma (* -9.0 (* t z)) y (* (* a b) 27.0))
     (if (<= t_1 6e+58)
       (fma (* a 27.0) b (* x 2.0))
       (fma (* y z) (* -9.0 t) (* x 2.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_1 <= -5e+155) {
		tmp = fma((-9.0 * (t * z)), y, ((a * b) * 27.0));
	} else if (t_1 <= 6e+58) {
		tmp = fma((a * 27.0), b, (x * 2.0));
	} else {
		tmp = fma((y * z), (-9.0 * t), (x * 2.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_1 <= -5e+155)
		tmp = fma(Float64(-9.0 * Float64(t * z)), y, Float64(Float64(a * b) * 27.0));
	elseif (t_1 <= 6e+58)
		tmp = fma(Float64(a * 27.0), b, Float64(x * 2.0));
	else
		tmp = fma(Float64(y * z), Float64(-9.0 * t), Float64(x * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+155], N[(N[(-9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision] * y + N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 6e+58], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * N[(-9.0 * t), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.9999999999999999e155

   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. Add Preprocessing

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 86.3

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

   5. Applied rewrites 86.3%

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

   if -4.9999999999999999e155 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 6.0000000000000005e58

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 93.8

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

   5. Applied rewrites 93.8%

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

   7. Applied rewrites 93.8%

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

   if 6.0000000000000005e58 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 84.1

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

   7. Applied rewrites 84.1%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 82.8

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

   9. Applied rewrites 82.8%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+155}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, \left(a \cdot b\right) \cdot 27\right)\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 6 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, -9 \cdot t, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, y \cdot -9, x \cdot 2\right)\\ \mathbf{elif}\;t\_1 \leq 6 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, -9 \cdot t, x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* 9.0 y) z) t)))
   (if (<= t_1 -2e+204)
     (fma (* t z) (* y -9.0) (* x 2.0))
     (if (<= t_1 6e+58)
       (fma (* a b) 27.0 (* x 2.0))
       (fma (* y z) (* -9.0 t) (* x 2.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_1 <= -2e+204) {
		tmp = fma((t * z), (y * -9.0), (x * 2.0));
	} else if (t_1 <= 6e+58) {
		tmp = fma((a * b), 27.0, (x * 2.0));
	} else {
		tmp = fma((y * z), (-9.0 * t), (x * 2.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_1 <= -2e+204)
		tmp = fma(Float64(t * z), Float64(y * -9.0), Float64(x * 2.0));
	elseif (t_1 <= 6e+58)
		tmp = fma(Float64(a * b), 27.0, Float64(x * 2.0));
	else
		tmp = fma(Float64(y * z), Float64(-9.0 * t), Float64(x * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+204], N[(N[(t * z), $MachinePrecision] * N[(y * -9.0), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 6e+58], N[(N[(a * b), $MachinePrecision] * 27.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * N[(-9.0 * t), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.99999999999999998e204

   1. Initial program 76.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 89.6%

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

   5. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 87.5

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

   7. Applied rewrites 87.5%

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

   if -1.99999999999999998e204 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 6.0000000000000005e58

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 92.4

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

   5. Applied rewrites 92.4%

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

   if 6.0000000000000005e58 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 84.1

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

   7. Applied rewrites 84.1%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 82.8

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

   9. Applied rewrites 82.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -2 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, y \cdot -9, x \cdot 2\right)\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 6 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, -9 \cdot t, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, y \cdot -9, x \cdot 2\right)\\ \mathbf{elif}\;t\_1 \leq 6 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* 9.0 y) z) t)))
   (if (<= t_1 -2e+204)
     (fma (* t z) (* y -9.0) (* x 2.0))
     (if (<= t_1 6e+58)
       (fma (* a b) 27.0 (* x 2.0))
       (fma (* -9.0 (* t z)) y (* x 2.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_1 <= -2e+204) {
		tmp = fma((t * z), (y * -9.0), (x * 2.0));
	} else if (t_1 <= 6e+58) {
		tmp = fma((a * b), 27.0, (x * 2.0));
	} else {
		tmp = fma((-9.0 * (t * z)), y, (x * 2.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_1 <= -2e+204)
		tmp = fma(Float64(t * z), Float64(y * -9.0), Float64(x * 2.0));
	elseif (t_1 <= 6e+58)
		tmp = fma(Float64(a * b), 27.0, Float64(x * 2.0));
	else
		tmp = fma(Float64(-9.0 * Float64(t * z)), y, Float64(x * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+204], N[(N[(t * z), $MachinePrecision] * N[(y * -9.0), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 6e+58], N[(N[(a * b), $MachinePrecision] * 27.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(-9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision] * y + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.99999999999999998e204

   1. Initial program 76.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 89.6%

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

   5. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 87.5

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

   7. Applied rewrites 87.5%

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

   if -1.99999999999999998e204 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 6.0000000000000005e58

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 92.4

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

   5. Applied rewrites 92.4%

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

   if 6.0000000000000005e58 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.1%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 84.1

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

   5. Applied rewrites 84.1%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -2 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, y \cdot -9, x \cdot 2\right)\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 6 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, x \cdot 2\right)\\ t_2 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 6 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (* -9.0 (* t z)) y (* x 2.0))) (t_2 (* (* (* 9.0 y) z) t)))
   (if (<= t_2 -2e+204)
     t_1
     (if (<= t_2 6e+58) (fma (* a b) 27.0 (* x 2.0)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((-9.0 * (t * z)), y, (x * 2.0));
	double t_2 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_2 <= -2e+204) {
		tmp = t_1;
	} else if (t_2 <= 6e+58) {
		tmp = fma((a * b), 27.0, (x * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-9.0 * Float64(t * z)), y, Float64(x * 2.0))
	t_2 = Float64(Float64(Float64(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_2 <= -2e+204)
		tmp = t_1;
	elseif (t_2 <= 6e+58)
		tmp = fma(Float64(a * b), 27.0, Float64(x * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(-9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision] * y + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+204], t$95$1, If[LessEqual[t$95$2, 6e+58], N[(N[(a * b), $MachinePrecision] * 27.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.99999999999999998e204 or 6.0000000000000005e58 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 83.6%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 85.4

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

   5. Applied rewrites 85.4%

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

   if -1.99999999999999998e204 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 6.0000000000000005e58

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 92.4

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

   5. Applied rewrites 92.4%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -2 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, x \cdot 2\right)\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 6 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(y \cdot -9\right) \cdot \left(t \cdot z\right)\\ t_2 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* y -9.0) (* t z))) (t_2 (* (* (* 9.0 y) z) t)))
   (if (<= t_2 -2e+204)
     t_1
     (if (<= t_2 5e+181) (fma (* a b) 27.0 (* 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 = (y * -9.0) * (t * z);
	double t_2 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_2 <= -2e+204) {
		tmp = t_1;
	} else if (t_2 <= 5e+181) {
		tmp = fma((a * b), 27.0, (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(Float64(y * -9.0) * Float64(t * z))
	t_2 = Float64(Float64(Float64(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_2 <= -2e+204)
		tmp = t_1;
	elseif (t_2 <= 5e+181)
		tmp = fma(Float64(a * b), 27.0, Float64(x * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * -9.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+204], t$95$1, If[LessEqual[t$95$2, 5e+181], N[(N[(a * b), $MachinePrecision] * 27.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.99999999999999998e204 or 5.0000000000000003e181 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 80.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 2.7

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

   5. Applied rewrites 2.7%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 79.8

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

   8. Applied rewrites 79.8%

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

   10. Applied rewrites 89.6%

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

   if -1.99999999999999998e204 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5.0000000000000003e181

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 89.8

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

   5. Applied rewrites 89.8%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -2 \cdot 10^{+204}:\\ \;\;\;\;\left(y \cdot -9\right) \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot -9\right) \cdot \left(t \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(y \cdot -9\right) \cdot \left(t \cdot z\right)\\ t_2 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* y -9.0) (* t z))) (t_2 (* (* (* 9.0 y) z) t)))
   (if (<= t_2 -2e+204)
     t_1
     (if (<= t_2 5e+181) (fma (* 27.0 b) a (* x 2.0)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * -9.0) * (t * z);
	double t_2 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_2 <= -2e+204) {
		tmp = t_1;
	} else if (t_2 <= 5e+181) {
		tmp = fma((27.0 * b), a, (x * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * -9.0) * Float64(t * z))
	t_2 = Float64(Float64(Float64(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_2 <= -2e+204)
		tmp = t_1;
	elseif (t_2 <= 5e+181)
		tmp = fma(Float64(27.0 * b), a, Float64(x * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * -9.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+204], t$95$1, If[LessEqual[t$95$2, 5e+181], N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.99999999999999998e204 or 5.0000000000000003e181 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 80.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 2.7

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

   5. Applied rewrites 2.7%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 79.8

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

   8. Applied rewrites 79.8%

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

   10. Applied rewrites 89.6%

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

   if -1.99999999999999998e204 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5.0000000000000003e181

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 89.8

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

   5. Applied rewrites 89.8%

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

   7. Applied rewrites 89.8%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -2 \cdot 10^{+204}:\\ \;\;\;\;\left(y \cdot -9\right) \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot -9\right) \cdot \left(t \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+67}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;t\_1 \leq 10^{-24}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \end{array} \end{array} \]

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 (* (* a 27.0) b)))
   (if (<= t_1 -1e+67)
     (* (* a b) 27.0)
     (if (<= t_1 1e-24) (* x 2.0) (* (* 27.0 b) a)))))

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -1e+67) {
		tmp = (a * b) * 27.0;
	} else if (t_1 <= 1e-24) {
		tmp = x * 2.0;
	} else {
		tmp = (27.0 * b) * a;
	}
	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 = (a * 27.0d0) * b
    if (t_1 <= (-1d+67)) then
        tmp = (a * b) * 27.0d0
    else if (t_1 <= 1d-24) then
        tmp = x * 2.0d0
    else
        tmp = (27.0d0 * b) * a
    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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -1e+67) {
		tmp = (a * b) * 27.0;
	} else if (t_1 <= 1e-24) {
		tmp = x * 2.0;
	} else {
		tmp = (27.0 * b) * a;
	}
	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 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -1e+67:
		tmp = (a * b) * 27.0
	elif t_1 <= 1e-24:
		tmp = x * 2.0
	else:
		tmp = (27.0 * b) * a
	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(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -1e+67)
		tmp = Float64(Float64(a * b) * 27.0);
	elseif (t_1 <= 1e-24)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(Float64(27.0 * b) * a);
	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 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -1e+67)
		tmp = (a * b) * 27.0;
	elseif (t_1 <= 1e-24)
		tmp = x * 2.0;
	else
		tmp = (27.0 * b) * a;
	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[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+67], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], If[LessEqual[t$95$1, 1e-24], N[(x * 2.0), $MachinePrecision], N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -9.99999999999999983e66

   1. Initial program 92.9%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 75.0

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

   5. Applied rewrites 75.0%

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

   if -9.99999999999999983e66 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.99999999999999924e-25

   1. Initial program 94.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 48.9

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

   5. Applied rewrites 48.9%

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

   if 9.99999999999999924e-25 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 91.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 61.3

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

   5. Applied rewrites 61.3%

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

   7. Applied rewrites 61.3%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -1 \cdot 10^{+67}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 10^{-24}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -20000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-24}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \end{array} \end{array} \]

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 (* (* a 27.0) b)))
   (if (<= t_1 -20000000.0)
     t_1
     (if (<= t_1 1e-24) (* x 2.0) (* (* 27.0 b) a)))))

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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -20000000.0) {
		tmp = t_1;
	} else if (t_1 <= 1e-24) {
		tmp = x * 2.0;
	} else {
		tmp = (27.0 * b) * a;
	}
	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 = (a * 27.0d0) * b
    if (t_1 <= (-20000000.0d0)) then
        tmp = t_1
    else if (t_1 <= 1d-24) then
        tmp = x * 2.0d0
    else
        tmp = (27.0d0 * b) * a
    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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -20000000.0) {
		tmp = t_1;
	} else if (t_1 <= 1e-24) {
		tmp = x * 2.0;
	} else {
		tmp = (27.0 * b) * a;
	}
	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 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -20000000.0:
		tmp = t_1
	elif t_1 <= 1e-24:
		tmp = x * 2.0
	else:
		tmp = (27.0 * b) * a
	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(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -20000000.0)
		tmp = t_1;
	elseif (t_1 <= 1e-24)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(Float64(27.0 * b) * a);
	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 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -20000000.0)
		tmp = t_1;
	elseif (t_1 <= 1e-24)
		tmp = x * 2.0;
	else
		tmp = (27.0 * b) * a;
	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[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -20000000.0], t$95$1, If[LessEqual[t$95$1, 1e-24], N[(x * 2.0), $MachinePrecision], N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2e7

   1. Initial program 92.7%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 69.5

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

   5. Applied rewrites 69.5%

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

   7. Applied rewrites 69.4%

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

   if -2e7 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.99999999999999924e-25

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 49.5

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

   5. Applied rewrites 49.5%

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

   if 9.99999999999999924e-25 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 91.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 61.3

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

   5. Applied rewrites 61.3%

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

   7. Applied rewrites 61.3%

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

Alternative 17: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := \left(27 \cdot b\right) \cdot a\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-24}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* (* a 27.0) b)) (t_2 (* (* 27.0 b) a)))
   (if (<= t_1 -1e+67) t_2 (if (<= t_1 1e-24) (* 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 = (a * 27.0) * b;
	double t_2 = (27.0 * b) * a;
	double tmp;
	if (t_1 <= -1e+67) {
		tmp = t_2;
	} else if (t_1 <= 1e-24) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    t_2 = (27.0d0 * b) * a
    if (t_1 <= (-1d+67)) then
        tmp = t_2
    else if (t_1 <= 1d-24) then
        tmp = x * 2.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = (27.0 * b) * a;
	double tmp;
	if (t_1 <= -1e+67) {
		tmp = t_2;
	} else if (t_1 <= 1e-24) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	t_2 = (27.0 * b) * a
	tmp = 0
	if t_1 <= -1e+67:
		tmp = t_2
	elif t_1 <= 1e-24:
		tmp = x * 2.0
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	t_2 = Float64(Float64(27.0 * b) * a)
	tmp = 0.0
	if (t_1 <= -1e+67)
		tmp = t_2;
	elseif (t_1 <= 1e-24)
		tmp = Float64(x * 2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	t_2 = (27.0 * b) * a;
	tmp = 0.0;
	if (t_1 <= -1e+67)
		tmp = t_2;
	elseif (t_1 <= 1e-24)
		tmp = x * 2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+67], t$95$2, If[LessEqual[t$95$1, 1e-24], N[(x * 2.0), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -9.99999999999999983e66 or 9.99999999999999924e-25 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 92.1%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 67.5

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

   5. Applied rewrites 67.5%

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

   7. Applied rewrites 67.5%

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

   if -9.99999999999999983e66 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.99999999999999924e-25

   1. Initial program 94.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 48.9

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

   5. Applied rewrites 48.9%

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

Alternative 18: 97.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, y \cdot -9, \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 3.8e+61)
   (fma (* t z) (* y -9.0) (fma (* 27.0 b) a (* x 2.0)))
   (fma (* (* y -9.0) t) z (* 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 <= 3.8e+61) {
		tmp = fma((t * z), (y * -9.0), fma((27.0 * b), a, (x * 2.0)));
	} else {
		tmp = fma(((y * -9.0) * t), z, (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 <= 3.8e+61)
		tmp = fma(Float64(t * z), Float64(y * -9.0), fma(Float64(27.0 * b), a, Float64(x * 2.0)));
	else
		tmp = fma(Float64(Float64(y * -9.0) * t), z, Float64(x * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 3.8e+61], N[(N[(t * z), $MachinePrecision] * N[(y * -9.0), $MachinePrecision] + N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * -9.0), $MachinePrecision] * t), $MachinePrecision] * z + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.79999999999999995e61

   1. Initial program 94.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 93.9%

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

   if 3.79999999999999995e61 < z

   1. Initial program 90.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

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

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 96.5%

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

   5. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 83.4

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

   7. Applied rewrites 83.4%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, y \cdot -9, \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 97.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-9 \cdot z\right) \cdot t, \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 3.8e+61)
   (fma y (* (* -9.0 z) t) (fma (* 27.0 b) a (* x 2.0)))
   (fma (* (* y -9.0) t) z (* 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 <= 3.8e+61) {
		tmp = fma(y, ((-9.0 * z) * t), fma((27.0 * b), a, (x * 2.0)));
	} else {
		tmp = fma(((y * -9.0) * t), z, (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 <= 3.8e+61)
		tmp = fma(y, Float64(Float64(-9.0 * z) * t), fma(Float64(27.0 * b), a, Float64(x * 2.0)));
	else
		tmp = fma(Float64(Float64(y * -9.0) * t), z, Float64(x * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 3.8e+61], N[(y * N[(N[(-9.0 * z), $MachinePrecision] * t), $MachinePrecision] + N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * -9.0), $MachinePrecision] * t), $MachinePrecision] * z + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.79999999999999995e61

   1. Initial program 94.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

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

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

      12. associate-*l* N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

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

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

      17. lower-*.f64 N/A

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

      18. metadata-eval N/A

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

   4. Applied rewrites 94.4%

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

   if 3.79999999999999995e61 < z

   1. Initial program 90.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

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

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 96.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)} \]

   5. Taylor expanded in b around 0

      \[\leadsto \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, \color{blue}{2 \cdot x}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, \color{blue}{x \cdot 2}\right) \]

      2. lower-*.f64 83.4

         \[\leadsto \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, \color{blue}{x \cdot 2}\right) \]

   7. Applied rewrites 83.4%

      \[\leadsto \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, \color{blue}{x \cdot 2}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-9 \cdot z\right) \cdot t, \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 30.7% accurate, 6.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ x \cdot 2 \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* x 2.0))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * 2.0d0
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return x * 2.0

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(x * 2.0)
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = x * 2.0;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(x * 2.0), $MachinePrecision]

Derivation

1. Initial program 93.4%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{2 \cdot x} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{x \cdot 2} \]

   2. lower-*.f64 29.0

      \[\leadsto \color{blue}{x \cdot 2} \]

5. Applied rewrites 29.0%

   \[\leadsto \color{blue}{x \cdot 2} \]
6. Add Preprocessing

Developer Target 1: 95.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (< y 7.590524218811189e-161)
   (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y < 7.590524218811189d-161) then
        tmp = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + (a * (27.0d0 * b))
    else
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (t * z)))) + ((a * 27.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y < 7.590524218811189e-161:
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b))
	else:
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y < 7.590524218811189e-161)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(t * z)))) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y < 7.590524218811189e-161)
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	else
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Less[y, 7.590524218811189e-161], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024240 
(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)))