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

Percentage Accurate: 95.3% → 98.5%

Time: 15.2s

Alternatives: 13

Speedup: 0.9×

• 27.6% 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: 95.3% 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

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3.9 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot a, b, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 3.9e+35)
   (fma (* 27.0 a) b (fma (* (* -9.0 y) t) z (* 2.0 x)))
   (fma (* -9.0 (* z y)) t (fma (* b 27.0) a (* 2.0 x)))))

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 (t <= 3.9e+35) {
		tmp = fma((27.0 * a), b, fma(((-9.0 * y) * t), z, (2.0 * x)));
	} else {
		tmp = fma((-9.0 * (z * y)), t, fma((b * 27.0), a, (2.0 * x)));
	}
	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 (t <= 3.9e+35)
		tmp = fma(Float64(27.0 * a), b, fma(Float64(Float64(-9.0 * y) * t), z, Float64(2.0 * x)));
	else
		tmp = fma(Float64(-9.0 * Float64(z * y)), t, fma(Float64(b * 27.0), a, Float64(2.0 * x)));
	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[t, 3.9e+35], N[(N[(27.0 * a), $MachinePrecision] * b + N[(N[(N[(-9.0 * y), $MachinePrecision] * t), $MachinePrecision] * z + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] * t + N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.8999999999999999e35

   1. Initial program 91.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 91.8

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 91.8

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

   4. Applied rewrites 97.2%

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

   if 3.8999999999999999e35 < t

   1. Initial program 98.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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. 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. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval N/A

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

      18. lower-*.f64 N/A

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

   4. Applied rewrites 98.4%

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

Alternative 2: 60.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(\left(-9 \cdot z\right) \cdot t\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+145}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+95}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{elif}\;t\_1 \leq 10^{+305}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \end{array} \end{array} \]

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) (* (* (* y 9.0) z) t))))
   (if (<= t_1 (- INFINITY))
     (* (* (* -9.0 z) t) y)
     (if (<= t_1 -5e+145)
       (* 2.0 x)
       (if (<= t_1 2e+95)
         (* (* 27.0 b) a)
         (if (<= t_1 1e+305) (* 2.0 x) (* (* (* t z) -9.0) y)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((-9.0 * z) * t) * y;
	} else if (t_1 <= -5e+145) {
		tmp = 2.0 * x;
	} else if (t_1 <= 2e+95) {
		tmp = (27.0 * b) * a;
	} else if (t_1 <= 1e+305) {
		tmp = 2.0 * x;
	} else {
		tmp = ((t * z) * -9.0) * y;
	}
	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) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((-9.0 * z) * t) * y;
	} else if (t_1 <= -5e+145) {
		tmp = 2.0 * x;
	} else if (t_1 <= 2e+95) {
		tmp = (27.0 * b) * a;
	} else if (t_1 <= 1e+305) {
		tmp = 2.0 * x;
	} else {
		tmp = ((t * z) * -9.0) * y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (((y * 9.0) * z) * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((-9.0 * z) * t) * y
	elif t_1 <= -5e+145:
		tmp = 2.0 * x
	elif t_1 <= 2e+95:
		tmp = (27.0 * b) * a
	elif t_1 <= 1e+305:
		tmp = 2.0 * x
	else:
		tmp = ((t * z) * -9.0) * y
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(-9.0 * z) * t) * y);
	elseif (t_1 <= -5e+145)
		tmp = Float64(2.0 * x);
	elseif (t_1 <= 2e+95)
		tmp = Float64(Float64(27.0 * b) * a);
	elseif (t_1 <= 1e+305)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(Float64(Float64(t * z) * -9.0) * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (((y * 9.0) * z) * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((-9.0 * z) * t) * y;
	elseif (t_1 <= -5e+145)
		tmp = 2.0 * x;
	elseif (t_1 <= 2e+95)
		tmp = (27.0 * b) * a;
	elseif (t_1 <= 1e+305)
		tmp = 2.0 * x;
	else
		tmp = ((t * z) * -9.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(-9.0 * z), $MachinePrecision] * t), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, -5e+145], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$1, 2e+95], N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t$95$1, 1e+305], N[(2.0 * x), $MachinePrecision], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y), $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 80.1%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 8.3

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

   5. Applied rewrites 8.3%

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

   6. Taylor expanded in y around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 94.7%

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

   9. Taylor expanded in y around inf

      \[\leadsto \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 95.0%

       \[\leadsto \left(\left(t \cdot z\right) \cdot -9\right) \cdot y \]
   12. Step-by-step derivation

   13. Applied rewrites 95.0%

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

   if -inf.0 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.99999999999999967e145 or 2.00000000000000004e95 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 9.9999999999999994e304

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 47.0

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

   5. Applied rewrites 47.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 47.0

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

   7. Applied rewrites 38.2%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 53.5

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

   10. Applied rewrites 53.5%

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

   if -4.99999999999999967e145 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 2.00000000000000004e95

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 92.1

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

   5. Applied rewrites 92.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 74.1%

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

   10. Applied rewrites 74.2%

       \[\leadsto \left(27 \cdot b\right) \cdot a \]

   if 9.9999999999999994e304 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 69.1%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 19.6

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

   5. Applied rewrites 19.6%

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

   6. Taylor expanded in y around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 97.4%

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

   9. Taylor expanded in y around inf

      \[\leadsto \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 84.0%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -\infty:\\ \;\;\;\;\left(\left(-9 \cdot z\right) \cdot t\right) \cdot y\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+145}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 2 \cdot 10^{+95}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 10^{+305}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(\left(-9 \cdot z\right) \cdot t\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+145}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+95}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{elif}\;t\_1 \leq 10^{+305}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ \end{array} \end{array} \]

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) (* (* (* y 9.0) z) t))))
   (if (<= t_1 (- INFINITY))
     (* (* (* -9.0 z) t) y)
     (if (<= t_1 -5e+145)
       (* 2.0 x)
       (if (<= t_1 2e+95)
         (* (* 27.0 b) a)
         (if (<= t_1 1e+305) (* 2.0 x) (* (* (* -9.0 t) z) y)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((-9.0 * z) * t) * y;
	} else if (t_1 <= -5e+145) {
		tmp = 2.0 * x;
	} else if (t_1 <= 2e+95) {
		tmp = (27.0 * b) * a;
	} else if (t_1 <= 1e+305) {
		tmp = 2.0 * x;
	} else {
		tmp = ((-9.0 * t) * z) * y;
	}
	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) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((-9.0 * z) * t) * y;
	} else if (t_1 <= -5e+145) {
		tmp = 2.0 * x;
	} else if (t_1 <= 2e+95) {
		tmp = (27.0 * b) * a;
	} else if (t_1 <= 1e+305) {
		tmp = 2.0 * x;
	} else {
		tmp = ((-9.0 * t) * z) * y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (((y * 9.0) * z) * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((-9.0 * z) * t) * y
	elif t_1 <= -5e+145:
		tmp = 2.0 * x
	elif t_1 <= 2e+95:
		tmp = (27.0 * b) * a
	elif t_1 <= 1e+305:
		tmp = 2.0 * x
	else:
		tmp = ((-9.0 * t) * z) * y
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(-9.0 * z) * t) * y);
	elseif (t_1 <= -5e+145)
		tmp = Float64(2.0 * x);
	elseif (t_1 <= 2e+95)
		tmp = Float64(Float64(27.0 * b) * a);
	elseif (t_1 <= 1e+305)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(Float64(Float64(-9.0 * t) * z) * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (((y * 9.0) * z) * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((-9.0 * z) * t) * y;
	elseif (t_1 <= -5e+145)
		tmp = 2.0 * x;
	elseif (t_1 <= 2e+95)
		tmp = (27.0 * b) * a;
	elseif (t_1 <= 1e+305)
		tmp = 2.0 * x;
	else
		tmp = ((-9.0 * t) * z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(-9.0 * z), $MachinePrecision] * t), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, -5e+145], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$1, 2e+95], N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t$95$1, 1e+305], N[(2.0 * x), $MachinePrecision], N[(N[(N[(-9.0 * t), $MachinePrecision] * z), $MachinePrecision] * y), $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 80.1%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 8.3

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

   5. Applied rewrites 8.3%

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

   6. Taylor expanded in y around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 94.7%

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

   9. Taylor expanded in y around inf

      \[\leadsto \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 95.0%

       \[\leadsto \left(\left(t \cdot z\right) \cdot -9\right) \cdot y \]
   12. Step-by-step derivation

   13. Applied rewrites 95.0%

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

   if -inf.0 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.99999999999999967e145 or 2.00000000000000004e95 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 9.9999999999999994e304

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 47.0

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

   5. Applied rewrites 47.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 47.0

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

   7. Applied rewrites 38.2%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 53.5

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

   10. Applied rewrites 53.5%

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

   if -4.99999999999999967e145 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 2.00000000000000004e95

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 92.1

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

   5. Applied rewrites 92.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 74.1%

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

   10. Applied rewrites 74.2%

       \[\leadsto \left(27 \cdot b\right) \cdot a \]

   if 9.9999999999999994e304 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 69.1%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 19.6

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

   5. Applied rewrites 19.6%

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

   6. Taylor expanded in y around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 97.4%

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

   9. Taylor expanded in y around inf

      \[\leadsto \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 84.0%

       \[\leadsto \left(\left(t \cdot z\right) \cdot -9\right) \cdot y \]
   12. Step-by-step derivation

   13. Applied rewrites 84.0%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -\infty:\\ \;\;\;\;\left(\left(-9 \cdot z\right) \cdot t\right) \cdot y\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+145}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 2 \cdot 10^{+95}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 10^{+305}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ t_2 := x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+145}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+95}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{elif}\;t\_2 \leq 10^{+305}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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) (* (* (* y 9.0) z) t))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e+145)
       (* 2.0 x)
       (if (<= t_2 2e+95)
         (* (* 27.0 b) a)
         (if (<= t_2 1e+305) (* 2.0 x) 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) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e+145) {
		tmp = 2.0 * x;
	} else if (t_2 <= 2e+95) {
		tmp = (27.0 * b) * a;
	} else if (t_2 <= 1e+305) {
		tmp = 2.0 * x;
	} 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) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e+145) {
		tmp = 2.0 * x;
	} else if (t_2 <= 2e+95) {
		tmp = (27.0 * b) * a;
	} else if (t_2 <= 1e+305) {
		tmp = 2.0 * x;
	} 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) - (((y * 9.0) * z) * t)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e+145:
		tmp = 2.0 * x
	elif t_2 <= 2e+95:
		tmp = (27.0 * b) * a
	elif t_2 <= 1e+305:
		tmp = 2.0 * x
	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(-9.0 * t) * z) * y)
	t_2 = Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e+145)
		tmp = Float64(2.0 * x);
	elseif (t_2 <= 2e+95)
		tmp = Float64(Float64(27.0 * b) * a);
	elseif (t_2 <= 1e+305)
		tmp = Float64(2.0 * x);
	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) - (((y * 9.0) * z) * t);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e+145)
		tmp = 2.0 * x;
	elseif (t_2 <= 2e+95)
		tmp = (27.0 * b) * a;
	elseif (t_2 <= 1e+305)
		tmp = 2.0 * x;
	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[(-9.0 * t), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e+145], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$2, 2e+95], N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t$95$2, 1e+305], N[(2.0 * x), $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 9.9999999999999994e304 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 72.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 16.0

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

   5. Applied rewrites 16.0%

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

   6. Taylor expanded in y around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 96.6%

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

   9. Taylor expanded in y around inf

      \[\leadsto \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 87.6%

       \[\leadsto \left(\left(t \cdot z\right) \cdot -9\right) \cdot y \]
   12. Step-by-step derivation

   13. Applied rewrites 87.5%

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

   if -inf.0 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.99999999999999967e145 or 2.00000000000000004e95 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 9.9999999999999994e304

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 47.0

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

   5. Applied rewrites 47.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 47.0

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

   7. Applied rewrites 38.2%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 53.5

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

   10. Applied rewrites 53.5%

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

   if -4.99999999999999967e145 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 2.00000000000000004e95

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 92.1

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

   5. Applied rewrites 92.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 74.1%

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

   10. Applied rewrites 74.2%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -\infty:\\ \;\;\;\;\left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+145}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 2 \cdot 10^{+95}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 10^{+305}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+104} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+120}\right):\\ \;\;\;\;\mathsf{fma}\left(27 \cdot a, b, \left(\left(y \cdot -9\right) \cdot z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, x \cdot 2\right)\\ \end{array} \end{array} \]

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 (* (* (* y 9.0) z) t)))
   (if (<= t_1 (- INFINITY))
     (* (* (* t z) -9.0) y)
     (if (or (<= t_1 -5e+104) (not (<= t_1 5e+120)))
       (fma (* 27.0 a) b (* (* (* y -9.0) z) t))
       (fma (* b 27.0) a (* 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 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((t * z) * -9.0) * y;
	} else if ((t_1 <= -5e+104) || !(t_1 <= 5e+120)) {
		tmp = fma((27.0 * a), b, (((y * -9.0) * z) * t));
	} else {
		tmp = fma((b * 27.0), a, (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(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(t * z) * -9.0) * y);
	elseif ((t_1 <= -5e+104) || !(t_1 <= 5e+120))
		tmp = fma(Float64(27.0 * a), b, Float64(Float64(Float64(y * -9.0) * z) * t));
	else
		tmp = fma(Float64(b * 27.0), a, 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[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision], If[Or[LessEqual[t$95$1, -5e+104], N[Not[LessEqual[t$95$1, 5e+120]], $MachinePrecision]], N[(N[(27.0 * a), $MachinePrecision] * b + N[(N[(N[(y * -9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(b * 27.0), $MachinePrecision] * a + 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) < -inf.0

   1. Initial program 69.1%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 19.6

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

   5. Applied rewrites 19.6%

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

   6. Taylor expanded in y around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 97.4%

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

   9. Taylor expanded in y around inf

      \[\leadsto \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 84.0%

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

   if -inf.0 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.9999999999999997e104 or 5.00000000000000019e120 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 93.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 94.9

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 94.9

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

   4. Applied rewrites 85.4%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 85.5

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

   7. Applied rewrites 85.5%

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

   9. Applied rewrites 85.4%

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

   if -4.9999999999999997e104 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5.00000000000000019e120

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 94.9

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

   5. Applied rewrites 94.9%

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

   7. Applied rewrites 94.9%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -\infty:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \mathbf{elif}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+104} \lor \neg \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+120}\right):\\ \;\;\;\;\mathsf{fma}\left(27 \cdot a, b, \left(\left(y \cdot -9\right) \cdot z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ t_2 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot y\right) \cdot t, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+148}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* (* t z) -9.0) y)) (t_2 (* (* (* y 9.0) z) t)))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e+104)
       (fma -9.0 (* (* z y) t) (* (* b a) 27.0))
       (if (<= t_2 1e+148) (fma (* b 27.0) 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 = ((t * z) * -9.0) * y;
	double t_2 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e+104) {
		tmp = fma(-9.0, ((z * y) * t), ((b * a) * 27.0));
	} else if (t_2 <= 1e+148) {
		tmp = fma((b * 27.0), 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(Float64(t * z) * -9.0) * y)
	t_2 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e+104)
		tmp = fma(-9.0, Float64(Float64(z * y) * t), Float64(Float64(b * a) * 27.0));
	elseif (t_2 <= 1e+148)
		tmp = fma(Float64(b * 27.0), 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[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e+104], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] + N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+148], N[(N[(b * 27.0), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -inf.0 or 1e148 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 77.5%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 16.4

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

   5. Applied rewrites 16.4%

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

   6. Taylor expanded in y around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 93.0%

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

   9. Taylor expanded in y around inf

      \[\leadsto \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 82.8%

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

   if -inf.0 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.9999999999999997e104

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 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. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 84.3

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

   5. Applied rewrites 84.3%

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

   if -4.9999999999999997e104 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1e148

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 94.4

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

   5. Applied rewrites 94.4%

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

   7. Applied rewrites 94.4%

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

Alternative 7: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+168} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+120}\right):\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, \left(\left(-9 \cdot t\right) \cdot y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(b \cdot a\right) \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (or (<= t_1 -5e+168) (not (<= t_1 5e+120)))
     (fma (* b 27.0) a (* (* (* -9.0 t) y) z))
     (fma 2.0 x (* (* b a) 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if ((t_1 <= -5e+168) || !(t_1 <= 5e+120)) {
		tmp = fma((b * 27.0), a, (((-9.0 * t) * y) * z));
	} else {
		tmp = fma(2.0, x, ((b * a) * 27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if ((t_1 <= -5e+168) || !(t_1 <= 5e+120))
		tmp = fma(Float64(b * 27.0), a, Float64(Float64(Float64(-9.0 * t) * y) * z));
	else
		tmp = fma(2.0, x, Float64(Float64(b * a) * 27.0));
	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[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+168], N[Not[LessEqual[t$95$1, 5e+120]], $MachinePrecision]], N[(N[(b * 27.0), $MachinePrecision] * a + N[(N[(N[(-9.0 * t), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(2.0 * x + N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999967e168 or 5.00000000000000019e120 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 81.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 79.7

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

   5. Applied rewrites 79.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 81.9

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

   7. Applied rewrites 83.3%

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

   9. Applied rewrites 83.3%

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

   if -4.99999999999999967e168 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5.00000000000000019e120

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 92.3

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

   5. Applied rewrites 92.3%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+168} \lor \neg \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+120}\right):\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, \left(\left(-9 \cdot t\right) \cdot y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(b \cdot a\right) \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+168}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, \left(\left(t \cdot y\right) \cdot -9\right) \cdot z\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, \left(\left(-9 \cdot t\right) \cdot y\right) \cdot z\right)\\ \end{array} \end{array} \]

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 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -5e+168)
     (fma (* b 27.0) a (* (* (* t y) -9.0) z))
     (if (<= t_1 5e+120)
       (fma 2.0 x (* (* b a) 27.0))
       (fma (* b 27.0) a (* (* (* -9.0 t) y) 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 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -5e+168) {
		tmp = fma((b * 27.0), a, (((t * y) * -9.0) * z));
	} else if (t_1 <= 5e+120) {
		tmp = fma(2.0, x, ((b * a) * 27.0));
	} else {
		tmp = fma((b * 27.0), a, (((-9.0 * t) * y) * 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(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -5e+168)
		tmp = fma(Float64(b * 27.0), a, Float64(Float64(Float64(t * y) * -9.0) * z));
	elseif (t_1 <= 5e+120)
		tmp = fma(2.0, x, Float64(Float64(b * a) * 27.0));
	else
		tmp = fma(Float64(b * 27.0), a, Float64(Float64(Float64(-9.0 * t) * y) * z));
	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[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+168], N[(N[(b * 27.0), $MachinePrecision] * a + N[(N[(N[(t * y), $MachinePrecision] * -9.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+120], N[(2.0 * x + N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], N[(N[(b * 27.0), $MachinePrecision] * a + N[(N[(N[(-9.0 * t), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999967e168

   1. Initial program 77.3%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 77.3

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

   5. Applied rewrites 77.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 79.1

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

   7. Applied rewrites 81.4%

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

   if -4.99999999999999967e168 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5.00000000000000019e120

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 92.3

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

   5. Applied rewrites 92.3%

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

   if 5.00000000000000019e120 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 83.5

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

   5. Applied rewrites 83.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 86.5

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

   7. Applied rewrites 86.4%

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

   9. Applied rewrites 86.4%

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

Alternative 9: 81.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+148}\right):\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(b \cdot a\right) \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+148)))
     (* (* (* t z) -9.0) y)
     (fma 2.0 x (* (* b a) 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+148)) {
		tmp = ((t * z) * -9.0) * y;
	} else {
		tmp = fma(2.0, x, ((b * a) * 27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+148))
		tmp = Float64(Float64(Float64(t * z) * -9.0) * y);
	else
		tmp = fma(2.0, x, Float64(Float64(b * a) * 27.0));
	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[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+148]], $MachinePrecision]], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision], N[(2.0 * x + N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -inf.0 or 1e148 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 77.5%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 16.4

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

   5. Applied rewrites 16.4%

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

   6. Taylor expanded in y around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 93.0%

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

   9. Taylor expanded in y around inf

      \[\leadsto \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 82.8%

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

   if -inf.0 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1e148

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 88.1

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

   5. Applied rewrites 88.1%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -\infty \lor \neg \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 10^{+148}\right):\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(b \cdot a\right) \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, \left(\left(-9 \cdot t\right) \cdot y\right) \cdot z\right)\\ \end{array} \end{array} \]

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
 (if (<= (* (* y 9.0) z) 5e+299)
   (fma (* -9.0 (* z y)) t (fma (* b 27.0) a (* 2.0 x)))
   (fma (* b 27.0) a (* (* (* -9.0 t) y) 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 tmp;
	if (((y * 9.0) * z) <= 5e+299) {
		tmp = fma((-9.0 * (z * y)), t, fma((b * 27.0), a, (2.0 * x)));
	} else {
		tmp = fma((b * 27.0), a, (((-9.0 * t) * y) * 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)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 5e+299)
		tmp = fma(Float64(-9.0 * Float64(z * y)), t, fma(Float64(b * 27.0), a, Float64(2.0 * x)));
	else
		tmp = fma(Float64(b * 27.0), a, Float64(Float64(Float64(-9.0 * t) * y) * z));
	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[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 5e+299], N[(N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] * t + N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * 27.0), $MachinePrecision] * a + N[(N[(N[(-9.0 * t), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 5.0000000000000003e299

   1. Initial program 96.5%

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

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

      9. lower-fma.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval N/A

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

      18. lower-*.f64 N/A

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

   4. Applied rewrites 96.6%

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

   if 5.0000000000000003e299 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 47.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 52.8

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

   5. Applied rewrites 52.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 52.8

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

   7. Applied rewrites 85.5%

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

   9. Applied rewrites 85.6%

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

Alternative 11: 52.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+14} \lor \neg \left(t\_1 \leq 10^{+98}\right):\\ \;\;\;\;\left(27 \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \end{array} \]

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 (or (<= t_1 -5e+14) (not (<= t_1 1e+98))) (* (* 27.0 a) b) (* 2.0 x))))

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 <= -5e+14) || !(t_1 <= 1e+98)) {
		tmp = (27.0 * a) * b;
	} else {
		tmp = 2.0 * x;
	}
	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 <= (-5d+14)) .or. (.not. (t_1 <= 1d+98))) then
        tmp = (27.0d0 * a) * b
    else
        tmp = 2.0d0 * x
    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 <= -5e+14) || !(t_1 <= 1e+98)) {
		tmp = (27.0 * a) * b;
	} else {
		tmp = 2.0 * x;
	}
	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 <= -5e+14) or not (t_1 <= 1e+98):
		tmp = (27.0 * a) * b
	else:
		tmp = 2.0 * x
	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 <= -5e+14) || !(t_1 <= 1e+98))
		tmp = Float64(Float64(27.0 * a) * b);
	else
		tmp = Float64(2.0 * x);
	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 <= -5e+14) || ~((t_1 <= 1e+98)))
		tmp = (27.0 * a) * b;
	else
		tmp = 2.0 * x;
	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[Or[LessEqual[t$95$1, -5e+14], N[Not[LessEqual[t$95$1, 1e+98]], $MachinePrecision]], N[(N[(27.0 * a), $MachinePrecision] * b), $MachinePrecision], N[(2.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -5e14 or 9.99999999999999998e97 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 91.1%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 76.9

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

   5. Applied rewrites 76.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 64.2%

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

   10. Applied rewrites 64.1%

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

   if -5e14 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.99999999999999998e97

   1. Initial program 95.3%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 52.2

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

   5. Applied rewrites 52.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 52.3

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

   7. Applied rewrites 51.1%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 47.3

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

   10. Applied rewrites 47.3%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -5 \cdot 10^{+14} \lor \neg \left(\left(a \cdot 27\right) \cdot b \leq 10^{+98}\right):\\ \;\;\;\;\left(27 \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+14}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{elif}\;t\_1 \leq 10^{+98}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(27 \cdot a\right) \cdot b\\ \end{array} \end{array} \]

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 -5e+14)
     (* (* 27.0 b) a)
     (if (<= t_1 1e+98) (* 2.0 x) (* (* 27.0 a) b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -5e+14) {
		tmp = (27.0 * b) * a;
	} else if (t_1 <= 1e+98) {
		tmp = 2.0 * x;
	} else {
		tmp = (27.0 * a) * b;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    if (t_1 <= (-5d+14)) then
        tmp = (27.0d0 * b) * a
    else if (t_1 <= 1d+98) then
        tmp = 2.0d0 * x
    else
        tmp = (27.0d0 * a) * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -5e+14) {
		tmp = (27.0 * b) * a;
	} else if (t_1 <= 1e+98) {
		tmp = 2.0 * x;
	} else {
		tmp = (27.0 * a) * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -5e+14:
		tmp = (27.0 * b) * a
	elif t_1 <= 1e+98:
		tmp = 2.0 * x
	else:
		tmp = (27.0 * a) * b
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -5e+14)
		tmp = Float64(Float64(27.0 * b) * a);
	elseif (t_1 <= 1e+98)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(Float64(27.0 * a) * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -5e+14)
		tmp = (27.0 * b) * a;
	elseif (t_1 <= 1e+98)
		tmp = 2.0 * x;
	else
		tmp = (27.0 * a) * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+14], N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t$95$1, 1e+98], N[(2.0 * x), $MachinePrecision], N[(N[(27.0 * a), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -5e14

   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 y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 78.1

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

   5. Applied rewrites 78.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 65.0%

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

   10. Applied rewrites 65.0%

       \[\leadsto \left(27 \cdot b\right) \cdot a \]

   if -5e14 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.99999999999999998e97

   1. Initial program 95.3%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 52.2

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

   5. Applied rewrites 52.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 52.3

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

   7. Applied rewrites 51.1%

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

   8. Taylor expanded in x around inf

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

      1. lower-*.f64 47.3

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

   10. Applied rewrites 47.3%

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

   if 9.99999999999999998e97 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 74.8

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 62.8%

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

   10. Applied rewrites 62.9%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -5 \cdot 10^{+14}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 10^{+98}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(27 \cdot a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 31.2% accurate, 6.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ 2 \cdot x \end{array} \]

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 (* 2.0 x))

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 2.0 * x;
}

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 = 2.0d0 * x
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 2.0 * x;
}

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 2.0 * x

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(2.0 * x)
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 = 2.0 * x;
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[(2.0 * x), $MachinePrecision]

Derivation

1. Initial program 93.1%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 66.3

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

5. Applied rewrites 66.3%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. *-commutative N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-fma.f64 67.2

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

7. Applied rewrites 67.1%

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

8. Taylor expanded in x around inf

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

   1. lower-*.f64 30.2

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

10. Applied rewrites 30.2%

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

11. Final simplification 30.2%

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

Developer Target 1: 94.8% 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 2024317 
(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)))