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

Percentage Accurate: 95.4% → 98.4%

Time: 7.2s

Alternatives: 18

Speedup: 0.9×

• 26.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.4% 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: 98.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(9 \cdot y\right)\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+225}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right) + \left(2 \cdot x - t \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, -9 \cdot y, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* z (* 9.0 y))))
   (if (<= t_1 5e+225)
     (+ (* b (* 27.0 a)) (- (* 2.0 x) (* t t_1)))
     (fma (* t z) (* -9.0 y) (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 t_1 = z * (9.0 * y);
	double tmp;
	if (t_1 <= 5e+225) {
		tmp = (b * (27.0 * a)) + ((2.0 * x) - (t * t_1));
	} else {
		tmp = fma((t * z), (-9.0 * y), 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)
	t_1 = Float64(z * Float64(9.0 * y))
	tmp = 0.0
	if (t_1 <= 5e+225)
		tmp = Float64(Float64(b * Float64(27.0 * a)) + Float64(Float64(2.0 * x) - Float64(t * t_1)));
	else
		tmp = fma(Float64(t * z), Float64(-9.0 * y), 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_] := Block[{t$95$1 = N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+225], N[(N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision] + N[(N[(2.0 * x), $MachinePrecision] - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision] + N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 4.99999999999999981e225

   1. Initial program 96.4%

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

   if 4.99999999999999981e225 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 76.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 99.8%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(9 \cdot y\right) \leq 5 \cdot 10^{+225}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right) + \left(2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, -9 \cdot y, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 58.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ t_2 := \left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{+141}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 3 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* 2.0 x) (* t (* z (* 9.0 y))))) (t_2 (* (* (* -9.0 t) z) y)))
   (if (<= t_1 (- INFINITY))
     (* (* -9.0 z) (* t y))
     (if (<= t_1 -4e+141)
       (* 2.0 x)
       (if (<= t_1 -4e-8)
         t_2
         (if (<= t_1 3e+81)
           (* b (* 27.0 a))
           (if (<= t_1 5e+306) (* 2.0 x) t_2)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (2.0 * x) - (t * (z * (9.0 * y)));
	double t_2 = ((-9.0 * t) * z) * y;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (-9.0 * z) * (t * y);
	} else if (t_1 <= -4e+141) {
		tmp = 2.0 * x;
	} else if (t_1 <= -4e-8) {
		tmp = t_2;
	} else if (t_1 <= 3e+81) {
		tmp = b * (27.0 * a);
	} else if (t_1 <= 5e+306) {
		tmp = 2.0 * x;
	} else {
		tmp = t_2;
	}
	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 = (2.0 * x) - (t * (z * (9.0 * y)));
	double t_2 = ((-9.0 * t) * z) * y;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (-9.0 * z) * (t * y);
	} else if (t_1 <= -4e+141) {
		tmp = 2.0 * x;
	} else if (t_1 <= -4e-8) {
		tmp = t_2;
	} else if (t_1 <= 3e+81) {
		tmp = b * (27.0 * a);
	} else if (t_1 <= 5e+306) {
		tmp = 2.0 * x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (2.0 * x) - (t * (z * (9.0 * y)))
	t_2 = ((-9.0 * t) * z) * y
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (-9.0 * z) * (t * y)
	elif t_1 <= -4e+141:
		tmp = 2.0 * x
	elif t_1 <= -4e-8:
		tmp = t_2
	elif t_1 <= 3e+81:
		tmp = b * (27.0 * a)
	elif t_1 <= 5e+306:
		tmp = 2.0 * x
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(2.0 * x) - Float64(t * Float64(z * Float64(9.0 * y))))
	t_2 = Float64(Float64(Float64(-9.0 * t) * z) * y)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(-9.0 * z) * Float64(t * y));
	elseif (t_1 <= -4e+141)
		tmp = Float64(2.0 * x);
	elseif (t_1 <= -4e-8)
		tmp = t_2;
	elseif (t_1 <= 3e+81)
		tmp = Float64(b * Float64(27.0 * a));
	elseif (t_1 <= 5e+306)
		tmp = Float64(2.0 * x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (2.0 * x) - (t * (z * (9.0 * y)));
	t_2 = ((-9.0 * t) * z) * y;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (-9.0 * z) * (t * y);
	elseif (t_1 <= -4e+141)
		tmp = 2.0 * x;
	elseif (t_1 <= -4e-8)
		tmp = t_2;
	elseif (t_1 <= 3e+81)
		tmp = b * (27.0 * a);
	elseif (t_1 <= 5e+306)
		tmp = 2.0 * x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(2.0 * x), $MachinePrecision] - N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(-9.0 * t), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(-9.0 * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e+141], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$1, -4e-8], t$95$2, If[LessEqual[t$95$1, 3e+81], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+306], N[(2.0 * x), $MachinePrecision], t$95$2]]]]]]]

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 75.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 5.7

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

   5. Applied rewrites 5.7%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 79.0

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

   8. Applied rewrites 79.0%

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

   10. Applied rewrites 92.8%

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

   if -inf.0 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.00000000000000007e141 or 2.99999999999999997e81 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 4.99999999999999993e306

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.8

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

   5. Applied rewrites 59.8%

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

   if -4.00000000000000007e141 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.0000000000000001e-8 or 4.99999999999999993e306 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 90.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 14.2

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

   5. Applied rewrites 14.2%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 65.0

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

   8. Applied rewrites 65.0%

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

   10. Applied rewrites 68.2%

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

   if -4.0000000000000001e-8 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 2.99999999999999997e81

   1. Initial program 98.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 64.2

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

   5. Applied rewrites 64.2%

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

   7. Applied rewrites 64.3%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -\infty:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -4 \cdot 10^{+141}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -4 \cdot 10^{-8}:\\ \;\;\;\;\left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 3 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ t_2 := 2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+117}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-8}:\\ \;\;\;\;\left(-9 \cdot t\right) \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;t\_2 \leq 3 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 z) (* t y))) (t_2 (- (* 2.0 x) (* t (* z (* 9.0 y))))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e+117)
       (* 2.0 x)
       (if (<= t_2 -4e-8)
         (* (* -9.0 t) (* z y))
         (if (<= t_2 3e+81)
           (* b (* 27.0 a))
           (if (<= t_2 5e+306) (* 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 * z) * (t * y);
	double t_2 = (2.0 * x) - (t * (z * (9.0 * y)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e+117) {
		tmp = 2.0 * x;
	} else if (t_2 <= -4e-8) {
		tmp = (-9.0 * t) * (z * y);
	} else if (t_2 <= 3e+81) {
		tmp = b * (27.0 * a);
	} else if (t_2 <= 5e+306) {
		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 * z) * (t * y);
	double t_2 = (2.0 * x) - (t * (z * (9.0 * y)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e+117) {
		tmp = 2.0 * x;
	} else if (t_2 <= -4e-8) {
		tmp = (-9.0 * t) * (z * y);
	} else if (t_2 <= 3e+81) {
		tmp = b * (27.0 * a);
	} else if (t_2 <= 5e+306) {
		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 * z) * (t * y)
	t_2 = (2.0 * x) - (t * (z * (9.0 * y)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e+117:
		tmp = 2.0 * x
	elif t_2 <= -4e-8:
		tmp = (-9.0 * t) * (z * y)
	elif t_2 <= 3e+81:
		tmp = b * (27.0 * a)
	elif t_2 <= 5e+306:
		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(-9.0 * z) * Float64(t * y))
	t_2 = Float64(Float64(2.0 * x) - Float64(t * Float64(z * Float64(9.0 * y))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e+117)
		tmp = Float64(2.0 * x);
	elseif (t_2 <= -4e-8)
		tmp = Float64(Float64(-9.0 * t) * Float64(z * y));
	elseif (t_2 <= 3e+81)
		tmp = Float64(b * Float64(27.0 * a));
	elseif (t_2 <= 5e+306)
		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 * z) * (t * y);
	t_2 = (2.0 * x) - (t * (z * (9.0 * y)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e+117)
		tmp = 2.0 * x;
	elseif (t_2 <= -4e-8)
		tmp = (-9.0 * t) * (z * y);
	elseif (t_2 <= 3e+81)
		tmp = b * (27.0 * a);
	elseif (t_2 <= 5e+306)
		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[(-9.0 * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * x), $MachinePrecision] - N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e+117], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$2, -4e-8], N[(N[(-9.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 3e+81], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+306], N[(2.0 * x), $MachinePrecision], t$95$1]]]]]]]

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 or 4.99999999999999993e306 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 76.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 4.0

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

   5. Applied rewrites 4.0%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 78.5

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

   8. Applied rewrites 78.5%

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

   10. Applied rewrites 92.6%

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

   if -inf.0 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.99999999999999983e117 or 2.99999999999999997e81 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 4.99999999999999993e306

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.1

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

   5. Applied rewrites 59.1%

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

   if -4.99999999999999983e117 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.0000000000000001e-8

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 22.8

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

   5. Applied rewrites 22.8%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 53.2

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

   8. Applied rewrites 53.2%

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

   10. Applied rewrites 53.2%

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

   if -4.0000000000000001e-8 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 2.99999999999999997e81

   1. Initial program 98.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 64.2

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

   5. Applied rewrites 64.2%

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

   7. Applied rewrites 64.3%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -\infty:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -5 \cdot 10^{+117}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -4 \cdot 10^{-8}:\\ \;\;\;\;\left(-9 \cdot t\right) \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 3 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ t_2 := 2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+117}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-8}:\\ \;\;\;\;\left(\left(z \cdot y\right) \cdot t\right) \cdot -9\\ \mathbf{elif}\;t\_2 \leq 3 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 z) (* t y))) (t_2 (- (* 2.0 x) (* t (* z (* 9.0 y))))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e+117)
       (* 2.0 x)
       (if (<= t_2 -4e-8)
         (* (* (* z y) t) -9.0)
         (if (<= t_2 3e+81)
           (* b (* 27.0 a))
           (if (<= t_2 5e+306) (* 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 * z) * (t * y);
	double t_2 = (2.0 * x) - (t * (z * (9.0 * y)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e+117) {
		tmp = 2.0 * x;
	} else if (t_2 <= -4e-8) {
		tmp = ((z * y) * t) * -9.0;
	} else if (t_2 <= 3e+81) {
		tmp = b * (27.0 * a);
	} else if (t_2 <= 5e+306) {
		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 * z) * (t * y);
	double t_2 = (2.0 * x) - (t * (z * (9.0 * y)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e+117) {
		tmp = 2.0 * x;
	} else if (t_2 <= -4e-8) {
		tmp = ((z * y) * t) * -9.0;
	} else if (t_2 <= 3e+81) {
		tmp = b * (27.0 * a);
	} else if (t_2 <= 5e+306) {
		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 * z) * (t * y)
	t_2 = (2.0 * x) - (t * (z * (9.0 * y)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e+117:
		tmp = 2.0 * x
	elif t_2 <= -4e-8:
		tmp = ((z * y) * t) * -9.0
	elif t_2 <= 3e+81:
		tmp = b * (27.0 * a)
	elif t_2 <= 5e+306:
		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(-9.0 * z) * Float64(t * y))
	t_2 = Float64(Float64(2.0 * x) - Float64(t * Float64(z * Float64(9.0 * y))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e+117)
		tmp = Float64(2.0 * x);
	elseif (t_2 <= -4e-8)
		tmp = Float64(Float64(Float64(z * y) * t) * -9.0);
	elseif (t_2 <= 3e+81)
		tmp = Float64(b * Float64(27.0 * a));
	elseif (t_2 <= 5e+306)
		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 * z) * (t * y);
	t_2 = (2.0 * x) - (t * (z * (9.0 * y)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e+117)
		tmp = 2.0 * x;
	elseif (t_2 <= -4e-8)
		tmp = ((z * y) * t) * -9.0;
	elseif (t_2 <= 3e+81)
		tmp = b * (27.0 * a);
	elseif (t_2 <= 5e+306)
		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[(-9.0 * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * x), $MachinePrecision] - N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e+117], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$2, -4e-8], N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * -9.0), $MachinePrecision], If[LessEqual[t$95$2, 3e+81], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+306], N[(2.0 * x), $MachinePrecision], t$95$1]]]]]]]

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 or 4.99999999999999993e306 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 76.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 4.0

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

   5. Applied rewrites 4.0%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 78.5

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

   8. Applied rewrites 78.5%

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

   10. Applied rewrites 92.6%

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

   if -inf.0 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.99999999999999983e117 or 2.99999999999999997e81 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 4.99999999999999993e306

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.1

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

   5. Applied rewrites 59.1%

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

   if -4.99999999999999983e117 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.0000000000000001e-8

   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 t around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 53.2

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

   5. Applied rewrites 53.2%

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

   if -4.0000000000000001e-8 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 2.99999999999999997e81

   1. Initial program 98.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 64.2

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

   5. Applied rewrites 64.2%

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

   7. Applied rewrites 64.3%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -\infty:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -5 \cdot 10^{+117}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -4 \cdot 10^{-8}:\\ \;\;\;\;\left(\left(z \cdot y\right) \cdot t\right) \cdot -9\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 3 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(z \cdot y\right) \cdot t\right) \cdot -9\\ t_2 := 2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+117}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 3 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* (* z y) t) -9.0)) (t_2 (- (* 2.0 x) (* t (* z (* 9.0 y))))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e+117)
       (* 2.0 x)
       (if (<= t_2 -4e-8)
         t_1
         (if (<= t_2 3e+81)
           (* b (* 27.0 a))
           (if (<= t_2 5e+306) (* 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 = ((z * y) * t) * -9.0;
	double t_2 = (2.0 * x) - (t * (z * (9.0 * y)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e+117) {
		tmp = 2.0 * x;
	} else if (t_2 <= -4e-8) {
		tmp = t_1;
	} else if (t_2 <= 3e+81) {
		tmp = b * (27.0 * a);
	} else if (t_2 <= 5e+306) {
		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 = ((z * y) * t) * -9.0;
	double t_2 = (2.0 * x) - (t * (z * (9.0 * y)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e+117) {
		tmp = 2.0 * x;
	} else if (t_2 <= -4e-8) {
		tmp = t_1;
	} else if (t_2 <= 3e+81) {
		tmp = b * (27.0 * a);
	} else if (t_2 <= 5e+306) {
		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 = ((z * y) * t) * -9.0
	t_2 = (2.0 * x) - (t * (z * (9.0 * y)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e+117:
		tmp = 2.0 * x
	elif t_2 <= -4e-8:
		tmp = t_1
	elif t_2 <= 3e+81:
		tmp = b * (27.0 * a)
	elif t_2 <= 5e+306:
		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(z * y) * t) * -9.0)
	t_2 = Float64(Float64(2.0 * x) - Float64(t * Float64(z * Float64(9.0 * y))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e+117)
		tmp = Float64(2.0 * x);
	elseif (t_2 <= -4e-8)
		tmp = t_1;
	elseif (t_2 <= 3e+81)
		tmp = Float64(b * Float64(27.0 * a));
	elseif (t_2 <= 5e+306)
		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 = ((z * y) * t) * -9.0;
	t_2 = (2.0 * x) - (t * (z * (9.0 * y)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e+117)
		tmp = 2.0 * x;
	elseif (t_2 <= -4e-8)
		tmp = t_1;
	elseif (t_2 <= 3e+81)
		tmp = b * (27.0 * a);
	elseif (t_2 <= 5e+306)
		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[(z * y), $MachinePrecision] * t), $MachinePrecision] * -9.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * x), $MachinePrecision] - N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e+117], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$2, -4e-8], t$95$1, If[LessEqual[t$95$2, 3e+81], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+306], 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 -4.99999999999999983e117 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.0000000000000001e-8 or 4.99999999999999993e306 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 84.8%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 69.6

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

   5. Applied rewrites 69.6%

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

   if -inf.0 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.99999999999999983e117 or 2.99999999999999997e81 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 4.99999999999999993e306

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.1

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

   5. Applied rewrites 59.1%

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

   if -4.0000000000000001e-8 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 2.99999999999999997e81

   1. Initial program 98.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 64.2

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

   5. Applied rewrites 64.2%

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

   7. Applied rewrites 64.3%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -\infty:\\ \;\;\;\;\left(\left(z \cdot y\right) \cdot t\right) \cdot -9\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -5 \cdot 10^{+117}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -4 \cdot 10^{-8}:\\ \;\;\;\;\left(\left(z \cdot y\right) \cdot t\right) \cdot -9\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 3 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot y\right) \cdot t\right) \cdot -9\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ t_2 := \mathsf{fma}\left(x, 2, \left(\left(z \cdot y\right) \cdot t\right) \cdot -9\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+131}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot x + b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+269}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \end{array} \end{array} \]

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 (* t (* z (* 9.0 y)))) (t_2 (fma x 2.0 (* (* (* z y) t) -9.0))))
   (if (<= t_1 (- INFINITY))
     (* (* (* -9.0 t) z) y)
     (if (<= t_1 -5e+131)
       t_2
       (if (<= t_1 2e-10)
         (+ (* 2.0 x) (* b (* 27.0 a)))
         (if (<= t_1 1e+269) t_2 (* (* -9.0 z) (* t 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 = t * (z * (9.0 * y));
	double t_2 = fma(x, 2.0, (((z * y) * t) * -9.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((-9.0 * t) * z) * y;
	} else if (t_1 <= -5e+131) {
		tmp = t_2;
	} else if (t_1 <= 2e-10) {
		tmp = (2.0 * x) + (b * (27.0 * a));
	} else if (t_1 <= 1e+269) {
		tmp = t_2;
	} else {
		tmp = (-9.0 * z) * (t * 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(t * Float64(z * Float64(9.0 * y)))
	t_2 = fma(x, 2.0, Float64(Float64(Float64(z * y) * t) * -9.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(-9.0 * t) * z) * y);
	elseif (t_1 <= -5e+131)
		tmp = t_2;
	elseif (t_1 <= 2e-10)
		tmp = Float64(Float64(2.0 * x) + Float64(b * Float64(27.0 * a)));
	elseif (t_1 <= 1e+269)
		tmp = t_2;
	else
		tmp = Float64(Float64(-9.0 * z) * Float64(t * y));
	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[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * 2.0 + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(-9.0 * t), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, -5e+131], t$95$2, If[LessEqual[t$95$1, 2e-10], N[(N[(2.0 * x), $MachinePrecision] + N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+269], t$95$2, N[(N[(-9.0 * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 78.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 2.3

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

   5. Applied rewrites 2.3%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 78.1

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

   8. Applied rewrites 78.1%

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

   10. Applied rewrites 92.2%

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

   if -inf.0 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999995e131 or 2.00000000000000007e-10 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1e269

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 26.7

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

   5. Applied rewrites 26.7%

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

   6. Taylor expanded in b around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 86.5

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

   8. Applied rewrites 86.5%

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

   if -4.99999999999999995e131 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.00000000000000007e-10

   1. Initial program 98.4%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 88.5

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

   5. Applied rewrites 88.5%

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

   if 1e269 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 77.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 5.3

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

   5. Applied rewrites 5.3%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 80.4

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

   8. Applied rewrites 80.4%

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

   10. Applied rewrites 90.2%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -\infty:\\ \;\;\;\;\left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -5 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \left(\left(z \cdot y\right) \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 2 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot x + b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 10^{+269}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \left(\left(z \cdot y\right) \cdot t\right) \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(-9 \cdot t\right) \cdot z, 2 \cdot x\right)\\ t_2 := t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \left(\left(z \cdot y\right) \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot x + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma y (* (* -9.0 t) z) (* 2.0 x))) (t_2 (* t (* z (* 9.0 y)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e+131)
       (fma x 2.0 (* (* (* z y) t) -9.0))
       (if (<= t_2 2e-10) (+ (* 2.0 x) (* b (* 27.0 a))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(y, ((-9.0 * t) * z), (2.0 * x));
	double t_2 = t * (z * (9.0 * y));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e+131) {
		tmp = fma(x, 2.0, (((z * y) * t) * -9.0));
	} else if (t_2 <= 2e-10) {
		tmp = (2.0 * x) + (b * (27.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(Float64(-9.0 * t) * z), Float64(2.0 * x))
	t_2 = Float64(t * Float64(z * Float64(9.0 * y)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e+131)
		tmp = fma(x, 2.0, Float64(Float64(Float64(z * y) * t) * -9.0));
	elseif (t_2 <= 2e-10)
		tmp = Float64(Float64(2.0 * x) + Float64(b * Float64(27.0 * a)));
	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[(y * N[(N[(-9.0 * t), $MachinePrecision] * z), $MachinePrecision] + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e+131], N[(x * 2.0 + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e-10], N[(N[(2.0 * x), $MachinePrecision] + N[(b * N[(27.0 * a), $MachinePrecision]), $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 2.00000000000000007e-10 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 87.5%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 91.3%

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

   5. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 85.3

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

   7. Applied rewrites 85.3%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 85.2

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 85.2

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

   9. Applied rewrites 85.2%

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

   if -inf.0 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999995e131

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 17.8

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

   5. Applied rewrites 17.8%

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

   6. Taylor expanded in b around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 82.9

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

   8. Applied rewrites 82.9%

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

   if -4.99999999999999995e131 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.00000000000000007e-10

   1. Initial program 98.4%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 88.5

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

   5. Applied rewrites 88.5%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-9 \cdot t\right) \cdot z, 2 \cdot x\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -5 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \left(\left(z \cdot y\right) \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 2 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot x + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-9 \cdot t\right) \cdot z, 2 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, 2 \cdot x\right)\\ t_2 := t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \left(\left(z \cdot y\right) \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot x + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (* -9.0 (* t z)) y (* 2.0 x))) (t_2 (* t (* z (* 9.0 y)))))
   (if (<= t_2 -2e+289)
     t_1
     (if (<= t_2 -5e+131)
       (fma x 2.0 (* (* (* z y) t) -9.0))
       (if (<= t_2 2e-10) (+ (* 2.0 x) (* b (* 27.0 a))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((-9.0 * (t * z)), y, (2.0 * x));
	double t_2 = t * (z * (9.0 * y));
	double tmp;
	if (t_2 <= -2e+289) {
		tmp = t_1;
	} else if (t_2 <= -5e+131) {
		tmp = fma(x, 2.0, (((z * y) * t) * -9.0));
	} else if (t_2 <= 2e-10) {
		tmp = (2.0 * x) + (b * (27.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-9.0 * Float64(t * z)), y, Float64(2.0 * x))
	t_2 = Float64(t * Float64(z * Float64(9.0 * y)))
	tmp = 0.0
	if (t_2 <= -2e+289)
		tmp = t_1;
	elseif (t_2 <= -5e+131)
		tmp = fma(x, 2.0, Float64(Float64(Float64(z * y) * t) * -9.0));
	elseif (t_2 <= 2e-10)
		tmp = Float64(Float64(2.0 * x) + Float64(b * Float64(27.0 * a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(-9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision] * y + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+289], t$95$1, If[LessEqual[t$95$2, -5e+131], N[(x * 2.0 + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e-10], N[(N[(2.0 * x), $MachinePrecision] + N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -2.0000000000000001e289 or 2.00000000000000007e-10 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 87.6%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 85.4

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

   5. Applied rewrites 85.4%

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

   if -2.0000000000000001e289 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999995e131

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 18.3

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

   5. Applied rewrites 18.3%

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

   6. Taylor expanded in b around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 82.0

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

   8. Applied rewrites 82.0%

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

   if -4.99999999999999995e131 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.00000000000000007e-10

   1. Initial program 98.4%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 88.5

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

   5. Applied rewrites 88.5%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -2 \cdot 10^{+289}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, 2 \cdot x\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -5 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \left(\left(z \cdot y\right) \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 2 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot x + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, 2 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot z, t \cdot y, 2 \cdot x\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot x + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-9 \cdot t\right) \cdot z, 2 \cdot x\right)\\ \end{array} \end{array} \]

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 (* t (* z (* 9.0 y)))))
   (if (<= t_1 -5e+131)
     (fma (* -9.0 z) (* t y) (* 2.0 x))
     (if (<= t_1 2e-10)
       (+ (* 2.0 x) (* b (* 27.0 a)))
       (fma y (* (* -9.0 t) z) (* 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 = t * (z * (9.0 * y));
	double tmp;
	if (t_1 <= -5e+131) {
		tmp = fma((-9.0 * z), (t * y), (2.0 * x));
	} else if (t_1 <= 2e-10) {
		tmp = (2.0 * x) + (b * (27.0 * a));
	} else {
		tmp = fma(y, ((-9.0 * t) * z), (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(t * Float64(z * Float64(9.0 * y)))
	tmp = 0.0
	if (t_1 <= -5e+131)
		tmp = fma(Float64(-9.0 * z), Float64(t * y), Float64(2.0 * x));
	elseif (t_1 <= 2e-10)
		tmp = Float64(Float64(2.0 * x) + Float64(b * Float64(27.0 * a)));
	else
		tmp = fma(y, Float64(Float64(-9.0 * t) * z), 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_] := Block[{t$95$1 = N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+131], N[(N[(-9.0 * z), $MachinePrecision] * N[(t * y), $MachinePrecision] + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-10], N[(N[(2.0 * x), $MachinePrecision] + N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(-9.0 * t), $MachinePrecision] * z), $MachinePrecision] + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999995e131

   1. Initial program 87.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 91.5%

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

   5. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 82.1

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

   7. Applied rewrites 82.1%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 75.9

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

   9. Applied rewrites 75.9%

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

   if -4.99999999999999995e131 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.00000000000000007e-10

   1. Initial program 98.4%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 88.5

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

   5. Applied rewrites 88.5%

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

   if 2.00000000000000007e-10 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 90.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 88.2%

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

   5. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 82.7

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

   7. Applied rewrites 82.7%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 82.7

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 82.7

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

   9. Applied rewrites 82.7%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -5 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot z, t \cdot y, 2 \cdot x\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 2 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot x + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-9 \cdot t\right) \cdot z, 2 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ t_2 := t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot x + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* (* -9.0 t) z) y)) (t_2 (* t (* z (* 9.0 y)))))
   (if (<= t_2 -5e+219)
     t_1
     (if (<= t_2 2e-10) (+ (* 2.0 x) (* b (* 27.0 a))) 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 = t * (z * (9.0 * y));
	double tmp;
	if (t_2 <= -5e+219) {
		tmp = t_1;
	} else if (t_2 <= 2e-10) {
		tmp = (2.0 * x) + (b * (27.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (((-9.0d0) * t) * z) * y
    t_2 = t * (z * (9.0d0 * y))
    if (t_2 <= (-5d+219)) then
        tmp = t_1
    else if (t_2 <= 2d-10) then
        tmp = (2.0d0 * x) + (b * (27.0d0 * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((-9.0 * t) * z) * y;
	double t_2 = t * (z * (9.0 * y));
	double tmp;
	if (t_2 <= -5e+219) {
		tmp = t_1;
	} else if (t_2 <= 2e-10) {
		tmp = (2.0 * x) + (b * (27.0 * a));
	} 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 = t * (z * (9.0 * y))
	tmp = 0
	if t_2 <= -5e+219:
		tmp = t_1
	elif t_2 <= 2e-10:
		tmp = (2.0 * x) + (b * (27.0 * a))
	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(t * Float64(z * Float64(9.0 * y)))
	tmp = 0.0
	if (t_2 <= -5e+219)
		tmp = t_1;
	elseif (t_2 <= 2e-10)
		tmp = Float64(Float64(2.0 * x) + Float64(b * Float64(27.0 * a)));
	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 = t * (z * (9.0 * y));
	tmp = 0.0;
	if (t_2 <= -5e+219)
		tmp = t_1;
	elseif (t_2 <= 2e-10)
		tmp = (2.0 * x) + (b * (27.0 * a));
	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[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+219], t$95$1, If[LessEqual[t$95$2, 2e-10], N[(N[(2.0 * x), $MachinePrecision] + N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5e219 or 2.00000000000000007e-10 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 15.8

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

   5. Applied rewrites 15.8%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 70.1

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

   8. Applied rewrites 70.1%

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

   10. Applied rewrites 71.8%

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

   if -5e219 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.00000000000000007e-10

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 84.7

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

   5. Applied rewrites 84.7%

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

4. Final simplification 79.2%

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

Alternative 11: 80.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ t_2 := t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot a, b, 2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* (* -9.0 t) z) y)) (t_2 (* t (* z (* 9.0 y)))))
   (if (<= t_2 -5e+219)
     t_1
     (if (<= t_2 2e-10) (fma (* 27.0 a) b (* 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 = t * (z * (9.0 * y));
	double tmp;
	if (t_2 <= -5e+219) {
		tmp = t_1;
	} else if (t_2 <= 2e-10) {
		tmp = fma((27.0 * a), b, (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(t * Float64(z * Float64(9.0 * y)))
	tmp = 0.0
	if (t_2 <= -5e+219)
		tmp = t_1;
	elseif (t_2 <= 2e-10)
		tmp = fma(Float64(27.0 * a), b, Float64(2.0 * x));
	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[(-9.0 * t), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+219], t$95$1, If[LessEqual[t$95$2, 2e-10], N[(N[(27.0 * a), $MachinePrecision] * b + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5e219 or 2.00000000000000007e-10 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 15.8

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

   5. Applied rewrites 15.8%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 70.1

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

   8. Applied rewrites 70.1%

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

   10. Applied rewrites 71.8%

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

   if -5e219 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.00000000000000007e-10

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 85.3

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

   5. Applied rewrites 85.3%

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

   7. Applied rewrites 84.7%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -5 \cdot 10^{+219}:\\ \;\;\;\;\left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot a, b, 2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 80.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ t_2 := t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* (* -9.0 t) z) y)) (t_2 (* t (* z (* 9.0 y)))))
   (if (<= t_2 -5e+219)
     t_1
     (if (<= t_2 2e-10) (fma (* b 27.0) a (* 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 = t * (z * (9.0 * y));
	double tmp;
	if (t_2 <= -5e+219) {
		tmp = t_1;
	} else if (t_2 <= 2e-10) {
		tmp = fma((b * 27.0), a, (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(t * Float64(z * Float64(9.0 * y)))
	tmp = 0.0
	if (t_2 <= -5e+219)
		tmp = t_1;
	elseif (t_2 <= 2e-10)
		tmp = fma(Float64(b * 27.0), a, Float64(2.0 * x));
	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[(-9.0 * t), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+219], t$95$1, If[LessEqual[t$95$2, 2e-10], N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5e219 or 2.00000000000000007e-10 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 15.8

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

   5. Applied rewrites 15.8%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 70.1

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

   8. Applied rewrites 70.1%

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

   10. Applied rewrites 71.8%

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

   if -5e219 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.00000000000000007e-10

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 85.3

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

   5. Applied rewrites 85.3%

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

   7. Applied rewrites 85.3%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -5 \cdot 10^{+219}:\\ \;\;\;\;\left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 92.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 6 \cdot 10^{+50}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(t \cdot y\right) \cdot z, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, 2 \cdot x\right)\\ \end{array} \end{array} \]

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 (* z (* 9.0 y))) 6e+50)
   (fma -9.0 (* (* t y) z) (fma (* b 27.0) a (* 2.0 x)))
   (fma (* -9.0 (* t z)) y (* 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 * (z * (9.0 * y))) <= 6e+50) {
		tmp = fma(-9.0, ((t * y) * z), fma((b * 27.0), a, (2.0 * x)));
	} else {
		tmp = fma((-9.0 * (t * z)), y, (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 (Float64(t * Float64(z * Float64(9.0 * y))) <= 6e+50)
		tmp = fma(-9.0, Float64(Float64(t * y) * z), fma(Float64(b * 27.0), a, Float64(2.0 * x)));
	else
		tmp = fma(Float64(-9.0 * Float64(t * z)), y, 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[N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 6e+50], N[(-9.0 * N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision] * y + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5.9999999999999996e50

   1. Initial program 95.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

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

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. metadata-eval N/A

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

      16. *-commutative N/A

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

      17. associate-*r* N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. lower-*.f64 N/A

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

   4. Applied rewrites 95.3%

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

   if 5.9999999999999996e50 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 89.1%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 80.1

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

   5. Applied rewrites 80.1%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 6 \cdot 10^{+50}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(t \cdot y\right) \cdot z, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(t \cdot z\right), y, 2 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(27 \cdot a\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+83}:\\ \;\;\;\;\left(b \cdot 27\right) \cdot a\\ \mathbf{elif}\;t\_1 \leq 200:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* b (* 27.0 a))))
   (if (<= t_1 -4e+83) (* (* b 27.0) a) (if (<= t_1 200.0) (* 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 = b * (27.0 * a);
	double tmp;
	if (t_1 <= -4e+83) {
		tmp = (b * 27.0) * a;
	} else if (t_1 <= 200.0) {
		tmp = 2.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (27.0d0 * a)
    if (t_1 <= (-4d+83)) then
        tmp = (b * 27.0d0) * a
    else if (t_1 <= 200.0d0) then
        tmp = 2.0d0 * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (27.0 * a);
	double tmp;
	if (t_1 <= -4e+83) {
		tmp = (b * 27.0) * a;
	} else if (t_1 <= 200.0) {
		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 = b * (27.0 * a)
	tmp = 0
	if t_1 <= -4e+83:
		tmp = (b * 27.0) * a
	elif t_1 <= 200.0:
		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(b * Float64(27.0 * a))
	tmp = 0.0
	if (t_1 <= -4e+83)
		tmp = Float64(Float64(b * 27.0) * a);
	elseif (t_1 <= 200.0)
		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 = b * (27.0 * a);
	tmp = 0.0;
	if (t_1 <= -4e+83)
		tmp = (b * 27.0) * a;
	elseif (t_1 <= 200.0)
		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[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+83], N[(N[(b * 27.0), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t$95$1, 200.0], N[(2.0 * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.00000000000000012e83

   1. Initial program 97.0%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 72.0

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

   5. Applied rewrites 72.0%

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

   7. Applied rewrites 72.2%

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

   if -4.00000000000000012e83 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 200

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 42.1

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

   5. Applied rewrites 42.1%

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

   if 200 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 94.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 61.8

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

   5. Applied rewrites 61.8%

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

   7. Applied rewrites 60.1%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(27 \cdot a\right) \leq -4 \cdot 10^{+83}:\\ \;\;\;\;\left(b \cdot 27\right) \cdot a\\ \mathbf{elif}\;b \cdot \left(27 \cdot a\right) \leq 200:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(27 \cdot a\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 200:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* b (* 27.0 a))))
   (if (<= t_1 -4e+83) t_1 (if (<= t_1 200.0) (* 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 = b * (27.0 * a);
	double tmp;
	if (t_1 <= -4e+83) {
		tmp = t_1;
	} else if (t_1 <= 200.0) {
		tmp = 2.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (27.0d0 * a)
    if (t_1 <= (-4d+83)) then
        tmp = t_1
    else if (t_1 <= 200.0d0) then
        tmp = 2.0d0 * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (27.0 * a);
	double tmp;
	if (t_1 <= -4e+83) {
		tmp = t_1;
	} else if (t_1 <= 200.0) {
		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 = b * (27.0 * a)
	tmp = 0
	if t_1 <= -4e+83:
		tmp = t_1
	elif t_1 <= 200.0:
		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(b * Float64(27.0 * a))
	tmp = 0.0
	if (t_1 <= -4e+83)
		tmp = t_1;
	elseif (t_1 <= 200.0)
		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 = b * (27.0 * a);
	tmp = 0.0;
	if (t_1 <= -4e+83)
		tmp = t_1;
	elseif (t_1 <= 200.0)
		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[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+83], t$95$1, If[LessEqual[t$95$1, 200.0], N[(2.0 * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.00000000000000012e83 or 200 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 95.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 65.9

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

   5. Applied rewrites 65.9%

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

   7. Applied rewrites 65.0%

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

   if -4.00000000000000012e83 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 200

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 42.1

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

   5. Applied rewrites 42.1%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(27 \cdot a\right) \leq -4 \cdot 10^{+83}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;b \cdot \left(27 \cdot a\right) \leq 200:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 98.5% accurate, 0.9× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (* b 27.0) a (* 2.0 x))))
   (if (<= z -5e-170)
     (fma (* t z) (* -9.0 y) t_1)
     (fma (* (- t) 9.0) (* z y) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b * 27.0), a, (2.0 * x));
	double tmp;
	if (z <= -5e-170) {
		tmp = fma((t * z), (-9.0 * y), t_1);
	} else {
		tmp = fma((-t * 9.0), (z * y), t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(Float64(b * 27.0), a, Float64(2.0 * x))
	tmp = 0.0
	if (z <= -5e-170)
		tmp = fma(Float64(t * z), Float64(-9.0 * y), t_1);
	else
		tmp = fma(Float64(Float64(-t) * 9.0), Float64(z * y), 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[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e-170], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[((-t) * 9.0), $MachinePrecision] * N[(z * y), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000001e-170

   1. Initial program 91.5%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 91.4%

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

   if -5.0000000000000001e-170 < z

   1. Initial program 96.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-*l* N/A

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

      13. associate-*r* N/A

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

      14. *-commutative N/A

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

      15. +-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. lower-neg.f64 N/A

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

      19. lower-*.f64 N/A

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

   4. Applied rewrites 96.1%

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

Alternative 17: 98.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\\ \mathbf{if}\;z \leq 2 \cdot 10^{-55}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, -9 \cdot y, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot y, -9 \cdot z, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (* b 27.0) a (* 2.0 x))))
   (if (<= z 2e-55)
     (fma (* t z) (* -9.0 y) t_1)
     (fma (* t y) (* -9.0 z) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b * 27.0), a, (2.0 * x));
	double tmp;
	if (z <= 2e-55) {
		tmp = fma((t * z), (-9.0 * y), t_1);
	} else {
		tmp = fma((t * y), (-9.0 * z), t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(Float64(b * 27.0), a, Float64(2.0 * x))
	tmp = 0.0
	if (z <= 2e-55)
		tmp = fma(Float64(t * z), Float64(-9.0 * y), t_1);
	else
		tmp = fma(Float64(t * y), Float64(-9.0 * z), t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 2e-55], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(t * y), $MachinePrecision] * N[(-9.0 * z), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 1.99999999999999999e-55

   1. Initial program 94.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 94.9%

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

   if 1.99999999999999999e-55 < z

   1. Initial program 93.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. associate-*r* N/A

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

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

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

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

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

      17. lower-*.f64 N/A

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

      18. metadata-eval N/A

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

   4. Applied rewrites 98.6%

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

Alternative 18: 30.7% accurate, 6.2× speedup

Math

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

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 94.2%

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

3. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 32.4

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

5. Applied rewrites 32.4%

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

6. Final simplification 32.4%

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

Developer Target 1: 95.2% 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 2024276 
(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)))