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

Percentage Accurate: 95.3% → 97.8%

Time: 23.1s

Alternatives: 13

Speedup: 0.8×

• 26.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(9 \cdot y\right)\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+146}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right) + \left(2 \cdot x - t \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right)\\ \end{array} \end{array} \]

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 2e+146)
     (+ (* b (* 27.0 a)) (- (* 2.0 x) (* t t_1)))
     (fma (* b a) 27.0 (fma (* (* -9.0 y) 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 = z * (9.0 * y);
	double tmp;
	if (t_1 <= 2e+146) {
		tmp = (b * (27.0 * a)) + ((2.0 * x) - (t * t_1));
	} else {
		tmp = fma((b * a), 27.0, fma(((-9.0 * y) * 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(z * Float64(9.0 * y))
	tmp = 0.0
	if (t_1 <= 2e+146)
		tmp = Float64(Float64(b * Float64(27.0 * a)) + Float64(Float64(2.0 * x) - Float64(t * t_1)));
	else
		tmp = fma(Float64(b * a), 27.0, fma(Float64(Float64(-9.0 * y) * 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[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+146], 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[(b * a), $MachinePrecision] * 27.0 + N[(N[(N[(-9.0 * y), $MachinePrecision] * t), $MachinePrecision] * z + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 1.99999999999999987e146

   1. Initial program 95.6%

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

   if 1.99999999999999987e146 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 87.4%

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

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 87.4

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*l* N/A

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

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

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

      18. *-commutative N/A

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

      19. associate-*r* N/A

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

      20. lower-fma.f64 N/A

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

   4. Applied rewrites 99.8%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(9 \cdot y\right) \leq 2 \cdot 10^{+146}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right) + \left(2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 60.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+301}:\\ \;\;\;\;\left(\left(-9 \cdot y\right) \cdot t\right) \cdot z\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+298}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* 2.0 x) (* t (* z (* 9.0 y))))))
   (if (<= t_1 -5e+301)
     (* (* (* -9.0 y) t) z)
     (if (<= t_1 -2e+128)
       (* 2.0 x)
       (if (<= t_1 5e+98)
         (* b (* 27.0 a))
         (if (<= t_1 2e+298) (* 2.0 x) (* (* (* t z) -9.0) y)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (2.0 * x) - (t * (z * (9.0 * y)));
	double tmp;
	if (t_1 <= -5e+301) {
		tmp = ((-9.0 * y) * t) * z;
	} else if (t_1 <= -2e+128) {
		tmp = 2.0 * x;
	} else if (t_1 <= 5e+98) {
		tmp = b * (27.0 * a);
	} else if (t_1 <= 2e+298) {
		tmp = 2.0 * x;
	} else {
		tmp = ((t * z) * -9.0) * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 * x) - (t * (z * (9.0d0 * y)))
    if (t_1 <= (-5d+301)) then
        tmp = (((-9.0d0) * y) * t) * z
    else if (t_1 <= (-2d+128)) then
        tmp = 2.0d0 * x
    else if (t_1 <= 5d+98) then
        tmp = b * (27.0d0 * a)
    else if (t_1 <= 2d+298) then
        tmp = 2.0d0 * x
    else
        tmp = ((t * z) * (-9.0d0)) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (2.0 * x) - (t * (z * (9.0 * y)));
	double tmp;
	if (t_1 <= -5e+301) {
		tmp = ((-9.0 * y) * t) * z;
	} else if (t_1 <= -2e+128) {
		tmp = 2.0 * x;
	} else if (t_1 <= 5e+98) {
		tmp = b * (27.0 * a);
	} else if (t_1 <= 2e+298) {
		tmp = 2.0 * x;
	} else {
		tmp = ((t * z) * -9.0) * y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (2.0 * x) - (t * (z * (9.0 * y)))
	tmp = 0
	if t_1 <= -5e+301:
		tmp = ((-9.0 * y) * t) * z
	elif t_1 <= -2e+128:
		tmp = 2.0 * x
	elif t_1 <= 5e+98:
		tmp = b * (27.0 * a)
	elif t_1 <= 2e+298:
		tmp = 2.0 * x
	else:
		tmp = ((t * z) * -9.0) * y
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(2.0 * x) - Float64(t * Float64(z * Float64(9.0 * y))))
	tmp = 0.0
	if (t_1 <= -5e+301)
		tmp = Float64(Float64(Float64(-9.0 * y) * t) * z);
	elseif (t_1 <= -2e+128)
		tmp = Float64(2.0 * x);
	elseif (t_1 <= 5e+98)
		tmp = Float64(b * Float64(27.0 * a));
	elseif (t_1 <= 2e+298)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(Float64(Float64(t * z) * -9.0) * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (2.0 * x) - (t * (z * (9.0 * y)));
	tmp = 0.0;
	if (t_1 <= -5e+301)
		tmp = ((-9.0 * y) * t) * z;
	elseif (t_1 <= -2e+128)
		tmp = 2.0 * x;
	elseif (t_1 <= 5e+98)
		tmp = b * (27.0 * a);
	elseif (t_1 <= 2e+298)
		tmp = 2.0 * x;
	else
		tmp = ((t * z) * -9.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(2.0 * x), $MachinePrecision] - N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+301], N[(N[(N[(-9.0 * y), $MachinePrecision] * t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, -2e+128], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$1, 5e+98], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+298], N[(2.0 * x), $MachinePrecision], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -5.0000000000000004e301

   1. Initial program 67.4%

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

   3. Taylor expanded in y 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 70.8

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

   5. Applied rewrites 70.8%

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

   7. Applied rewrites 86.4%

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

   if -5.0000000000000004e301 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -2.0000000000000002e128 or 4.9999999999999998e98 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 1.9999999999999999e298

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 53.3

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

   5. Applied rewrites 53.3%

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

   if -2.0000000000000002e128 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 4.9999999999999998e98

   1. Initial program 99.0%

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

   3. Taylor expanded in a 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 61.1

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

   5. Applied rewrites 61.1%

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

   7. Applied rewrites 61.1%

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

   if 1.9999999999999999e298 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 89.0%

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

   3. Taylor expanded in y 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 85.4

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

   5. Applied rewrites 85.4%

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

   7. Applied rewrites 85.4%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -5 \cdot 10^{+301}:\\ \;\;\;\;\left(\left(-9 \cdot y\right) \cdot t\right) \cdot z\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -2 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 5 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 2 \cdot 10^{+298}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+301}:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+298}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* 2.0 x) (* t (* z (* 9.0 y))))))
   (if (<= t_1 -5e+301)
     (* (* -9.0 z) (* t y))
     (if (<= t_1 -2e+128)
       (* 2.0 x)
       (if (<= t_1 5e+98)
         (* b (* 27.0 a))
         (if (<= t_1 2e+298) (* 2.0 x) (* (* (* t z) -9.0) y)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (2.0 * x) - (t * (z * (9.0 * y)));
	double tmp;
	if (t_1 <= -5e+301) {
		tmp = (-9.0 * z) * (t * y);
	} else if (t_1 <= -2e+128) {
		tmp = 2.0 * x;
	} else if (t_1 <= 5e+98) {
		tmp = b * (27.0 * a);
	} else if (t_1 <= 2e+298) {
		tmp = 2.0 * x;
	} else {
		tmp = ((t * z) * -9.0) * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 * x) - (t * (z * (9.0d0 * y)))
    if (t_1 <= (-5d+301)) then
        tmp = ((-9.0d0) * z) * (t * y)
    else if (t_1 <= (-2d+128)) then
        tmp = 2.0d0 * x
    else if (t_1 <= 5d+98) then
        tmp = b * (27.0d0 * a)
    else if (t_1 <= 2d+298) then
        tmp = 2.0d0 * x
    else
        tmp = ((t * z) * (-9.0d0)) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (2.0 * x) - (t * (z * (9.0 * y)));
	double tmp;
	if (t_1 <= -5e+301) {
		tmp = (-9.0 * z) * (t * y);
	} else if (t_1 <= -2e+128) {
		tmp = 2.0 * x;
	} else if (t_1 <= 5e+98) {
		tmp = b * (27.0 * a);
	} else if (t_1 <= 2e+298) {
		tmp = 2.0 * x;
	} else {
		tmp = ((t * z) * -9.0) * y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (2.0 * x) - (t * (z * (9.0 * y)))
	tmp = 0
	if t_1 <= -5e+301:
		tmp = (-9.0 * z) * (t * y)
	elif t_1 <= -2e+128:
		tmp = 2.0 * x
	elif t_1 <= 5e+98:
		tmp = b * (27.0 * a)
	elif t_1 <= 2e+298:
		tmp = 2.0 * x
	else:
		tmp = ((t * z) * -9.0) * y
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(2.0 * x) - Float64(t * Float64(z * Float64(9.0 * y))))
	tmp = 0.0
	if (t_1 <= -5e+301)
		tmp = Float64(Float64(-9.0 * z) * Float64(t * y));
	elseif (t_1 <= -2e+128)
		tmp = Float64(2.0 * x);
	elseif (t_1 <= 5e+98)
		tmp = Float64(b * Float64(27.0 * a));
	elseif (t_1 <= 2e+298)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(Float64(Float64(t * z) * -9.0) * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (2.0 * x) - (t * (z * (9.0 * y)));
	tmp = 0.0;
	if (t_1 <= -5e+301)
		tmp = (-9.0 * z) * (t * y);
	elseif (t_1 <= -2e+128)
		tmp = 2.0 * x;
	elseif (t_1 <= 5e+98)
		tmp = b * (27.0 * a);
	elseif (t_1 <= 2e+298)
		tmp = 2.0 * x;
	else
		tmp = ((t * z) * -9.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(2.0 * x), $MachinePrecision] - N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+301], N[(N[(-9.0 * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+128], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$1, 5e+98], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+298], N[(2.0 * x), $MachinePrecision], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -5.0000000000000004e301

   1. Initial program 67.4%

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

   3. Taylor expanded in y 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 70.8

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

   5. Applied rewrites 70.8%

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

   7. Applied rewrites 86.4%

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

   if -5.0000000000000004e301 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -2.0000000000000002e128 or 4.9999999999999998e98 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 1.9999999999999999e298

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 53.3

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

   5. Applied rewrites 53.3%

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

   if -2.0000000000000002e128 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 4.9999999999999998e98

   1. Initial program 99.0%

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

   3. Taylor expanded in a 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 61.1

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

   5. Applied rewrites 61.1%

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

   7. Applied rewrites 61.1%

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

   if 1.9999999999999999e298 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 89.0%

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

   3. Taylor expanded in y 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 85.4

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

   5. Applied rewrites 85.4%

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

   7. Applied rewrites 85.4%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -5 \cdot 10^{+301}:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -2 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 5 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 2 \cdot 10^{+298}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ t_2 := 2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+298}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* (* t z) -9.0) y)) (t_2 (- (* 2.0 x) (* t (* z (* 9.0 y))))))
   (if (<= t_2 -5e+301)
     t_1
     (if (<= t_2 -2e+128)
       (* 2.0 x)
       (if (<= t_2 5e+98)
         (* b (* 27.0 a))
         (if (<= t_2 2e+298) (* 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 = ((t * z) * -9.0) * y;
	double t_2 = (2.0 * x) - (t * (z * (9.0 * y)));
	double tmp;
	if (t_2 <= -5e+301) {
		tmp = t_1;
	} else if (t_2 <= -2e+128) {
		tmp = 2.0 * x;
	} else if (t_2 <= 5e+98) {
		tmp = b * (27.0 * a);
	} else if (t_2 <= 2e+298) {
		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) :: t_2
    real(8) :: tmp
    t_1 = ((t * z) * (-9.0d0)) * y
    t_2 = (2.0d0 * x) - (t * (z * (9.0d0 * y)))
    if (t_2 <= (-5d+301)) then
        tmp = t_1
    else if (t_2 <= (-2d+128)) then
        tmp = 2.0d0 * x
    else if (t_2 <= 5d+98) then
        tmp = b * (27.0d0 * a)
    else if (t_2 <= 2d+298) 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 = ((t * z) * -9.0) * y;
	double t_2 = (2.0 * x) - (t * (z * (9.0 * y)));
	double tmp;
	if (t_2 <= -5e+301) {
		tmp = t_1;
	} else if (t_2 <= -2e+128) {
		tmp = 2.0 * x;
	} else if (t_2 <= 5e+98) {
		tmp = b * (27.0 * a);
	} else if (t_2 <= 2e+298) {
		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 = ((t * z) * -9.0) * y
	t_2 = (2.0 * x) - (t * (z * (9.0 * y)))
	tmp = 0
	if t_2 <= -5e+301:
		tmp = t_1
	elif t_2 <= -2e+128:
		tmp = 2.0 * x
	elif t_2 <= 5e+98:
		tmp = b * (27.0 * a)
	elif t_2 <= 2e+298:
		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(t * z) * -9.0) * y)
	t_2 = Float64(Float64(2.0 * x) - Float64(t * Float64(z * Float64(9.0 * y))))
	tmp = 0.0
	if (t_2 <= -5e+301)
		tmp = t_1;
	elseif (t_2 <= -2e+128)
		tmp = Float64(2.0 * x);
	elseif (t_2 <= 5e+98)
		tmp = Float64(b * Float64(27.0 * a));
	elseif (t_2 <= 2e+298)
		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 = ((t * z) * -9.0) * y;
	t_2 = (2.0 * x) - (t * (z * (9.0 * y)));
	tmp = 0.0;
	if (t_2 <= -5e+301)
		tmp = t_1;
	elseif (t_2 <= -2e+128)
		tmp = 2.0 * x;
	elseif (t_2 <= 5e+98)
		tmp = b * (27.0 * a);
	elseif (t_2 <= 2e+298)
		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[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y), $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, -5e+301], t$95$1, If[LessEqual[t$95$2, -2e+128], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$2, 5e+98], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+298], 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)) < -5.0000000000000004e301 or 1.9999999999999999e298 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 77.8%

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

   3. Taylor expanded in y 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 77.9

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

   5. Applied rewrites 77.9%

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

   7. Applied rewrites 85.9%

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

   if -5.0000000000000004e301 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -2.0000000000000002e128 or 4.9999999999999998e98 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 1.9999999999999999e298

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 53.3

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

   5. Applied rewrites 53.3%

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

   if -2.0000000000000002e128 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 4.9999999999999998e98

   1. Initial program 99.0%

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

   3. Taylor expanded in a 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 61.1

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

   5. Applied rewrites 61.1%

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

   7. Applied rewrites 61.1%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -5 \cdot 10^{+301}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -2 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 5 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;2 \cdot x - t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 2 \cdot 10^{+298}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+205}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq 10^{+14}:\\ \;\;\;\;2 \cdot x + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot -9, t, 2 \cdot x\right)\\ \end{array} \end{array} \]

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 -1e+205)
     (* (* (* t z) -9.0) y)
     (if (<= t_1 1e+14)
       (+ (* 2.0 x) (* b (* 27.0 a)))
       (fma (* (* z y) -9.0) t (* 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 <= -1e+205) {
		tmp = ((t * z) * -9.0) * y;
	} else if (t_1 <= 1e+14) {
		tmp = (2.0 * x) + (b * (27.0 * a));
	} else {
		tmp = fma(((z * y) * -9.0), t, (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 <= -1e+205)
		tmp = Float64(Float64(Float64(t * z) * -9.0) * y);
	elseif (t_1 <= 1e+14)
		tmp = Float64(Float64(2.0 * x) + Float64(b * Float64(27.0 * a)));
	else
		tmp = fma(Float64(Float64(z * y) * -9.0), t, 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, -1e+205], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 1e+14], N[(N[(2.0 * x), $MachinePrecision] + N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * y), $MachinePrecision] * -9.0), $MachinePrecision] * t + 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) < -1.00000000000000002e205

   1. Initial program 91.3%

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

   3. Taylor expanded in y 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 88.5

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

   5. Applied rewrites 88.5%

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

   7. Applied rewrites 83.5%

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

   if -1.00000000000000002e205 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1e14

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} + \left(a \cdot 27\right) \cdot b \]
   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 90.6

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

   5. Applied rewrites 90.6%

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

   if 1e14 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 83.9%

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

   3. Taylor expanded in a 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

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 76.6

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

   5. Applied rewrites 76.6%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -1 \cdot 10^{+205}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 10^{+14}:\\ \;\;\;\;2 \cdot x + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot -9, t, 2 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+205}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+115}:\\ \;\;\;\;2 \cdot x + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot y\right) \cdot t\right) \cdot z\\ \end{array} \end{array} \]

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 -1e+205)
     (* (* (* t z) -9.0) y)
     (if (<= t_1 2e+115)
       (+ (* 2.0 x) (* b (* 27.0 a)))
       (* (* (* -9.0 y) t) z)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * (9.0 * y));
	double tmp;
	if (t_1 <= -1e+205) {
		tmp = ((t * z) * -9.0) * y;
	} else if (t_1 <= 2e+115) {
		tmp = (2.0 * x) + (b * (27.0 * a));
	} else {
		tmp = ((-9.0 * y) * t) * z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (z * (9.0d0 * y))
    if (t_1 <= (-1d+205)) then
        tmp = ((t * z) * (-9.0d0)) * y
    else if (t_1 <= 2d+115) then
        tmp = (2.0d0 * x) + (b * (27.0d0 * a))
    else
        tmp = (((-9.0d0) * y) * t) * z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * (9.0 * y));
	double tmp;
	if (t_1 <= -1e+205) {
		tmp = ((t * z) * -9.0) * y;
	} else if (t_1 <= 2e+115) {
		tmp = (2.0 * x) + (b * (27.0 * a));
	} else {
		tmp = ((-9.0 * y) * t) * z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = t * (z * (9.0 * y))
	tmp = 0
	if t_1 <= -1e+205:
		tmp = ((t * z) * -9.0) * y
	elif t_1 <= 2e+115:
		tmp = (2.0 * x) + (b * (27.0 * a))
	else:
		tmp = ((-9.0 * y) * t) * z
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(z * Float64(9.0 * y)))
	tmp = 0.0
	if (t_1 <= -1e+205)
		tmp = Float64(Float64(Float64(t * z) * -9.0) * y);
	elseif (t_1 <= 2e+115)
		tmp = Float64(Float64(2.0 * x) + Float64(b * Float64(27.0 * a)));
	else
		tmp = Float64(Float64(Float64(-9.0 * y) * t) * z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (z * (9.0 * y));
	tmp = 0.0;
	if (t_1 <= -1e+205)
		tmp = ((t * z) * -9.0) * y;
	elseif (t_1 <= 2e+115)
		tmp = (2.0 * x) + (b * (27.0 * a));
	else
		tmp = ((-9.0 * y) * t) * z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+205], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 2e+115], N[(N[(2.0 * x), $MachinePrecision] + N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-9.0 * y), $MachinePrecision] * t), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.00000000000000002e205

   1. Initial program 91.3%

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

   3. Taylor expanded in y 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 88.5

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

   5. Applied rewrites 88.5%

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

   7. Applied rewrites 83.5%

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

   if -1.00000000000000002e205 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2e115

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} + \left(a \cdot 27\right) \cdot b \]
   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 87.7

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

   5. Applied rewrites 87.7%

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

   if 2e115 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 78.0%

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

   3. Taylor expanded in y 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 71.4

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

   5. Applied rewrites 71.4%

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

   7. Applied rewrites 75.3%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -1 \cdot 10^{+205}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 2 \cdot 10^{+115}:\\ \;\;\;\;2 \cdot x + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot y\right) \cdot t\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+205}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot a, b, 2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot y\right) \cdot t\right) \cdot z\\ \end{array} \end{array} \]

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 -1e+205)
     (* (* (* t z) -9.0) y)
     (if (<= t_1 2e+115)
       (fma (* 27.0 a) b (* 2.0 x))
       (* (* (* -9.0 y) t) z)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * (9.0 * y));
	double tmp;
	if (t_1 <= -1e+205) {
		tmp = ((t * z) * -9.0) * y;
	} else if (t_1 <= 2e+115) {
		tmp = fma((27.0 * a), b, (2.0 * x));
	} else {
		tmp = ((-9.0 * y) * t) * z;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(z * Float64(9.0 * y)))
	tmp = 0.0
	if (t_1 <= -1e+205)
		tmp = Float64(Float64(Float64(t * z) * -9.0) * y);
	elseif (t_1 <= 2e+115)
		tmp = fma(Float64(27.0 * a), b, Float64(2.0 * x));
	else
		tmp = Float64(Float64(Float64(-9.0 * y) * t) * z);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+205], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 2e+115], N[(N[(27.0 * a), $MachinePrecision] * b + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-9.0 * y), $MachinePrecision] * t), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.00000000000000002e205

   1. Initial program 91.3%

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

   3. Taylor expanded in y 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 88.5

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

   5. Applied rewrites 88.5%

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

   7. Applied rewrites 83.5%

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

   if -1.00000000000000002e205 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2e115

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} + \left(a \cdot 27\right) \cdot b \]
   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 87.7

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

   5. Applied rewrites 87.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 87.7

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

   7. Applied rewrites 87.7%

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

   if 2e115 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 78.0%

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

   3. Taylor expanded in y 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 71.4

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

   5. Applied rewrites 71.4%

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

   7. Applied rewrites 75.3%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -1 \cdot 10^{+205}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 2 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot a, b, 2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot y\right) \cdot t\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+205}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot y\right) \cdot t\right) \cdot z\\ \end{array} \end{array} \]

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 -1e+205)
     (* (* (* t z) -9.0) y)
     (if (<= t_1 2e+115)
       (fma x 2.0 (* (* b a) 27.0))
       (* (* (* -9.0 y) t) z)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * (9.0 * y));
	double tmp;
	if (t_1 <= -1e+205) {
		tmp = ((t * z) * -9.0) * y;
	} else if (t_1 <= 2e+115) {
		tmp = fma(x, 2.0, ((b * a) * 27.0));
	} else {
		tmp = ((-9.0 * y) * t) * z;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(z * Float64(9.0 * y)))
	tmp = 0.0
	if (t_1 <= -1e+205)
		tmp = Float64(Float64(Float64(t * z) * -9.0) * y);
	elseif (t_1 <= 2e+115)
		tmp = fma(x, 2.0, Float64(Float64(b * a) * 27.0));
	else
		tmp = Float64(Float64(Float64(-9.0 * y) * t) * z);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+205], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 2e+115], N[(x * 2.0 + N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-9.0 * y), $MachinePrecision] * t), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.00000000000000002e205

   1. Initial program 91.3%

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

   3. Taylor expanded in y 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 88.5

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

   5. Applied rewrites 88.5%

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

   7. Applied rewrites 83.5%

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

   if -1.00000000000000002e205 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2e115

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 87.7

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

   5. Applied rewrites 87.7%

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

   if 2e115 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 78.0%

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

   3. Taylor expanded in y 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 71.4

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

   5. Applied rewrites 71.4%

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

   7. Applied rewrites 75.3%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq -1 \cdot 10^{+205}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(9 \cdot y\right)\right) \leq 2 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot y\right) \cdot t\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot \left(9 \cdot y\right) \leq 5 \cdot 10^{+217}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, -9, \mathsf{fma}\left(b \cdot a, 27, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* z (* 9.0 y)) 5e+217)
   (fma (* (* z y) t) -9.0 (fma (* b a) 27.0 (* 2.0 x)))
   (fma (* b a) 27.0 (fma (* (* -9.0 y) 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 tmp;
	if ((z * (9.0 * y)) <= 5e+217) {
		tmp = fma(((z * y) * t), -9.0, fma((b * a), 27.0, (2.0 * x)));
	} else {
		tmp = fma((b * a), 27.0, fma(((-9.0 * y) * 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)
	tmp = 0.0
	if (Float64(z * Float64(9.0 * y)) <= 5e+217)
		tmp = fma(Float64(Float64(z * y) * t), -9.0, fma(Float64(b * a), 27.0, Float64(2.0 * x)));
	else
		tmp = fma(Float64(b * a), 27.0, fma(Float64(Float64(-9.0 * y) * 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_] := If[LessEqual[N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision], 5e+217], N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * -9.0 + N[(N[(b * a), $MachinePrecision] * 27.0 + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * a), $MachinePrecision] * 27.0 + N[(N[(N[(-9.0 * y), $MachinePrecision] * t), $MachinePrecision] * z + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 5.00000000000000041e217

   1. Initial program 95.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 93.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 95.1

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 95.1

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

      14. lift-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

      18. associate-*l* N/A

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

      19. lift-*.f64 N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. lift-*.f64 N/A

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

      23. lower-fma.f64 95.6

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

   6. Applied rewrites 95.6%

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

   if 5.00000000000000041e217 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 87.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 86.9

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*l* N/A

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

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

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

      18. *-commutative N/A

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

      19. associate-*r* N/A

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

      20. lower-fma.f64 N/A

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

   4. Applied rewrites 99.8%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(9 \cdot y\right) \leq 5 \cdot 10^{+217}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, -9, \mathsf{fma}\left(b \cdot a, 27, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;9 \cdot y \leq -5 \cdot 10^{-64}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, -9 \cdot y, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* 9.0 y) -5e-64)
   (fma (* t z) (* -9.0 y) (fma (* b 27.0) a (* 2.0 x)))
   (fma (* b a) 27.0 (fma (* (* -9.0 y) 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 tmp;
	if ((9.0 * y) <= -5e-64) {
		tmp = fma((t * z), (-9.0 * y), fma((b * 27.0), a, (2.0 * x)));
	} else {
		tmp = fma((b * a), 27.0, fma(((-9.0 * y) * 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)
	tmp = 0.0
	if (Float64(9.0 * y) <= -5e-64)
		tmp = fma(Float64(t * z), Float64(-9.0 * y), fma(Float64(b * 27.0), a, Float64(2.0 * x)));
	else
		tmp = fma(Float64(b * a), 27.0, fma(Float64(Float64(-9.0 * y) * 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_] := If[LessEqual[N[(9.0 * y), $MachinePrecision], -5e-64], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision] + N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * a), $MachinePrecision] * 27.0 + N[(N[(N[(-9.0 * y), $MachinePrecision] * t), $MachinePrecision] * z + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y #s(literal 9 binary64)) < -5.00000000000000033e-64

   1. Initial program 94.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. 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 98.2%

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

   if -5.00000000000000033e-64 < (*.f64 y #s(literal 9 binary64))

   1. Initial program 94.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 94.9

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*l* N/A

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

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

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

      18. *-commutative N/A

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

      19. associate-*r* N/A

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

      20. lower-fma.f64 N/A

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

   4. Applied rewrites 96.3%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;9 \cdot y \leq -5 \cdot 10^{-64}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, -9 \cdot y, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(27 \cdot a\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -1e+31) t_1 (if (<= t_1 4e+59) (* 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 <= -1e+31) {
		tmp = t_1;
	} else if (t_1 <= 4e+59) {
		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 <= (-1d+31)) then
        tmp = t_1
    else if (t_1 <= 4d+59) 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 <= -1e+31) {
		tmp = t_1;
	} else if (t_1 <= 4e+59) {
		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 <= -1e+31:
		tmp = t_1
	elif t_1 <= 4e+59:
		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 <= -1e+31)
		tmp = t_1;
	elseif (t_1 <= 4e+59)
		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 <= -1e+31)
		tmp = t_1;
	elseif (t_1 <= 4e+59)
		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, -1e+31], t$95$1, If[LessEqual[t$95$1, 4e+59], 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) < -9.9999999999999996e30 or 3.99999999999999989e59 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 94.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 69.3

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

   5. Applied rewrites 69.3%

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

   7. Applied rewrites 69.3%

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

   if -9.9999999999999996e30 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 3.99999999999999989e59

   1. Initial program 94.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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 53.4

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

   5. Applied rewrites 53.4%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(27 \cdot a\right) \leq -1 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;b \cdot \left(27 \cdot a\right) \leq 4 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 92.7% accurate, 1.1× speedup

Math

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

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
 (fma (* b a) 27.0 (fma (* (* -9.0 y) 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) {
	return fma((b * a), 27.0, fma(((-9.0 * y) * t), z, (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 fma(Float64(b * a), 27.0, fma(Float64(Float64(-9.0 * y) * t), z, Float64(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[(N[(b * a), $MachinePrecision] * 27.0 + N[(N[(N[(-9.0 * y), $MachinePrecision] * t), $MachinePrecision] * z + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.6%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. *-commutative N/A

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

   7. associate-*r* N/A

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

   8. lower-fma.f64 N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 94.6

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

   11. lift--.f64 N/A

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

   12. sub-neg N/A

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

   13. +-commutative N/A

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

   14. lift-*.f64 N/A

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

   15. lift-*.f64 N/A

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

   16. associate-*l* N/A

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

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

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

   18. *-commutative N/A

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

   19. associate-*r* N/A

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

   20. lower-fma.f64 N/A

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

4. Applied rewrites 95.0%

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

Alternative 13: 30.9% 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 94.6%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
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 32.1

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

5. Applied rewrites 32.1%

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

6. Final simplification 32.1%

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

Developer Target 1: 94.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (< y 7.590524218811189e-161)
   (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y < 7.590524218811189d-161) then
        tmp = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + (a * (27.0d0 * b))
    else
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (t * z)))) + ((a * 27.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y < 7.590524218811189e-161:
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b))
	else:
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y < 7.590524218811189e-161)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(t * z)))) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y < 7.590524218811189e-161)
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	else
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Less[y, 7.590524218811189e-161], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024235 
(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)))