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

Percentage Accurate: 95.6% → 98.5%

Time: 13.8s

Alternatives: 14

Speedup: 0.9×

• 27.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\\ \mathbf{if}\;z \leq 1.25 \cdot 10^{-69}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, -9 \cdot y, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot y, -9 \cdot z, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (* b 27.0) a (* 2.0 x))))
   (if (<= z 1.25e-69)
     (fma (* t z) (* -9.0 y) t_1)
     (fma (* t y) (* -9.0 z) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b * 27.0), a, (2.0 * x));
	double tmp;
	if (z <= 1.25e-69) {
		tmp = fma((t * z), (-9.0 * y), t_1);
	} else {
		tmp = fma((t * y), (-9.0 * z), t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(Float64(b * 27.0), a, Float64(2.0 * x))
	tmp = 0.0
	if (z <= 1.25e-69)
		tmp = fma(Float64(t * z), Float64(-9.0 * y), t_1);
	else
		tmp = fma(Float64(t * y), Float64(-9.0 * z), t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 1.25e-69], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(t * y), $MachinePrecision] * N[(-9.0 * z), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 1.25000000000000008e-69

   1. Initial program 97.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 95.5%

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

   if 1.25000000000000008e-69 < z

   1. Initial program 92.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. associate-*r* N/A

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

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

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

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

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

      17. lower-*.f64 N/A

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

      18. metadata-eval N/A

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

   4. Applied rewrites 96.0%

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

Alternative 2: 57.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(\left(-9 \cdot z\right) \cdot y\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+58}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+154}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{elif}\;t\_1 \leq 10^{+218} \lor \neg \left(t\_1 \leq 4 \cdot 10^{+288}\right):\\ \;\;\;\;\left(\left(y \cdot z\right) \cdot -9\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* x 2.0) (* (* (* y 9.0) z) t))))
   (if (<= t_1 (- INFINITY))
     (* (* (* -9.0 z) y) t)
     (if (<= t_1 -2e+58)
       (* 2.0 x)
       (if (<= t_1 5e+154)
         (* (* 27.0 b) a)
         (if (or (<= t_1 1e+218) (not (<= t_1 4e+288)))
           (* (* (* y z) -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 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((-9.0 * z) * y) * t;
	} else if (t_1 <= -2e+58) {
		tmp = 2.0 * x;
	} else if (t_1 <= 5e+154) {
		tmp = (27.0 * b) * a;
	} else if ((t_1 <= 1e+218) || !(t_1 <= 4e+288)) {
		tmp = ((y * z) * -9.0) * t;
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((-9.0 * z) * y) * t;
	} else if (t_1 <= -2e+58) {
		tmp = 2.0 * x;
	} else if (t_1 <= 5e+154) {
		tmp = (27.0 * b) * a;
	} else if ((t_1 <= 1e+218) || !(t_1 <= 4e+288)) {
		tmp = ((y * z) * -9.0) * t;
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (((y * 9.0) * z) * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((-9.0 * z) * y) * t
	elif t_1 <= -2e+58:
		tmp = 2.0 * x
	elif t_1 <= 5e+154:
		tmp = (27.0 * b) * a
	elif (t_1 <= 1e+218) or not (t_1 <= 4e+288):
		tmp = ((y * z) * -9.0) * t
	else:
		tmp = 2.0 * x
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(-9.0 * z) * y) * t);
	elseif (t_1 <= -2e+58)
		tmp = Float64(2.0 * x);
	elseif (t_1 <= 5e+154)
		tmp = Float64(Float64(27.0 * b) * a);
	elseif ((t_1 <= 1e+218) || !(t_1 <= 4e+288))
		tmp = Float64(Float64(Float64(y * z) * -9.0) * t);
	else
		tmp = Float64(2.0 * x);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (((y * 9.0) * z) * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((-9.0 * z) * y) * t;
	elseif (t_1 <= -2e+58)
		tmp = 2.0 * x;
	elseif (t_1 <= 5e+154)
		tmp = (27.0 * b) * a;
	elseif ((t_1 <= 1e+218) || ~((t_1 <= 4e+288)))
		tmp = ((y * z) * -9.0) * t;
	else
		tmp = 2.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(-9.0 * z), $MachinePrecision] * y), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, -2e+58], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$1, 5e+154], N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision], If[Or[LessEqual[t$95$1, 1e+218], N[Not[LessEqual[t$95$1, 4e+288]], $MachinePrecision]], N[(N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision] * t), $MachinePrecision], N[(2.0 * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 86.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 15.1

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

   5. Applied rewrites 15.1%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 83.3%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 87.1%

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

   13. Applied rewrites 87.1%

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

   if -inf.0 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -1.99999999999999989e58 or 1.00000000000000008e218 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 4e288

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 80.6

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

   5. Applied rewrites 80.6%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 75.4%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 62.5%

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

   if -1.99999999999999989e58 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 5.00000000000000004e154

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 84.8

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

   5. Applied rewrites 84.8%

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

   7. Applied rewrites 84.8%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 63.9%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 63.9%

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

   if 5.00000000000000004e154 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 1.00000000000000008e218 or 4e288 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 88.4%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 36.2

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

   5. Applied rewrites 36.2%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 86.4%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 68.2%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -\infty:\\ \;\;\;\;\left(\left(-9 \cdot z\right) \cdot y\right) \cdot t\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -2 \cdot 10^{+58}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+154}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 10^{+218} \lor \neg \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 4 \cdot 10^{+288}\right):\\ \;\;\;\;\left(\left(y \cdot z\right) \cdot -9\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(-9 \cdot z\right) \cdot y\right) \cdot t\\ t_2 := x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+58}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+154}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{elif}\;t\_2 \leq 10^{+218} \lor \neg \left(t\_2 \leq 4 \cdot 10^{+288}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* -9.0 z) y) t)) (t_2 (- (* x 2.0) (* (* (* y 9.0) z) t))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e+58)
       (* 2.0 x)
       (if (<= t_2 5e+154)
         (* (* 27.0 b) a)
         (if (or (<= t_2 1e+218) (not (<= t_2 4e+288))) t_1 (* 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 = ((-9.0 * z) * y) * t;
	double t_2 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e+58) {
		tmp = 2.0 * x;
	} else if (t_2 <= 5e+154) {
		tmp = (27.0 * b) * a;
	} else if ((t_2 <= 1e+218) || !(t_2 <= 4e+288)) {
		tmp = t_1;
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((-9.0 * z) * y) * t;
	double t_2 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e+58) {
		tmp = 2.0 * x;
	} else if (t_2 <= 5e+154) {
		tmp = (27.0 * b) * a;
	} else if ((t_2 <= 1e+218) || !(t_2 <= 4e+288)) {
		tmp = t_1;
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = ((-9.0 * z) * y) * t
	t_2 = (x * 2.0) - (((y * 9.0) * z) * t)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e+58:
		tmp = 2.0 * x
	elif t_2 <= 5e+154:
		tmp = (27.0 * b) * a
	elif (t_2 <= 1e+218) or not (t_2 <= 4e+288):
		tmp = t_1
	else:
		tmp = 2.0 * x
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(-9.0 * z) * y) * t)
	t_2 = Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e+58)
		tmp = Float64(2.0 * x);
	elseif (t_2 <= 5e+154)
		tmp = Float64(Float64(27.0 * b) * a);
	elseif ((t_2 <= 1e+218) || !(t_2 <= 4e+288))
		tmp = t_1;
	else
		tmp = Float64(2.0 * x);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((-9.0 * z) * y) * t;
	t_2 = (x * 2.0) - (((y * 9.0) * z) * t);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e+58)
		tmp = 2.0 * x;
	elseif (t_2 <= 5e+154)
		tmp = (27.0 * b) * a;
	elseif ((t_2 <= 1e+218) || ~((t_2 <= 4e+288)))
		tmp = t_1;
	else
		tmp = 2.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(-9.0 * z), $MachinePrecision] * y), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e+58], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$2, 5e+154], N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision], If[Or[LessEqual[t$95$2, 1e+218], N[Not[LessEqual[t$95$2, 4e+288]], $MachinePrecision]], t$95$1, N[(2.0 * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -inf.0 or 5.00000000000000004e154 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 1.00000000000000008e218 or 4e288 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 87.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 28.4

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

   5. Applied rewrites 28.4%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 85.3%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 75.2%

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

   13. Applied rewrites 75.1%

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

   if -inf.0 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -1.99999999999999989e58 or 1.00000000000000008e218 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 4e288

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 80.6

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

   5. Applied rewrites 80.6%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 75.4%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 62.5%

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

   if -1.99999999999999989e58 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 5.00000000000000004e154

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 84.8

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

   5. Applied rewrites 84.8%

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

   7. Applied rewrites 84.8%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 63.9%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 63.9%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -\infty:\\ \;\;\;\;\left(\left(-9 \cdot z\right) \cdot y\right) \cdot t\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -2 \cdot 10^{+58}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+154}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 10^{+218} \lor \neg \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 4 \cdot 10^{+288}\right):\\ \;\;\;\;\left(\left(-9 \cdot z\right) \cdot y\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(-9 \cdot z\right) \cdot y\right) \cdot t\\ t_2 := x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+58}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+154}:\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{elif}\;t\_2 \leq 10^{+218}:\\ \;\;\;\;\left(\left(y \cdot -9\right) \cdot z\right) \cdot t\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+288}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* -9.0 z) y) t)) (t_2 (- (* x 2.0) (* (* (* y 9.0) z) t))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e+58)
       (* 2.0 x)
       (if (<= t_2 5e+154)
         (* (* 27.0 b) a)
         (if (<= t_2 1e+218)
           (* (* (* y -9.0) z) t)
           (if (<= t_2 4e+288) (* 2.0 x) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((-9.0 * z) * y) * t;
	double t_2 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e+58) {
		tmp = 2.0 * x;
	} else if (t_2 <= 5e+154) {
		tmp = (27.0 * b) * a;
	} else if (t_2 <= 1e+218) {
		tmp = ((y * -9.0) * z) * t;
	} else if (t_2 <= 4e+288) {
		tmp = 2.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((-9.0 * z) * y) * t;
	double t_2 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e+58) {
		tmp = 2.0 * x;
	} else if (t_2 <= 5e+154) {
		tmp = (27.0 * b) * a;
	} else if (t_2 <= 1e+218) {
		tmp = ((y * -9.0) * z) * t;
	} else if (t_2 <= 4e+288) {
		tmp = 2.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = ((-9.0 * z) * y) * t
	t_2 = (x * 2.0) - (((y * 9.0) * z) * t)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e+58:
		tmp = 2.0 * x
	elif t_2 <= 5e+154:
		tmp = (27.0 * b) * a
	elif t_2 <= 1e+218:
		tmp = ((y * -9.0) * z) * t
	elif t_2 <= 4e+288:
		tmp = 2.0 * x
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(-9.0 * z) * y) * t)
	t_2 = Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e+58)
		tmp = Float64(2.0 * x);
	elseif (t_2 <= 5e+154)
		tmp = Float64(Float64(27.0 * b) * a);
	elseif (t_2 <= 1e+218)
		tmp = Float64(Float64(Float64(y * -9.0) * z) * t);
	elseif (t_2 <= 4e+288)
		tmp = Float64(2.0 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((-9.0 * z) * y) * t;
	t_2 = (x * 2.0) - (((y * 9.0) * z) * t);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e+58)
		tmp = 2.0 * x;
	elseif (t_2 <= 5e+154)
		tmp = (27.0 * b) * a;
	elseif (t_2 <= 1e+218)
		tmp = ((y * -9.0) * z) * t;
	elseif (t_2 <= 4e+288)
		tmp = 2.0 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(-9.0 * z), $MachinePrecision] * y), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e+58], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$2, 5e+154], N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t$95$2, 1e+218], N[(N[(N[(y * -9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$2, 4e+288], N[(2.0 * x), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -inf.0 or 4e288 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 83.4%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 21.7

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

   5. Applied rewrites 21.7%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 83.3%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 83.5%

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

   13. Applied rewrites 83.5%

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

   if -inf.0 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -1.99999999999999989e58 or 1.00000000000000008e218 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 4e288

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 80.6

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

   5. Applied rewrites 80.6%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 75.4%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 62.5%

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

   if -1.99999999999999989e58 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 5.00000000000000004e154

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 84.8

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

   5. Applied rewrites 84.8%

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

   7. Applied rewrites 84.8%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 63.9%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 63.9%

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

   if 5.00000000000000004e154 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 1.00000000000000008e218

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 46.2

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

   5. Applied rewrites 46.2%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 90.6%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 52.8%

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

   13. Applied rewrites 52.7%

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

Alternative 5: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot y\right) \cdot t, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+223}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(27 \cdot b\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, -9 \cdot y, \left(a \cdot b\right) \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -5e+142)
     (fma -9.0 (* (* z y) t) (* (* b a) 27.0))
     (if (<= t_1 4e+223)
       (fma 2.0 x (* (* 27.0 b) a))
       (fma (* t z) (* -9.0 y) (* (* a b) 27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -5e+142) {
		tmp = fma(-9.0, ((z * y) * t), ((b * a) * 27.0));
	} else if (t_1 <= 4e+223) {
		tmp = fma(2.0, x, ((27.0 * b) * a));
	} else {
		tmp = fma((t * z), (-9.0 * y), ((a * b) * 27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -5e+142)
		tmp = fma(-9.0, Float64(Float64(z * y) * t), Float64(Float64(b * a) * 27.0));
	elseif (t_1 <= 4e+223)
		tmp = fma(2.0, x, Float64(Float64(27.0 * b) * a));
	else
		tmp = fma(Float64(t * z), Float64(-9.0 * y), Float64(Float64(a * b) * 27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+142], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] + N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+223], N[(2.0 * x + N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000001e142

   1. Initial program 88.5%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 82.3

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

   5. Applied rewrites 82.3%

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

   if -5.0000000000000001e142 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 4.00000000000000019e223

   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. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 88.3

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

   5. Applied rewrites 88.3%

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

   7. Applied rewrites 88.3%

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

   if 4.00000000000000019e223 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 89.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. 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 87.2%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 87.2

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

   7. Applied rewrites 87.2%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot y\right) \cdot t, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{elif}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 4 \cdot 10^{+223}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(27 \cdot b\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, -9 \cdot y, \left(a \cdot b\right) \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot y\right) \cdot t, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+231}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(27 \cdot b\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot y, -9 \cdot z, \left(a \cdot b\right) \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -5e+142)
     (fma -9.0 (* (* z y) t) (* (* b a) 27.0))
     (if (<= t_1 5e+231)
       (fma 2.0 x (* (* 27.0 b) a))
       (fma (* t y) (* -9.0 z) (* (* a b) 27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -5e+142) {
		tmp = fma(-9.0, ((z * y) * t), ((b * a) * 27.0));
	} else if (t_1 <= 5e+231) {
		tmp = fma(2.0, x, ((27.0 * b) * a));
	} else {
		tmp = fma((t * y), (-9.0 * z), ((a * b) * 27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -5e+142)
		tmp = fma(-9.0, Float64(Float64(z * y) * t), Float64(Float64(b * a) * 27.0));
	elseif (t_1 <= 5e+231)
		tmp = fma(2.0, x, Float64(Float64(27.0 * b) * a));
	else
		tmp = fma(Float64(t * y), Float64(-9.0 * z), Float64(Float64(a * b) * 27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+142], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] + N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+231], N[(2.0 * x + N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(t * y), $MachinePrecision] * N[(-9.0 * z), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000001e142

   1. Initial program 88.5%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 82.3

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

   5. Applied rewrites 82.3%

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

   if -5.0000000000000001e142 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5.00000000000000028e231

   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. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 88.4

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

   5. Applied rewrites 88.4%

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

   7. Applied rewrites 88.4%

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

   if 5.00000000000000028e231 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. associate-*r* N/A

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

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

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

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

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

      17. lower-*.f64 N/A

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

      18. metadata-eval N/A

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

   4. Applied rewrites 94.2%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 94.2

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

   7. Applied rewrites 94.2%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot y\right) \cdot t, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{elif}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+231}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(27 \cdot b\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot y, -9 \cdot z, \left(a \cdot b\right) \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot y\right) \cdot t, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+231}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(27 \cdot b\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot z\right) \cdot y\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -5e+142)
     (fma -9.0 (* (* z y) t) (* (* b a) 27.0))
     (if (<= t_1 5e+231)
       (fma 2.0 x (* (* 27.0 b) a))
       (* (* (* -9.0 z) y) t)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -5e+142) {
		tmp = fma(-9.0, ((z * y) * t), ((b * a) * 27.0));
	} else if (t_1 <= 5e+231) {
		tmp = fma(2.0, x, ((27.0 * b) * a));
	} else {
		tmp = ((-9.0 * z) * y) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -5e+142)
		tmp = fma(-9.0, Float64(Float64(z * y) * t), Float64(Float64(b * a) * 27.0));
	elseif (t_1 <= 5e+231)
		tmp = fma(2.0, x, Float64(Float64(27.0 * b) * a));
	else
		tmp = Float64(Float64(Float64(-9.0 * z) * y) * t);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+142], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] + N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+231], N[(2.0 * x + N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-9.0 * z), $MachinePrecision] * y), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000001e142

   1. Initial program 88.5%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 82.3

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

   5. Applied rewrites 82.3%

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

   if -5.0000000000000001e142 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5.00000000000000028e231

   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. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 88.4

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

   5. Applied rewrites 88.4%

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

   7. Applied rewrites 88.4%

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

   if 5.00000000000000028e231 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 10.6

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

   5. Applied rewrites 10.6%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 85.7%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 91.5%

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

   13. Applied rewrites 91.6%

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

Alternative 8: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+142}:\\ \;\;\;\;\left(\left(y \cdot z\right) \cdot -9\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+231}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(27 \cdot b\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot z\right) \cdot y\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -5e+142)
     (* (* (* y z) -9.0) t)
     (if (<= t_1 5e+231)
       (fma 2.0 x (* (* 27.0 b) a))
       (* (* (* -9.0 z) y) t)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -5e+142) {
		tmp = ((y * z) * -9.0) * t;
	} else if (t_1 <= 5e+231) {
		tmp = fma(2.0, x, ((27.0 * b) * a));
	} else {
		tmp = ((-9.0 * z) * y) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -5e+142)
		tmp = Float64(Float64(Float64(y * z) * -9.0) * t);
	elseif (t_1 <= 5e+231)
		tmp = fma(2.0, x, Float64(Float64(27.0 * b) * a));
	else
		tmp = Float64(Float64(Float64(-9.0 * z) * y) * t);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+142], N[(N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 5e+231], N[(2.0 * x + N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-9.0 * z), $MachinePrecision] * y), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000001e142

   1. Initial program 88.5%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 28.2

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

   5. Applied rewrites 28.2%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 90.4%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 76.4%

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

   if -5.0000000000000001e142 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5.00000000000000028e231

   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. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 88.4

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

   5. Applied rewrites 88.4%

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

   7. Applied rewrites 88.4%

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

   if 5.00000000000000028e231 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 10.6

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

   5. Applied rewrites 10.6%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 85.7%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 91.5%

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

   13. Applied rewrites 91.6%

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

Alternative 9: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+117} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+49}\right):\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (or (<= t_1 -1e+117) (not (<= t_1 5e+49))) (* (* 27.0 b) a) (* 2.0 x))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if ((t_1 <= -1e+117) || !(t_1 <= 5e+49)) {
		tmp = (27.0 * b) * a;
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    if ((t_1 <= (-1d+117)) .or. (.not. (t_1 <= 5d+49))) then
        tmp = (27.0d0 * b) * a
    else
        tmp = 2.0d0 * x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if ((t_1 <= -1e+117) || !(t_1 <= 5e+49)) {
		tmp = (27.0 * b) * a;
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if (t_1 <= -1e+117) or not (t_1 <= 5e+49):
		tmp = (27.0 * b) * a
	else:
		tmp = 2.0 * x
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if ((t_1 <= -1e+117) || !(t_1 <= 5e+49))
		tmp = Float64(Float64(27.0 * b) * a);
	else
		tmp = Float64(2.0 * x);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	tmp = 0.0;
	if ((t_1 <= -1e+117) || ~((t_1 <= 5e+49)))
		tmp = (27.0 * b) * a;
	else
		tmp = 2.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+117], N[Not[LessEqual[t$95$1, 5e+49]], $MachinePrecision]], N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision], N[(2.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.00000000000000005e117 or 5.0000000000000004e49 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 94.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 79.5

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

   5. Applied rewrites 79.5%

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

   7. Applied rewrites 79.5%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 68.5%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 68.5%

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

   if -1.00000000000000005e117 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 5.0000000000000004e49

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 55.5

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

   5. Applied rewrites 55.5%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 82.6%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 45.9%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -1 \cdot 10^{+117} \lor \neg \left(\left(a \cdot 27\right) \cdot b \leq 5 \cdot 10^{+49}\right):\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+117} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+49}\right):\\ \;\;\;\;\left(27 \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (or (<= t_1 -1e+117) (not (<= t_1 5e+49))) (* (* 27.0 a) b) (* 2.0 x))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if ((t_1 <= -1e+117) || !(t_1 <= 5e+49)) {
		tmp = (27.0 * a) * b;
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    if ((t_1 <= (-1d+117)) .or. (.not. (t_1 <= 5d+49))) then
        tmp = (27.0d0 * a) * b
    else
        tmp = 2.0d0 * x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if ((t_1 <= -1e+117) || !(t_1 <= 5e+49)) {
		tmp = (27.0 * a) * b;
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if (t_1 <= -1e+117) or not (t_1 <= 5e+49):
		tmp = (27.0 * a) * b
	else:
		tmp = 2.0 * x
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if ((t_1 <= -1e+117) || !(t_1 <= 5e+49))
		tmp = Float64(Float64(27.0 * a) * b);
	else
		tmp = Float64(2.0 * x);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	tmp = 0.0;
	if ((t_1 <= -1e+117) || ~((t_1 <= 5e+49)))
		tmp = (27.0 * a) * b;
	else
		tmp = 2.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+117], N[Not[LessEqual[t$95$1, 5e+49]], $MachinePrecision]], N[(N[(27.0 * a), $MachinePrecision] * b), $MachinePrecision], N[(2.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.00000000000000005e117 or 5.0000000000000004e49 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 94.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 79.5

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

   5. Applied rewrites 79.5%

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

   7. Applied rewrites 79.5%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 68.5%

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

   12. Applied rewrites 68.6%

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

   if -1.00000000000000005e117 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 5.0000000000000004e49

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 55.5

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

   5. Applied rewrites 55.5%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 82.6%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 45.9%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -1 \cdot 10^{+117} \lor \neg \left(\left(a \cdot 27\right) \cdot b \leq 5 \cdot 10^{+49}\right):\\ \;\;\;\;\left(27 \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\\ \mathbf{if}\;z \leq 10^{-69}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-9 \cdot z\right) \cdot t, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot y, -9 \cdot z, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (* b 27.0) a (* 2.0 x))))
   (if (<= z 1e-69)
     (fma y (* (* -9.0 z) t) t_1)
     (fma (* t y) (* -9.0 z) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b * 27.0), a, (2.0 * x));
	double tmp;
	if (z <= 1e-69) {
		tmp = fma(y, ((-9.0 * z) * t), t_1);
	} else {
		tmp = fma((t * y), (-9.0 * z), t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(Float64(b * 27.0), a, Float64(2.0 * x))
	tmp = 0.0
	if (z <= 1e-69)
		tmp = fma(y, Float64(Float64(-9.0 * z) * t), t_1);
	else
		tmp = fma(Float64(t * y), Float64(-9.0 * z), t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 1e-69], N[(y * N[(N[(-9.0 * z), $MachinePrecision] * t), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(t * y), $MachinePrecision] * N[(-9.0 * z), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 9.9999999999999996e-70

   1. Initial program 97.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

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

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

      12. associate-*l* N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

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

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

      17. lower-*.f64 N/A

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

      18. metadata-eval N/A

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

   4. Applied rewrites 95.4%

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

   if 9.9999999999999996e-70 < z

   1. Initial program 92.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. associate-*r* N/A

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

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

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

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

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

      17. lower-*.f64 N/A

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

      18. metadata-eval N/A

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

   4. Applied rewrites 96.0%

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

Alternative 12: 98.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-112}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-9 \cdot z\right) \cdot t, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right)\\ \end{array} \end{array} \]

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 2e-112)
   (fma y (* (* -9.0 z) t) (fma (* b 27.0) a (* 2.0 x)))
   (fma (* b 27.0) a (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 <= 2e-112) {
		tmp = fma(y, ((-9.0 * z) * t), fma((b * 27.0), a, (2.0 * x)));
	} else {
		tmp = fma((b * 27.0), a, 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 (z <= 2e-112)
		tmp = fma(y, Float64(Float64(-9.0 * z) * t), fma(Float64(b * 27.0), a, Float64(2.0 * x)));
	else
		tmp = fma(Float64(b * 27.0), a, 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[z, 2e-112], N[(y * N[(N[(-9.0 * z), $MachinePrecision] * t), $MachinePrecision] + N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * 27.0), $MachinePrecision] * a + N[(N[(N[(-9.0 * y), $MachinePrecision] * t), $MachinePrecision] * z + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.9999999999999999e-112

   1. Initial program 97.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

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

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

      12. associate-*l* N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

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

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

      17. lower-*.f64 N/A

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

      18. metadata-eval N/A

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

   4. Applied rewrites 95.2%

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

   if 1.9999999999999999e-112 < z

   1. Initial program 92.9%

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

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 94.1

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

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

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

      17. *-commutative N/A

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

      18. associate-*r* N/A

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

      19. lower-fma.f64 N/A

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

   4. Applied rewrites 96.4%

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

Alternative 13: 97.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 9.5 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-9 \cdot z\right) \cdot t, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot y, -9 \cdot z, \left(a \cdot b\right) \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 9.5e+96)
   (fma y (* (* -9.0 z) t) (fma (* b 27.0) a (* 2.0 x)))
   (fma (* t y) (* -9.0 z) (* (* a b) 27.0))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 9.5e+96) {
		tmp = fma(y, ((-9.0 * z) * t), fma((b * 27.0), a, (2.0 * x)));
	} else {
		tmp = fma((t * y), (-9.0 * z), ((a * b) * 27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 9.5e+96)
		tmp = fma(y, Float64(Float64(-9.0 * z) * t), fma(Float64(b * 27.0), a, Float64(2.0 * x)));
	else
		tmp = fma(Float64(t * y), Float64(-9.0 * z), Float64(Float64(a * b) * 27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 9.5e+96], N[(y * N[(N[(-9.0 * z), $MachinePrecision] * t), $MachinePrecision] + N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * y), $MachinePrecision] * N[(-9.0 * z), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 9.50000000000000089e96

   1. Initial program 96.6%

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

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

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

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

      12. associate-*l* N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

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

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

      17. lower-*.f64 N/A

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

      18. metadata-eval N/A

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

   4. Applied rewrites 95.7%

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

   if 9.50000000000000089e96 < z

   1. Initial program 90.6%

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

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. associate-*r* N/A

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

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

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

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

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

      17. lower-*.f64 N/A

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

      18. metadata-eval N/A

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

   4. Applied rewrites 95.2%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 77.5

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

   7. Applied rewrites 77.5%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 9.5 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-9 \cdot z\right) \cdot t, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot y, -9 \cdot z, \left(a \cdot b\right) \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.0% 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 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. Taylor expanded in y around 0

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

   1. lower-fma.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 65.6

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

5. Applied rewrites 65.6%

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

6. Taylor expanded in t around inf

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

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

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

   2. metadata-eval N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

8. Applied rewrites 82.2%

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

9. Taylor expanded in x around inf

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

11. Applied rewrites 31.4%

    \[\leadsto 2 \cdot \color{blue}{x} \]
12. Add Preprocessing

Developer Target 1: 95.3% 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 2024324 
(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)))