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

Percentage Accurate: 95.3% → 98.9%

Time: 22.2s

Alternatives: 18

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: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 8.8 \cdot 10^{-20}:\\ \;\;\;\;\mathsf{fma}\left(-y, \left(t \cdot z\right) \cdot 9, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot a, b, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right)\\ \end{array} \end{array} \]

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 8.8e-20)
   (fma (- y) (* (* t z) 9.0) (fma (* b 27.0) a (* 2.0 x)))
   (fma (* 27.0 a) b (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 <= 8.8e-20) {
		tmp = fma(-y, ((t * z) * 9.0), fma((b * 27.0), a, (2.0 * x)));
	} else {
		tmp = fma((27.0 * a), b, 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 <= 8.8e-20)
		tmp = fma(Float64(-y), Float64(Float64(t * z) * 9.0), fma(Float64(b * 27.0), a, Float64(2.0 * x)));
	else
		tmp = fma(Float64(27.0 * a), b, 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, 8.8e-20], N[((-y) * N[(N[(t * z), $MachinePrecision] * 9.0), $MachinePrecision] + N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * a), $MachinePrecision] * b + 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 < 8.79999999999999964e-20

   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. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

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

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

   4. Applied rewrites 97.2%

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

   if 8.79999999999999964e-20 < z

   1. Initial program 89.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 92.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 92.0

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

   4. Applied rewrites 98.4%

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

Alternative 2: 59.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+174}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+108}:\\ \;\;\;\;\left(b \cdot 27\right) \cdot a\\ \mathbf{elif}\;t\_1 \leq 10^{+293}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* x 2.0) (* (* (* y 9.0) z) t))))
   (if (<= t_1 (- INFINITY))
     (* (* -9.0 z) (* t y))
     (if (<= t_1 -5e+174)
       (* 2.0 x)
       (if (<= t_1 5e+108)
         (* (* b 27.0) a)
         (if (<= t_1 1e+293) (* 2.0 x) (* (* (* -9.0 t) z) y)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (-9.0 * z) * (t * y);
	} else if (t_1 <= -5e+174) {
		tmp = 2.0 * x;
	} else if (t_1 <= 5e+108) {
		tmp = (b * 27.0) * a;
	} else if (t_1 <= 1e+293) {
		tmp = 2.0 * x;
	} else {
		tmp = ((-9.0 * t) * z) * y;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (-9.0 * z) * (t * y);
	} else if (t_1 <= -5e+174) {
		tmp = 2.0 * x;
	} else if (t_1 <= 5e+108) {
		tmp = (b * 27.0) * a;
	} else if (t_1 <= 1e+293) {
		tmp = 2.0 * x;
	} else {
		tmp = ((-9.0 * t) * z) * y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (((y * 9.0) * z) * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (-9.0 * z) * (t * y)
	elif t_1 <= -5e+174:
		tmp = 2.0 * x
	elif t_1 <= 5e+108:
		tmp = (b * 27.0) * a
	elif t_1 <= 1e+293:
		tmp = 2.0 * x
	else:
		tmp = ((-9.0 * t) * z) * y
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(-9.0 * z) * Float64(t * y));
	elseif (t_1 <= -5e+174)
		tmp = Float64(2.0 * x);
	elseif (t_1 <= 5e+108)
		tmp = Float64(Float64(b * 27.0) * a);
	elseif (t_1 <= 1e+293)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(Float64(Float64(-9.0 * t) * z) * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (((y * 9.0) * z) * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (-9.0 * z) * (t * y);
	elseif (t_1 <= -5e+174)
		tmp = 2.0 * x;
	elseif (t_1 <= 5e+108)
		tmp = (b * 27.0) * a;
	elseif (t_1 <= 1e+293)
		tmp = 2.0 * x;
	else
		tmp = ((-9.0 * t) * z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(-9.0 * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+174], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$1, 5e+108], N[(N[(b * 27.0), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t$95$1, 1e+293], N[(2.0 * x), $MachinePrecision], N[(N[(N[(-9.0 * t), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 78.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 86.1

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 86.1

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

   4. Applied rewrites 99.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 99.8

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-fma.f64 N/A

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

      8. associate-+l+ N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-*l* N/A

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

      23. lift-*.f64 N/A

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

      24. +-commutative N/A

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

   6. Applied rewrites 78.7%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 86.1

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

   9. Applied rewrites 86.1%

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

   11. Applied rewrites 96.5%

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

   if -inf.0 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.9999999999999997e174 or 4.99999999999999991e108 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 9.9999999999999992e292

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

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

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

   4. Applied rewrites 90.9%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 56.6

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

   7. Applied rewrites 56.6%

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

   if -4.9999999999999997e174 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 4.99999999999999991e108

   1. Initial program 99.0%

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

   3. Taylor expanded in 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 80.2

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

   5. Applied rewrites 80.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 54.2%

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

   10. Applied rewrites 54.1%

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

   if 9.9999999999999992e292 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 76.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 79.6

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 79.6

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

   4. Applied rewrites 87.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 87.2

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-fma.f64 N/A

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

      8. associate-+l+ N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-*l* N/A

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

      23. lift-*.f64 N/A

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

      24. +-commutative N/A

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

   6. Applied rewrites 82.9%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 83.2

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

   9. Applied rewrites 83.2%

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

   11. Applied rewrites 80.4%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -\infty:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+174}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+108}:\\ \;\;\;\;\left(b \cdot 27\right) \cdot a\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 10^{+293}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-9 \cdot t\right) \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+174}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+108}:\\ \;\;\;\;\left(b \cdot 27\right) \cdot a\\ \mathbf{elif}\;t\_1 \leq 10^{+293}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* x 2.0) (* (* (* y 9.0) z) t))))
   (if (<= t_1 (- INFINITY))
     (* (* -9.0 z) (* t y))
     (if (<= t_1 -5e+174)
       (* 2.0 x)
       (if (<= t_1 5e+108)
         (* (* b 27.0) a)
         (if (<= t_1 1e+293) (* 2.0 x) (* (* t z) (* -9.0 y))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (-9.0 * z) * (t * y);
	} else if (t_1 <= -5e+174) {
		tmp = 2.0 * x;
	} else if (t_1 <= 5e+108) {
		tmp = (b * 27.0) * a;
	} else if (t_1 <= 1e+293) {
		tmp = 2.0 * x;
	} else {
		tmp = (t * z) * (-9.0 * y);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (-9.0 * z) * (t * y);
	} else if (t_1 <= -5e+174) {
		tmp = 2.0 * x;
	} else if (t_1 <= 5e+108) {
		tmp = (b * 27.0) * a;
	} else if (t_1 <= 1e+293) {
		tmp = 2.0 * x;
	} else {
		tmp = (t * z) * (-9.0 * y);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (((y * 9.0) * z) * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (-9.0 * z) * (t * y)
	elif t_1 <= -5e+174:
		tmp = 2.0 * x
	elif t_1 <= 5e+108:
		tmp = (b * 27.0) * a
	elif t_1 <= 1e+293:
		tmp = 2.0 * x
	else:
		tmp = (t * z) * (-9.0 * y)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(-9.0 * z) * Float64(t * y));
	elseif (t_1 <= -5e+174)
		tmp = Float64(2.0 * x);
	elseif (t_1 <= 5e+108)
		tmp = Float64(Float64(b * 27.0) * a);
	elseif (t_1 <= 1e+293)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(Float64(t * z) * Float64(-9.0 * y));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (((y * 9.0) * z) * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (-9.0 * z) * (t * y);
	elseif (t_1 <= -5e+174)
		tmp = 2.0 * x;
	elseif (t_1 <= 5e+108)
		tmp = (b * 27.0) * a;
	elseif (t_1 <= 1e+293)
		tmp = 2.0 * x;
	else
		tmp = (t * z) * (-9.0 * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(-9.0 * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+174], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$1, 5e+108], N[(N[(b * 27.0), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t$95$1, 1e+293], N[(2.0 * x), $MachinePrecision], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 78.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 86.1

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 86.1

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

   4. Applied rewrites 99.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 99.8

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-fma.f64 N/A

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

      8. associate-+l+ N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-*l* N/A

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

      23. lift-*.f64 N/A

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

      24. +-commutative N/A

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

   6. Applied rewrites 78.7%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 86.1

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

   9. Applied rewrites 86.1%

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

   11. Applied rewrites 96.5%

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

   if -inf.0 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.9999999999999997e174 or 4.99999999999999991e108 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 9.9999999999999992e292

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

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

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

   4. Applied rewrites 90.9%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 56.6

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

   7. Applied rewrites 56.6%

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

   if -4.9999999999999997e174 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 4.99999999999999991e108

   1. Initial program 99.0%

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

   3. Taylor expanded in 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 80.2

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

   5. Applied rewrites 80.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 54.2%

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

   10. Applied rewrites 54.1%

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

   if 9.9999999999999992e292 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 76.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 79.6

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 79.6

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

   4. Applied rewrites 87.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 87.2

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-fma.f64 N/A

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

      8. associate-+l+ N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-*l* N/A

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

      23. lift-*.f64 N/A

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

      24. +-commutative N/A

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

   6. Applied rewrites 82.9%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 83.2

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

   9. Applied rewrites 83.2%

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

   11. Applied rewrites 80.3%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -\infty:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+174}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+108}:\\ \;\;\;\;\left(b \cdot 27\right) \cdot a\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 10^{+293}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ t_2 := x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+174}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+108}:\\ \;\;\;\;\left(b \cdot 27\right) \cdot a\\ \mathbf{elif}\;t\_2 \leq 10^{+293}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* -9.0 z) (* t y))) (t_2 (- (* x 2.0) (* (* (* y 9.0) z) t))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e+174)
       (* 2.0 x)
       (if (<= t_2 5e+108)
         (* (* b 27.0) a)
         (if (<= t_2 1e+293) (* 2.0 x) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-9.0 * z) * (t * y);
	double t_2 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e+174) {
		tmp = 2.0 * x;
	} else if (t_2 <= 5e+108) {
		tmp = (b * 27.0) * a;
	} else if (t_2 <= 1e+293) {
		tmp = 2.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-9.0 * z) * (t * y);
	double t_2 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e+174) {
		tmp = 2.0 * x;
	} else if (t_2 <= 5e+108) {
		tmp = (b * 27.0) * a;
	} else if (t_2 <= 1e+293) {
		tmp = 2.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (-9.0 * z) * (t * y)
	t_2 = (x * 2.0) - (((y * 9.0) * z) * t)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e+174:
		tmp = 2.0 * x
	elif t_2 <= 5e+108:
		tmp = (b * 27.0) * a
	elif t_2 <= 1e+293:
		tmp = 2.0 * x
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-9.0 * z) * Float64(t * y))
	t_2 = Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e+174)
		tmp = Float64(2.0 * x);
	elseif (t_2 <= 5e+108)
		tmp = Float64(Float64(b * 27.0) * a);
	elseif (t_2 <= 1e+293)
		tmp = Float64(2.0 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (-9.0 * z) * (t * y);
	t_2 = (x * 2.0) - (((y * 9.0) * z) * t);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e+174)
		tmp = 2.0 * x;
	elseif (t_2 <= 5e+108)
		tmp = (b * 27.0) * a;
	elseif (t_2 <= 1e+293)
		tmp = 2.0 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(-9.0 * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e+174], N[(2.0 * x), $MachinePrecision], If[LessEqual[t$95$2, 5e+108], N[(N[(b * 27.0), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t$95$2, 1e+293], N[(2.0 * x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -inf.0 or 9.9999999999999992e292 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 77.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 82.7

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 82.7

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

   4. Applied rewrites 93.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 93.3

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-fma.f64 N/A

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

      8. associate-+l+ N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-*l* N/A

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

      23. lift-*.f64 N/A

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

      24. +-commutative N/A

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

   6. Applied rewrites 80.9%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 84.6

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

   9. Applied rewrites 84.6%

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

   11. Applied rewrites 86.5%

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

   if -inf.0 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.9999999999999997e174 or 4.99999999999999991e108 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 9.9999999999999992e292

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

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

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

   4. Applied rewrites 90.9%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 56.6

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

   7. Applied rewrites 56.6%

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

   if -4.9999999999999997e174 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 4.99999999999999991e108

   1. Initial program 99.0%

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

   3. Taylor expanded in 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 80.2

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

   5. Applied rewrites 80.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 54.2%

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

   10. Applied rewrites 54.1%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -\infty:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+174}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+108}:\\ \;\;\;\;\left(b \cdot 27\right) \cdot a\\ \mathbf{elif}\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 10^{+293}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-9 \cdot z\right) \cdot \left(t \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -200000000:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot -9\right) \cdot y, t, 2 \cdot x\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(\left(z \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -200000000.0)
     (fma (* (* z -9.0) y) t (* 2.0 x))
     (if (<= t_1 2e+14)
       (fma 2.0 x (* (* b a) 27.0))
       (+ (* -9.0 (* (* z y) t)) (* (* a 27.0) b))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -200000000.0) {
		tmp = fma(((z * -9.0) * y), t, (2.0 * x));
	} else if (t_1 <= 2e+14) {
		tmp = fma(2.0, x, ((b * a) * 27.0));
	} else {
		tmp = (-9.0 * ((z * y) * t)) + ((a * 27.0) * b);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -200000000.0)
		tmp = fma(Float64(Float64(z * -9.0) * y), t, Float64(2.0 * x));
	elseif (t_1 <= 2e+14)
		tmp = fma(2.0, x, Float64(Float64(b * a) * 27.0));
	else
		tmp = Float64(Float64(-9.0 * Float64(Float64(z * y) * t)) + Float64(Float64(a * 27.0) * b));
	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, -200000000.0], N[(N[(N[(z * -9.0), $MachinePrecision] * y), $MachinePrecision] * t + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+14], N[(2.0 * x + N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], N[(N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -2e8

   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 38.2

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

   5. Applied rewrites 38.2%

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

   7. Applied rewrites 38.2%

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

   8. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 79.1

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

   10. Applied rewrites 79.1%

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

   12. Applied rewrites 80.6%

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

   if -2e8 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2e14

   1. Initial program 99.1%

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

   3. Taylor expanded in 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 95.0

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

   5. Applied rewrites 95.0%

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

   if 2e14 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 90.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 80.7

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

   5. Applied rewrites 80.7%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -200000000:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot -9\right) \cdot y, t, 2 \cdot x\right)\\ \mathbf{elif}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 2 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(\left(z \cdot y\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ t_2 := \left(b \cdot a\right) \cdot 27\\ \mathbf{if}\;t\_1 \leq -200000000:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot -9\right) \cdot y, t, 2 \cdot x\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(2, x, t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot y\right) \cdot t, t\_2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)) (t_2 (* (* b a) 27.0)))
   (if (<= t_1 -200000000.0)
     (fma (* (* z -9.0) y) t (* 2.0 x))
     (if (<= t_1 2e+14) (fma 2.0 x t_2) (fma -9.0 (* (* z y) t) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double t_2 = (b * a) * 27.0;
	double tmp;
	if (t_1 <= -200000000.0) {
		tmp = fma(((z * -9.0) * y), t, (2.0 * x));
	} else if (t_1 <= 2e+14) {
		tmp = fma(2.0, x, t_2);
	} else {
		tmp = fma(-9.0, ((z * y) * t), t_2);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	t_2 = Float64(Float64(b * a) * 27.0)
	tmp = 0.0
	if (t_1 <= -200000000.0)
		tmp = fma(Float64(Float64(z * -9.0) * y), t, Float64(2.0 * x));
	elseif (t_1 <= 2e+14)
		tmp = fma(2.0, x, t_2);
	else
		tmp = fma(-9.0, Float64(Float64(z * y) * t), t_2);
	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]}, Block[{t$95$2 = N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]}, If[LessEqual[t$95$1, -200000000.0], N[(N[(N[(z * -9.0), $MachinePrecision] * y), $MachinePrecision] * t + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+14], N[(2.0 * x + t$95$2), $MachinePrecision], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -2e8

   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 38.2

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

   5. Applied rewrites 38.2%

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

   7. Applied rewrites 38.2%

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

   8. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 79.1

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

   10. Applied rewrites 79.1%

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

   12. Applied rewrites 80.6%

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

   if -2e8 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2e14

   1. Initial program 99.1%

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

   3. Taylor expanded in 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 95.0

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

   5. Applied rewrites 95.0%

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

   if 2e14 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 90.0%

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

   3. Taylor expanded in x around 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 80.7

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

   5. Applied rewrites 80.7%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -200000000:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot -9\right) \cdot y, t, 2 \cdot x\right)\\ \mathbf{elif}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 2 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot y\right) \cdot t, \left(b \cdot a\right) \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -200000000 \lor \neg \left(t\_1 \leq 4 \cdot 10^{+74}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot y\right) \cdot z, t, 2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (or (<= t_1 -200000000.0) (not (<= t_1 4e+74)))
     (fma (* (* -9.0 y) z) t (* 2.0 x))
     (fma (* 27.0 b) a (* x 2.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if ((t_1 <= -200000000.0) || !(t_1 <= 4e+74)) {
		tmp = fma(((-9.0 * y) * z), t, (2.0 * x));
	} else {
		tmp = fma((27.0 * b), a, (x * 2.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if ((t_1 <= -200000000.0) || !(t_1 <= 4e+74))
		tmp = fma(Float64(Float64(-9.0 * y) * z), t, Float64(2.0 * x));
	else
		tmp = fma(Float64(27.0 * b), a, Float64(x * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -200000000.0], N[Not[LessEqual[t$95$1, 4e+74]], $MachinePrecision]], N[(N[(N[(-9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -2e8 or 3.99999999999999981e74 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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 31.1

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

   5. Applied rewrites 31.1%

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

   7. Applied rewrites 31.2%

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

   8. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 81.7

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

   10. Applied rewrites 81.7%

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

   if -2e8 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 3.99999999999999981e74

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 93.3

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

   5. Applied rewrites 93.3%

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

   7. Applied rewrites 93.3%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -200000000 \lor \neg \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 4 \cdot 10^{+74}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot y\right) \cdot z, t, 2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -200000000:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot -9\right) \cdot y, t, 2 \cdot x\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot y\right) \cdot z, t, 2 \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -200000000.0)
     (fma (* (* z -9.0) y) t (* 2.0 x))
     (if (<= t_1 4e+74)
       (fma (* 27.0 b) a (* x 2.0))
       (fma (* (* -9.0 y) z) 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 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -200000000.0) {
		tmp = fma(((z * -9.0) * y), t, (2.0 * x));
	} else if (t_1 <= 4e+74) {
		tmp = fma((27.0 * b), a, (x * 2.0));
	} else {
		tmp = fma(((-9.0 * y) * z), t, (2.0 * x));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -200000000.0)
		tmp = fma(Float64(Float64(z * -9.0) * y), t, Float64(2.0 * x));
	elseif (t_1 <= 4e+74)
		tmp = fma(Float64(27.0 * b), a, Float64(x * 2.0));
	else
		tmp = fma(Float64(Float64(-9.0 * y) * z), t, Float64(2.0 * x));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -200000000.0], N[(N[(N[(z * -9.0), $MachinePrecision] * y), $MachinePrecision] * t + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+74], N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -2e8

   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 38.2

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

   5. Applied rewrites 38.2%

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

   7. Applied rewrites 38.2%

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

   8. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 79.1

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

   10. Applied rewrites 79.1%

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

   12. Applied rewrites 80.6%

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

   if -2e8 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 3.99999999999999981e74

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 93.3

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

   5. Applied rewrites 93.3%

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

   7. Applied rewrites 93.3%

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

   if 3.99999999999999981e74 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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 22.9

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

   5. Applied rewrites 22.9%

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

   7. Applied rewrites 23.0%

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

   8. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 84.8

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

   10. Applied rewrites 84.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -200000000:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot -9\right) \cdot y, t, 2 \cdot x\right)\\ \mathbf{elif}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 4 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot y\right) \cdot z, t, 2 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+229}:\\ \;\;\;\;\left(\left(y \cdot z\right) \cdot t\right) \cdot -9\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -1e+229)
     (* (* (* y z) t) -9.0)
     (if (<= t_1 5e+100)
       (fma (* 27.0 b) a (* x 2.0))
       (* (* t z) (* -9.0 y))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -1e+229) {
		tmp = ((y * z) * t) * -9.0;
	} else if (t_1 <= 5e+100) {
		tmp = fma((27.0 * b), a, (x * 2.0));
	} else {
		tmp = (t * z) * (-9.0 * y);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -1e+229)
		tmp = Float64(Float64(Float64(y * z) * t) * -9.0);
	elseif (t_1 <= 5e+100)
		tmp = fma(Float64(27.0 * b), a, Float64(x * 2.0));
	else
		tmp = Float64(Float64(t * z) * Float64(-9.0 * y));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+229], N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * -9.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+100], N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -9.9999999999999999e228

   1. Initial program 79.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 82.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 82.0

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

   4. Applied rewrites 86.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 86.0

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-fma.f64 N/A

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

      8. associate-+l+ N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-*l* N/A

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

      23. lift-*.f64 N/A

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

      24. +-commutative N/A

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

   6. Applied rewrites 85.0%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 80.4

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

   9. Applied rewrites 80.4%

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

   if -9.9999999999999999e228 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 4.9999999999999999e100

   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 86.0

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

   5. Applied rewrites 86.0%

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

   7. Applied rewrites 85.9%

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

   if 4.9999999999999999e100 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 87.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 91.7

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 91.7

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

   4. Applied rewrites 97.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 97.8

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-fma.f64 N/A

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

      8. associate-+l+ N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-*l* N/A

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

      23. lift-*.f64 N/A

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

      24. +-commutative N/A

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

   6. Applied rewrites 87.3%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 82.4

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

   9. Applied rewrites 82.4%

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

   11. Applied rewrites 78.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -1 \cdot 10^{+229}:\\ \;\;\;\;\left(\left(y \cdot z\right) \cdot t\right) \cdot -9\\ \mathbf{elif}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+229}:\\ \;\;\;\;\left(\left(y \cdot z\right) \cdot t\right) \cdot -9\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -1e+229)
     (* (* (* y z) t) -9.0)
     (if (<= t_1 5e+100)
       (fma 2.0 x (* (* b a) 27.0))
       (* (* t z) (* -9.0 y))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -1e+229) {
		tmp = ((y * z) * t) * -9.0;
	} else if (t_1 <= 5e+100) {
		tmp = fma(2.0, x, ((b * a) * 27.0));
	} else {
		tmp = (t * z) * (-9.0 * y);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -1e+229)
		tmp = Float64(Float64(Float64(y * z) * t) * -9.0);
	elseif (t_1 <= 5e+100)
		tmp = fma(2.0, x, Float64(Float64(b * a) * 27.0));
	else
		tmp = Float64(Float64(t * z) * Float64(-9.0 * y));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+229], N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * -9.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+100], N[(2.0 * x + N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -9.9999999999999999e228

   1. Initial program 79.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 82.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 82.0

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

   4. Applied rewrites 86.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 86.0

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-fma.f64 N/A

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

      8. associate-+l+ N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-*l* N/A

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

      23. lift-*.f64 N/A

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

      24. +-commutative N/A

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

   6. Applied rewrites 85.0%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 80.4

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

   9. Applied rewrites 80.4%

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

   if -9.9999999999999999e228 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 4.9999999999999999e100

   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 86.0

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

   5. Applied rewrites 86.0%

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

   if 4.9999999999999999e100 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 87.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 91.7

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 91.7

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

   4. Applied rewrites 97.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 97.8

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-fma.f64 N/A

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

      8. associate-+l+ N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-*l* N/A

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

      23. lift-*.f64 N/A

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

      24. +-commutative N/A

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

   6. Applied rewrites 87.3%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 82.4

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

   9. Applied rewrites 82.4%

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

   11. Applied rewrites 78.8%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -1 \cdot 10^{+229}:\\ \;\;\;\;\left(\left(y \cdot z\right) \cdot t\right) \cdot -9\\ \mathbf{elif}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-7} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+81}\right):\\ \;\;\;\;\left(\left(y \cdot z\right) \cdot t\right) \cdot -9\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot 27\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (or (<= t_1 -2e-7) (not (<= t_1 5e+81)))
     (* (* (* y z) t) -9.0)
     (* (* b 27.0) a))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if ((t_1 <= -2e-7) || !(t_1 <= 5e+81)) {
		tmp = ((y * z) * t) * -9.0;
	} else {
		tmp = (b * 27.0) * a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y * 9.0d0) * z) * t
    if ((t_1 <= (-2d-7)) .or. (.not. (t_1 <= 5d+81))) then
        tmp = ((y * z) * t) * (-9.0d0)
    else
        tmp = (b * 27.0d0) * a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if ((t_1 <= -2e-7) || !(t_1 <= 5e+81)) {
		tmp = ((y * z) * t) * -9.0;
	} else {
		tmp = (b * 27.0) * a;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = ((y * 9.0) * z) * t
	tmp = 0
	if (t_1 <= -2e-7) or not (t_1 <= 5e+81):
		tmp = ((y * z) * t) * -9.0
	else:
		tmp = (b * 27.0) * a
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if ((t_1 <= -2e-7) || !(t_1 <= 5e+81))
		tmp = Float64(Float64(Float64(y * z) * t) * -9.0);
	else
		tmp = Float64(Float64(b * 27.0) * a);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * 9.0) * z) * t;
	tmp = 0.0;
	if ((t_1 <= -2e-7) || ~((t_1 <= 5e+81)))
		tmp = ((y * z) * t) * -9.0;
	else
		tmp = (b * 27.0) * a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-7], N[Not[LessEqual[t$95$1, 5e+81]], $MachinePrecision]], N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * -9.0), $MachinePrecision], N[(N[(b * 27.0), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.9999999999999999e-7 or 4.9999999999999998e81 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 91.4

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 91.4

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. lower-fma.f64 N/A

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

   4. Applied rewrites 90.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 90.0

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-fma.f64 N/A

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

      8. associate-+l+ N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. lift-*.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. associate-*l* N/A

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

      23. lift-*.f64 N/A

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

      24. +-commutative N/A

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

   6. Applied rewrites 90.5%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 69.1

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

   9. Applied rewrites 69.1%

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

   if -1.9999999999999999e-7 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 4.9999999999999998e81

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 93.3

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

   5. Applied rewrites 93.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 51.8%

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

   10. Applied rewrites 51.8%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -2 \cdot 10^{-7} \lor \neg \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+81}\right):\\ \;\;\;\;\left(\left(y \cdot z\right) \cdot t\right) \cdot -9\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot 27\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+83} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-47}\right):\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \end{array} \]

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 -2e+83) (not (<= t_1 2e-47))) (* (* a b) 27.0) (* 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 <= -2e+83) || !(t_1 <= 2e-47)) {
		tmp = (a * b) * 27.0;
	} 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 <= (-2d+83)) .or. (.not. (t_1 <= 2d-47))) then
        tmp = (a * b) * 27.0d0
    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 <= -2e+83) || !(t_1 <= 2e-47)) {
		tmp = (a * b) * 27.0;
	} 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 <= -2e+83) or not (t_1 <= 2e-47):
		tmp = (a * b) * 27.0
	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 <= -2e+83) || !(t_1 <= 2e-47))
		tmp = Float64(Float64(a * b) * 27.0);
	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 <= -2e+83) || ~((t_1 <= 2e-47)))
		tmp = (a * b) * 27.0;
	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, -2e+83], N[Not[LessEqual[t$95$1, 2e-47]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], N[(2.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2.00000000000000006e83 or 1.9999999999999999e-47 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 92.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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 70.8

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

   5. Applied rewrites 70.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 60.4%

      \[\leadsto \left(a \cdot b\right) \cdot \color{blue}{27} \]

   if -2.00000000000000006e83 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.9999999999999999e-47

   1. Initial program 96.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      11. distribute-lft-neg-in N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot \left(9 \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      12. +-commutative N/A

          \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot \left(9 \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(y\right), 9 \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      14. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-y}, 9 \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(z \cdot t\right) \cdot 9}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(z \cdot t\right) \cdot 9}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(t \cdot z\right)} \cdot 9, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      18. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(t \cdot z\right)} \cdot 9, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

   4. Applied rewrites 95.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, \left(t \cdot z\right) \cdot 9, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 51.3

         \[\leadsto \color{blue}{2 \cdot x} \]

   7. Applied rewrites 51.3%

      \[\leadsto \color{blue}{2 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{+83} \lor \neg \left(\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{-47}\right):\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+83} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-47}\right):\\ \;\;\;\;\left(27 \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \end{array} \]

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 -2e+83) (not (<= t_1 2e-47))) (* (* 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 <= -2e+83) || !(t_1 <= 2e-47)) {
		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 <= (-2d+83)) .or. (.not. (t_1 <= 2d-47))) 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 <= -2e+83) || !(t_1 <= 2e-47)) {
		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 <= -2e+83) or not (t_1 <= 2e-47):
		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 <= -2e+83) || !(t_1 <= 2e-47))
		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 <= -2e+83) || ~((t_1 <= 2e-47)))
		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, -2e+83], N[Not[LessEqual[t$95$1, 2e-47]], $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) < -2.00000000000000006e83 or 1.9999999999999999e-47 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 92.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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 70.8

         \[\leadsto \mathsf{fma}\left(2, x, \color{blue}{\left(b \cdot a\right)} \cdot 27\right) \]

   5. Applied rewrites 70.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, \left(b \cdot a\right) \cdot 27\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 60.4%

      \[\leadsto \left(a \cdot b\right) \cdot \color{blue}{27} \]
   9. Step-by-step derivation

   10. Applied rewrites 60.4%

       \[\leadsto \left(27 \cdot a\right) \cdot b \]

   if -2.00000000000000006e83 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.9999999999999999e-47

   1. Initial program 96.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      11. distribute-lft-neg-in N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot \left(9 \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      12. +-commutative N/A

          \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot \left(9 \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(y\right), 9 \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      14. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-y}, 9 \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(z \cdot t\right) \cdot 9}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(z \cdot t\right) \cdot 9}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(t \cdot z\right)} \cdot 9, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      18. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(t \cdot z\right)} \cdot 9, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

   4. Applied rewrites 95.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, \left(t \cdot z\right) \cdot 9, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 51.3

         \[\leadsto \color{blue}{2 \cdot x} \]

   7. Applied rewrites 51.3%

      \[\leadsto \color{blue}{2 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{+83} \lor \neg \left(\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{-47}\right):\\ \;\;\;\;\left(27 \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+83}:\\ \;\;\;\;\left(b \cdot 27\right) \cdot a\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= t_1 -2e+83)
     (* (* b 27.0) a)
     (if (<= t_1 2e-47) (* 2.0 x) (* (* 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 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -2e+83) {
		tmp = (b * 27.0) * a;
	} else if (t_1 <= 2e-47) {
		tmp = 2.0 * x;
	} else {
		tmp = (a * b) * 27.0;
	}
	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 <= (-2d+83)) then
        tmp = (b * 27.0d0) * a
    else if (t_1 <= 2d-47) then
        tmp = 2.0d0 * x
    else
        tmp = (a * b) * 27.0d0
    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 <= -2e+83) {
		tmp = (b * 27.0) * a;
	} else if (t_1 <= 2e-47) {
		tmp = 2.0 * x;
	} else {
		tmp = (a * b) * 27.0;
	}
	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 <= -2e+83:
		tmp = (b * 27.0) * a
	elif t_1 <= 2e-47:
		tmp = 2.0 * x
	else:
		tmp = (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(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -2e+83)
		tmp = Float64(Float64(b * 27.0) * a);
	elseif (t_1 <= 2e-47)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(Float64(a * b) * 27.0);
	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 <= -2e+83)
		tmp = (b * 27.0) * a;
	elseif (t_1 <= 2e-47)
		tmp = 2.0 * x;
	else
		tmp = (a * b) * 27.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+83], N[(N[(b * 27.0), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t$95$1, 2e-47], N[(2.0 * x), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2.00000000000000006e83

   1. Initial program 93.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(2, x, \color{blue}{\left(a \cdot b\right) \cdot 27}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, \color{blue}{\left(a \cdot b\right) \cdot 27}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(2, x, \color{blue}{\left(b \cdot a\right)} \cdot 27\right) \]

      5. lower-*.f64 74.6

         \[\leadsto \mathsf{fma}\left(2, x, \color{blue}{\left(b \cdot a\right)} \cdot 27\right) \]

   5. Applied rewrites 74.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, \left(b \cdot a\right) \cdot 27\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 68.7%

      \[\leadsto \left(a \cdot b\right) \cdot \color{blue}{27} \]
   9. Step-by-step derivation

   10. Applied rewrites 68.6%

       \[\leadsto \color{blue}{\left(b \cdot 27\right) \cdot a} \]

   if -2.00000000000000006e83 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.9999999999999999e-47

   1. Initial program 96.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      11. distribute-lft-neg-in N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot \left(9 \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      12. +-commutative N/A

          \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot \left(9 \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(y\right), 9 \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      14. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-y}, 9 \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(z \cdot t\right) \cdot 9}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(z \cdot t\right) \cdot 9}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(t \cdot z\right)} \cdot 9, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      18. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(t \cdot z\right)} \cdot 9, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

   4. Applied rewrites 95.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, \left(t \cdot z\right) \cdot 9, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 51.3

         \[\leadsto \color{blue}{2 \cdot x} \]

   7. Applied rewrites 51.3%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if 1.9999999999999999e-47 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 91.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(2, x, \color{blue}{\left(a \cdot b\right) \cdot 27}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, \color{blue}{\left(a \cdot b\right) \cdot 27}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(2, x, \color{blue}{\left(b \cdot a\right)} \cdot 27\right) \]

      5. lower-*.f64 67.8

         \[\leadsto \mathsf{fma}\left(2, x, \color{blue}{\left(b \cdot a\right)} \cdot 27\right) \]

   5. Applied rewrites 67.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, \left(b \cdot a\right) \cdot 27\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 53.7%

      \[\leadsto \left(a \cdot b\right) \cdot \color{blue}{27} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{+83}:\\ \;\;\;\;\left(b \cdot 27\right) \cdot a\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 98.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot a, b, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, -9, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \end{array} \end{array} \]

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 -2.1e+59)
   (fma (* 27.0 a) b (fma (* (* -9.0 y) t) z (* 2.0 x)))
   (fma (* (* z y) t) -9.0 (fma a (* 27.0 b) (* x 2.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.1e+59) {
		tmp = fma((27.0 * a), b, fma(((-9.0 * y) * t), z, (2.0 * x)));
	} else {
		tmp = fma(((z * y) * t), -9.0, fma(a, (27.0 * b), (x * 2.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.1e+59)
		tmp = fma(Float64(27.0 * a), b, fma(Float64(Float64(-9.0 * y) * t), z, Float64(2.0 * x)));
	else
		tmp = fma(Float64(Float64(z * y) * t), -9.0, fma(a, Float64(27.0 * b), Float64(x * 2.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.1e+59], N[(N[(27.0 * a), $MachinePrecision] * b + N[(N[(N[(-9.0 * y), $MachinePrecision] * t), $MachinePrecision] * z + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * -9.0 + N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.09999999999999984e59

   1. Initial program 90.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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. lower-fma.f64 93.2

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{a \cdot 27}, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot a}, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      7. lower-*.f64 93.2

         \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot a}, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      8. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right) + x \cdot 2\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right)\right) + x \cdot 2\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + x \cdot 2\right) \]

      14. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot \left(z \cdot t\right)} + x \cdot 2\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot \color{blue}{\left(t \cdot z\right)} + x \cdot 2\right) \]

      16. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t\right) \cdot z} + x \cdot 2\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t, z, x \cdot 2\right)}\right) \]

   4. Applied rewrites 97.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot a, b, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right)} \]

   if -2.09999999999999984e59 < z

   1. Initial program 95.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      4. lower-fma.f64 96.2

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{a \cdot 27}, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot a}, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      7. lower-*.f64 96.2

         \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot a}, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      8. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right) + x \cdot 2\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right)\right) + x \cdot 2\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + x \cdot 2\right) \]

      14. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot \left(z \cdot t\right)} + x \cdot 2\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot \color{blue}{\left(t \cdot z\right)} + x \cdot 2\right) \]

      16. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t\right) \cdot z} + x \cdot 2\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t, z, x \cdot 2\right)}\right) \]

   4. Applied rewrites 94.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot a, b, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot a}, b, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{a \cdot 27}, b, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right) \]

      3. lift-*.f64 94.5

         \[\leadsto \mathsf{fma}\left(\color{blue}{a \cdot 27}, b, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right) \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right) + \left(a \cdot 27\right) \cdot b} \]

      7. lift-fma.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(-9 \cdot y\right) \cdot t\right) \cdot z + 2 \cdot x\right)} + \left(a \cdot 27\right) \cdot b \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\left(-9 \cdot y\right) \cdot t\right) \cdot z + \left(2 \cdot x + \left(a \cdot 27\right) \cdot b\right)} \]

      9. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(-9 \cdot y\right) \cdot t\right)} + \left(2 \cdot x + \left(a \cdot 27\right) \cdot b\right) \]

      10. lift-*.f64 N/A

          \[\leadsto z \cdot \color{blue}{\left(\left(-9 \cdot y\right) \cdot t\right)} + \left(2 \cdot x + \left(a \cdot 27\right) \cdot b\right) \]

      11. lift-*.f64 N/A

          \[\leadsto z \cdot \left(\color{blue}{\left(-9 \cdot y\right)} \cdot t\right) + \left(2 \cdot x + \left(a \cdot 27\right) \cdot b\right) \]

      12. associate-*l* N/A

          \[\leadsto z \cdot \color{blue}{\left(-9 \cdot \left(y \cdot t\right)\right)} + \left(2 \cdot x + \left(a \cdot 27\right) \cdot b\right) \]

      13. *-commutative N/A

          \[\leadsto z \cdot \color{blue}{\left(\left(y \cdot t\right) \cdot -9\right)} + \left(2 \cdot x + \left(a \cdot 27\right) \cdot b\right) \]

      14. associate-*l* N/A

          \[\leadsto \color{blue}{\left(z \cdot \left(y \cdot t\right)\right) \cdot -9} + \left(2 \cdot x + \left(a \cdot 27\right) \cdot b\right) \]

      15. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\left(z \cdot y\right) \cdot t\right)} \cdot -9 + \left(2 \cdot x + \left(a \cdot 27\right) \cdot b\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot -9 + \left(2 \cdot x + \left(a \cdot 27\right) \cdot b\right) \]

      17. lift-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(z \cdot y\right) \cdot t\right)} \cdot -9 + \left(2 \cdot x + \left(a \cdot 27\right) \cdot b\right) \]

      18. lift-*.f64 N/A

          \[\leadsto \left(\left(z \cdot y\right) \cdot t\right) \cdot -9 + \left(2 \cdot x + \color{blue}{\left(a \cdot 27\right) \cdot b}\right) \]

      19. *-commutative N/A

          \[\leadsto \left(\left(z \cdot y\right) \cdot t\right) \cdot -9 + \left(2 \cdot x + \color{blue}{b \cdot \left(a \cdot 27\right)}\right) \]

      20. lift-*.f64 N/A

          \[\leadsto \left(\left(z \cdot y\right) \cdot t\right) \cdot -9 + \left(2 \cdot x + b \cdot \color{blue}{\left(a \cdot 27\right)}\right) \]

      21. *-commutative N/A

          \[\leadsto \left(\left(z \cdot y\right) \cdot t\right) \cdot -9 + \left(2 \cdot x + b \cdot \color{blue}{\left(27 \cdot a\right)}\right) \]

      22. associate-*l* N/A

          \[\leadsto \left(\left(z \cdot y\right) \cdot t\right) \cdot -9 + \left(2 \cdot x + \color{blue}{\left(b \cdot 27\right) \cdot a}\right) \]

      23. lift-*.f64 N/A

          \[\leadsto \left(\left(z \cdot y\right) \cdot t\right) \cdot -9 + \left(2 \cdot x + \color{blue}{\left(b \cdot 27\right)} \cdot a\right) \]

      24. +-commutative N/A

          \[\leadsto \left(\left(z \cdot y\right) \cdot t\right) \cdot -9 + \color{blue}{\left(\left(b \cdot 27\right) \cdot a + 2 \cdot x\right)} \]

   6. Applied rewrites 96.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, -9, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 98.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 8.8 \cdot 10^{-20}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, -9 \cdot y, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot a, b, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right)\\ \end{array} \end{array} \]

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 8.8e-20)
   (fma (* t z) (* -9.0 y) (fma (* b 27.0) a (* 2.0 x)))
   (fma (* 27.0 a) b (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 <= 8.8e-20) {
		tmp = fma((t * z), (-9.0 * y), fma((b * 27.0), a, (2.0 * x)));
	} else {
		tmp = fma((27.0 * a), b, 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 <= 8.8e-20)
		tmp = fma(Float64(t * z), Float64(-9.0 * y), fma(Float64(b * 27.0), a, Float64(2.0 * x)));
	else
		tmp = fma(Float64(27.0 * a), b, 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, 8.8e-20], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision] + N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * a), $MachinePrecision] * b + 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 < 8.79999999999999964e-20

   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. 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 96.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot z, -9 \cdot y, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)} \]

   if 8.79999999999999964e-20 < z

   1. Initial program 89.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      4. lower-fma.f64 92.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{a \cdot 27}, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot a}, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      7. lower-*.f64 92.0

         \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot a}, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      8. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right) + x \cdot 2\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right)\right) + x \cdot 2\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + x \cdot 2\right) \]

      14. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot \left(z \cdot t\right)} + x \cdot 2\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot \color{blue}{\left(t \cdot z\right)} + x \cdot 2\right) \]

      16. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t\right) \cdot z} + x \cdot 2\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t, z, x \cdot 2\right)}\right) \]

   4. Applied rewrites 98.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot a, b, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 94.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \mathsf{fma}\left(27 \cdot a, b, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right) \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (fma (* 27.0 a) b (fma (* (* -9.0 y) t) z (* 2.0 x))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return fma((27.0 * a), b, fma(((-9.0 * y) * t), z, (2.0 * x)));
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return fma(Float64(27.0 * a), b, fma(Float64(Float64(-9.0 * y) * t), z, Float64(2.0 * x)))
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(27.0 * a), $MachinePrecision] * b + N[(N[(N[(-9.0 * y), $MachinePrecision] * t), $MachinePrecision] * z + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.5%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

   4. lower-fma.f64 95.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

   5. lift-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{a \cdot 27}, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot a}, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

   7. lower-*.f64 95.7

      \[\leadsto \mathsf{fma}\left(\color{blue}{27 \cdot a}, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

   8. lift--.f64 N/A

      \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) \]

   9. sub-neg N/A

      \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right) \]

   10. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2}\right) \]

   11. lift-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right) + x \cdot 2\right) \]

   12. lift-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right)\right) + x \cdot 2\right) \]

   13. associate-*l* N/A

       \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + x \cdot 2\right) \]

   14. distribute-lft-neg-in N/A

       \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot \left(z \cdot t\right)} + x \cdot 2\right) \]

   15. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot \color{blue}{\left(t \cdot z\right)} + x \cdot 2\right) \]

   16. associate-*r* N/A

       \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t\right) \cdot z} + x \cdot 2\right) \]

   17. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(27 \cdot a, b, \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t, z, x \cdot 2\right)}\right) \]

4. Applied rewrites 95.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot a, b, \mathsf{fma}\left(\left(-9 \cdot y\right) \cdot t, z, 2 \cdot x\right)\right)} \]
5. Add Preprocessing

Alternative 18: 30.1% accurate, 6.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ 2 \cdot x \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* 2.0 x))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return 2.0 * x;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = 2.0d0 * x
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return 2.0 * x;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return 2.0 * x

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(2.0 * x)
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = 2.0 * x;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(2.0 * x), $MachinePrecision]

Derivation

1. Initial program 94.5%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

   2. lift--.f64 N/A

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

   3. sub-neg N/A

      \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

   4. +-commutative N/A

      \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

   5. associate-+l+ N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

   6. lift-*.f64 N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

   7. lift-*.f64 N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

   8. associate-*l* N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

   10. associate-*l* N/A

       \[\leadsto \left(\mathsf{neg}\left(\color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

   11. distribute-lft-neg-in N/A

       \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot \left(9 \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

   12. +-commutative N/A

       \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot \left(9 \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

   13. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(y\right), 9 \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

   14. lower-neg.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{-y}, 9 \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

   15. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(z \cdot t\right) \cdot 9}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

   16. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(z \cdot t\right) \cdot 9}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

   17. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(t \cdot z\right)} \cdot 9, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

   18. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(-y, \color{blue}{\left(t \cdot z\right)} \cdot 9, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

4. Applied rewrites 94.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-y, \left(t \cdot z\right) \cdot 9, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)} \]

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{2 \cdot x} \]
6. Step-by-step derivation

   1. lower-*.f64 30.7

      \[\leadsto \color{blue}{2 \cdot x} \]

7. Applied rewrites 30.7%

   \[\leadsto \color{blue}{2 \cdot x} \]
8. Add Preprocessing

Developer Target 1: 94.9% 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 2024313 
(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)))