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

Percentage Accurate: 95.6% → 98.3%

Time: 20.7s

Alternatives: 15

Speedup: 0.9×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{if}\;t \leq 4 \cdot 10^{-145}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(9 \cdot y\right) \cdot z, -t, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (* 27.0 b) a (* x 2.0))))
   (if (<= t 4e-145)
     (fma (* (* y -9.0) t) z t_1)
     (fma (* (* 9.0 y) z) (- t) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((27.0 * b), a, (x * 2.0));
	double tmp;
	if (t <= 4e-145) {
		tmp = fma(((y * -9.0) * t), z, t_1);
	} else {
		tmp = fma(((9.0 * y) * z), -t, t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(Float64(27.0 * b), a, Float64(x * 2.0))
	tmp = 0.0
	if (t <= 4e-145)
		tmp = fma(Float64(Float64(y * -9.0) * t), z, t_1);
	else
		tmp = fma(Float64(Float64(9.0 * y) * z), Float64(-t), t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 4e-145], N[(N[(N[(y * -9.0), $MachinePrecision] * t), $MachinePrecision] * z + t$95$1), $MachinePrecision], N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * (-t) + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 3.99999999999999966e-145

   1. Initial program 91.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

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

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 97.1%

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

   if 3.99999999999999966e-145 < t

   1. Initial program 93.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-neg.f64 N/A

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

      17. lift-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. associate-*l* N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 94.5

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

      24. lift-*.f64 N/A

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

      25. *-commutative N/A

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

      26. lower-*.f64 94.5

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

   4. Applied rewrites 94.5%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4 \cdot 10^{-145}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(9 \cdot y\right) \cdot z, -t, \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 55.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+59}:\\ \;\;\;\;\left(z \cdot \left(y \cdot -9\right)\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_1 \leq 10^{+183}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot t\right) \cdot -9\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* 9.0 y) z) t)))
   (if (<= t_1 -2e+59)
     (* (* z (* y -9.0)) t)
     (if (<= t_1 2e-236)
       (* x 2.0)
       (if (<= t_1 1e+183) (* (* a b) 27.0) (* (* (* z t) -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 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_1 <= -2e+59) {
		tmp = (z * (y * -9.0)) * t;
	} else if (t_1 <= 2e-236) {
		tmp = x * 2.0;
	} else if (t_1 <= 1e+183) {
		tmp = (a * b) * 27.0;
	} else {
		tmp = ((z * t) * -9.0) * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((9.0d0 * y) * z) * t
    if (t_1 <= (-2d+59)) then
        tmp = (z * (y * (-9.0d0))) * t
    else if (t_1 <= 2d-236) then
        tmp = x * 2.0d0
    else if (t_1 <= 1d+183) then
        tmp = (a * b) * 27.0d0
    else
        tmp = ((z * t) * (-9.0d0)) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_1 <= -2e+59) {
		tmp = (z * (y * -9.0)) * t;
	} else if (t_1 <= 2e-236) {
		tmp = x * 2.0;
	} else if (t_1 <= 1e+183) {
		tmp = (a * b) * 27.0;
	} else {
		tmp = ((z * t) * -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 = ((9.0 * y) * z) * t
	tmp = 0
	if t_1 <= -2e+59:
		tmp = (z * (y * -9.0)) * t
	elif t_1 <= 2e-236:
		tmp = x * 2.0
	elif t_1 <= 1e+183:
		tmp = (a * b) * 27.0
	else:
		tmp = ((z * t) * -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(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_1 <= -2e+59)
		tmp = Float64(Float64(z * Float64(y * -9.0)) * t);
	elseif (t_1 <= 2e-236)
		tmp = Float64(x * 2.0);
	elseif (t_1 <= 1e+183)
		tmp = Float64(Float64(a * b) * 27.0);
	else
		tmp = Float64(Float64(Float64(z * t) * -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 = ((9.0 * y) * z) * t;
	tmp = 0.0;
	if (t_1 <= -2e+59)
		tmp = (z * (y * -9.0)) * t;
	elseif (t_1 <= 2e-236)
		tmp = x * 2.0;
	elseif (t_1 <= 1e+183)
		tmp = (a * b) * 27.0;
	else
		tmp = ((z * t) * -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[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+59], N[(N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2e-236], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+183], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.99999999999999994e59

   1. Initial program 82.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 8.3

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

   5. Applied rewrites 8.3%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 71.8

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

   8. Applied rewrites 71.8%

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

   10. Applied rewrites 71.9%

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

   if -1.99999999999999994e59 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.0000000000000001e-236

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 53.0

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

   5. Applied rewrites 53.0%

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

   if 2.0000000000000001e-236 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 9.99999999999999947e182

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 48.0

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

   5. Applied rewrites 48.0%

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

   if 9.99999999999999947e182 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 79.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 2.5

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

   5. Applied rewrites 2.5%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 79.5

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

   8. Applied rewrites 79.5%

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

   10. Applied rewrites 90.8%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -2 \cdot 10^{+59}:\\ \;\;\;\;\left(z \cdot \left(y \cdot -9\right)\right) \cdot t\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 10^{+183}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot t\right) \cdot -9\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 55.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(z \cdot \left(y \cdot -9\right)\right) \cdot t\\ t_2 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+139}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z (* y -9.0)) t)) (t_2 (* (* (* 9.0 y) z) t)))
   (if (<= t_2 -2e+59)
     t_1
     (if (<= t_2 2e-236)
       (* x 2.0)
       (if (<= t_2 4e+139) (* (* a b) 27.0) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (y * -9.0)) * t;
	double t_2 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_2 <= -2e+59) {
		tmp = t_1;
	} else if (t_2 <= 2e-236) {
		tmp = x * 2.0;
	} else if (t_2 <= 4e+139) {
		tmp = (a * b) * 27.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * (y * (-9.0d0))) * t
    t_2 = ((9.0d0 * y) * z) * t
    if (t_2 <= (-2d+59)) then
        tmp = t_1
    else if (t_2 <= 2d-236) then
        tmp = x * 2.0d0
    else if (t_2 <= 4d+139) then
        tmp = (a * b) * 27.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (y * -9.0)) * t;
	double t_2 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_2 <= -2e+59) {
		tmp = t_1;
	} else if (t_2 <= 2e-236) {
		tmp = x * 2.0;
	} else if (t_2 <= 4e+139) {
		tmp = (a * b) * 27.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (z * (y * -9.0)) * t
	t_2 = ((9.0 * y) * z) * t
	tmp = 0
	if t_2 <= -2e+59:
		tmp = t_1
	elif t_2 <= 2e-236:
		tmp = x * 2.0
	elif t_2 <= 4e+139:
		tmp = (a * b) * 27.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(y * -9.0)) * t)
	t_2 = Float64(Float64(Float64(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_2 <= -2e+59)
		tmp = t_1;
	elseif (t_2 <= 2e-236)
		tmp = Float64(x * 2.0);
	elseif (t_2 <= 4e+139)
		tmp = Float64(Float64(a * b) * 27.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (y * -9.0)) * t;
	t_2 = ((9.0 * y) * z) * t;
	tmp = 0.0;
	if (t_2 <= -2e+59)
		tmp = t_1;
	elseif (t_2 <= 2e-236)
		tmp = x * 2.0;
	elseif (t_2 <= 4e+139)
		tmp = (a * b) * 27.0;
	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[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+59], t$95$1, If[LessEqual[t$95$2, 2e-236], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$2, 4e+139], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.99999999999999994e59 or 4.00000000000000013e139 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 82.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 6.6

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

   5. Applied rewrites 6.6%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 74.5

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

   8. Applied rewrites 74.5%

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

   10. Applied rewrites 74.6%

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

   if -1.99999999999999994e59 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.0000000000000001e-236

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 53.0

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

   5. Applied rewrites 53.0%

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

   if 2.0000000000000001e-236 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 4.00000000000000013e139

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 50.3

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

   5. Applied rewrites 50.3%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -2 \cdot 10^{+59}:\\ \;\;\;\;\left(z \cdot \left(y \cdot -9\right)\right) \cdot t\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 4 \cdot 10^{+139}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(y \cdot -9\right)\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(z \cdot y\right) \cdot t\right) \cdot -9\\ t_2 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+139}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* z y) t) -9.0)) (t_2 (* (* (* 9.0 y) z) t)))
   (if (<= t_2 -2e+59)
     t_1
     (if (<= t_2 2e-236)
       (* x 2.0)
       (if (<= t_2 4e+139) (* (* a b) 27.0) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * y) * t) * -9.0;
	double t_2 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_2 <= -2e+59) {
		tmp = t_1;
	} else if (t_2 <= 2e-236) {
		tmp = x * 2.0;
	} else if (t_2 <= 4e+139) {
		tmp = (a * b) * 27.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((z * y) * t) * (-9.0d0)
    t_2 = ((9.0d0 * y) * z) * t
    if (t_2 <= (-2d+59)) then
        tmp = t_1
    else if (t_2 <= 2d-236) then
        tmp = x * 2.0d0
    else if (t_2 <= 4d+139) then
        tmp = (a * b) * 27.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * y) * t) * -9.0;
	double t_2 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_2 <= -2e+59) {
		tmp = t_1;
	} else if (t_2 <= 2e-236) {
		tmp = x * 2.0;
	} else if (t_2 <= 4e+139) {
		tmp = (a * b) * 27.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = ((z * y) * t) * -9.0
	t_2 = ((9.0 * y) * z) * t
	tmp = 0
	if t_2 <= -2e+59:
		tmp = t_1
	elif t_2 <= 2e-236:
		tmp = x * 2.0
	elif t_2 <= 4e+139:
		tmp = (a * b) * 27.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * y) * t) * -9.0)
	t_2 = Float64(Float64(Float64(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_2 <= -2e+59)
		tmp = t_1;
	elseif (t_2 <= 2e-236)
		tmp = Float64(x * 2.0);
	elseif (t_2 <= 4e+139)
		tmp = Float64(Float64(a * b) * 27.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z * y) * t) * -9.0;
	t_2 = ((9.0 * y) * z) * t;
	tmp = 0.0;
	if (t_2 <= -2e+59)
		tmp = t_1;
	elseif (t_2 <= 2e-236)
		tmp = x * 2.0;
	elseif (t_2 <= 4e+139)
		tmp = (a * b) * 27.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * -9.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+59], t$95$1, If[LessEqual[t$95$2, 2e-236], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$2, 4e+139], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.99999999999999994e59 or 4.00000000000000013e139 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 82.3%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 74.5

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

   5. Applied rewrites 74.5%

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

   if -1.99999999999999994e59 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.0000000000000001e-236

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 53.0

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

   5. Applied rewrites 53.0%

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

   if 2.0000000000000001e-236 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 4.00000000000000013e139

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 50.3

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

   5. Applied rewrites 50.3%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -2 \cdot 10^{+59}:\\ \;\;\;\;\left(\left(z \cdot y\right) \cdot t\right) \cdot -9\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 4 \cdot 10^{+139}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot y\right) \cdot t\right) \cdot -9\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(t, z \cdot \left(y \cdot -9\right), x \cdot 2\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+150}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(y \cdot t\right) \cdot z, \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot t\right) \cdot -9, y, \left(a \cdot b\right) \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* 9.0 y) z) t)))
   (if (<= t_1 -5e+181)
     (fma t (* z (* y -9.0)) (* x 2.0))
     (if (<= t_1 4e+150)
       (fma -9.0 (* (* y t) z) (fma (* 27.0 b) a (* x 2.0)))
       (fma (* (* z t) -9.0) y (* (* a b) 27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_1 <= -5e+181) {
		tmp = fma(t, (z * (y * -9.0)), (x * 2.0));
	} else if (t_1 <= 4e+150) {
		tmp = fma(-9.0, ((y * t) * z), fma((27.0 * b), a, (x * 2.0)));
	} else {
		tmp = fma(((z * t) * -9.0), y, ((a * b) * 27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_1 <= -5e+181)
		tmp = fma(t, Float64(z * Float64(y * -9.0)), Float64(x * 2.0));
	elseif (t_1 <= 4e+150)
		tmp = fma(-9.0, Float64(Float64(y * t) * z), fma(Float64(27.0 * b), a, Float64(x * 2.0)));
	else
		tmp = fma(Float64(Float64(z * t) * -9.0), y, Float64(Float64(a * b) * 27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+181], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+150], N[(-9.0 * N[(N[(y * t), $MachinePrecision] * z), $MachinePrecision] + N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision] * y + N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000003e181

   1. Initial program 78.1%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 88.9

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

   5. Applied rewrites 88.9%

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

   7. Applied rewrites 78.4%

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

   if -5.0000000000000003e181 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 3.99999999999999992e150

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

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

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. metadata-eval N/A

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

      16. *-commutative N/A

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

      17. associate-*r* N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. lower-*.f64 N/A

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

   4. Applied rewrites 96.8%

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

   if 3.99999999999999992e150 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 80.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   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. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 93.5

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

   5. Applied rewrites 93.5%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(t, z \cdot \left(y \cdot -9\right), x \cdot 2\right)\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 4 \cdot 10^{+150}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(y \cdot t\right) \cdot z, \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot t\right) \cdot -9, y, \left(a \cdot b\right) \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(t, z \cdot \left(y \cdot -9\right), x \cdot 2\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot t\right) \cdot -9, y, \left(a \cdot b\right) \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* 9.0 y) z) t)))
   (if (<= t_1 -2e+59)
     (fma t (* z (* y -9.0)) (* x 2.0))
     (if (<= t_1 2e+65)
       (fma (* a b) 27.0 (* x 2.0))
       (fma (* (* z t) -9.0) y (* (* a b) 27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_1 <= -2e+59) {
		tmp = fma(t, (z * (y * -9.0)), (x * 2.0));
	} else if (t_1 <= 2e+65) {
		tmp = fma((a * b), 27.0, (x * 2.0));
	} else {
		tmp = fma(((z * t) * -9.0), y, ((a * b) * 27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_1 <= -2e+59)
		tmp = fma(t, Float64(z * Float64(y * -9.0)), Float64(x * 2.0));
	elseif (t_1 <= 2e+65)
		tmp = fma(Float64(a * b), 27.0, Float64(x * 2.0));
	else
		tmp = fma(Float64(Float64(z * t) * -9.0), y, Float64(Float64(a * b) * 27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+59], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+65], N[(N[(a * b), $MachinePrecision] * 27.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision] * y + N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.99999999999999994e59

   1. Initial program 82.7%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 84.2

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

   5. Applied rewrites 84.2%

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

   7. Applied rewrites 77.6%

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

   if -1.99999999999999994e59 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2e65

   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 t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 93.1

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

   5. Applied rewrites 93.1%

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

   if 2e65 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 85.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   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. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 89.3

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

   5. Applied rewrites 89.3%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -2 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(t, z \cdot \left(y \cdot -9\right), x \cdot 2\right)\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 2 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot t\right) \cdot -9, y, \left(a \cdot b\right) \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(t, z \cdot \left(y \cdot -9\right), x \cdot 2\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot t\right) \cdot -9, y, x \cdot 2\right)\\ \end{array} \end{array} \]

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 (* (* (* 9.0 y) z) t)))
   (if (<= t_1 -2e+59)
     (fma t (* z (* y -9.0)) (* x 2.0))
     (if (<= t_1 1e+183)
       (fma (* a b) 27.0 (* x 2.0))
       (fma (* (* z t) -9.0) y (* 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 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_1 <= -2e+59) {
		tmp = fma(t, (z * (y * -9.0)), (x * 2.0));
	} else if (t_1 <= 1e+183) {
		tmp = fma((a * b), 27.0, (x * 2.0));
	} else {
		tmp = fma(((z * t) * -9.0), y, (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(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_1 <= -2e+59)
		tmp = fma(t, Float64(z * Float64(y * -9.0)), Float64(x * 2.0));
	elseif (t_1 <= 1e+183)
		tmp = fma(Float64(a * b), 27.0, Float64(x * 2.0));
	else
		tmp = fma(Float64(Float64(z * t) * -9.0), y, 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[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+59], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+183], N[(N[(a * b), $MachinePrecision] * 27.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision] * y + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.99999999999999994e59

   1. Initial program 82.7%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 84.2

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

   5. Applied rewrites 84.2%

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

   7. Applied rewrites 77.6%

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

   if -1.99999999999999994e59 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 9.99999999999999947e182

   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 t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 90.2

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

   5. Applied rewrites 90.2%

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

   if 9.99999999999999947e182 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 79.7%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 90.8

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

   5. Applied rewrites 90.8%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -2 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(t, z \cdot \left(y \cdot -9\right), x \cdot 2\right)\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot t\right) \cdot -9, y, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(t, z \cdot \left(y \cdot -9\right), x \cdot 2\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot t\right) \cdot -9\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* 9.0 y) z) t)))
   (if (<= t_1 -2e+59)
     (fma t (* z (* y -9.0)) (* x 2.0))
     (if (<= t_1 1e+183)
       (fma (* a b) 27.0 (* x 2.0))
       (* (* (* z t) -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 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_1 <= -2e+59) {
		tmp = fma(t, (z * (y * -9.0)), (x * 2.0));
	} else if (t_1 <= 1e+183) {
		tmp = fma((a * b), 27.0, (x * 2.0));
	} else {
		tmp = ((z * t) * -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(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_1 <= -2e+59)
		tmp = fma(t, Float64(z * Float64(y * -9.0)), Float64(x * 2.0));
	elseif (t_1 <= 1e+183)
		tmp = fma(Float64(a * b), 27.0, Float64(x * 2.0));
	else
		tmp = Float64(Float64(Float64(z * t) * -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[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+59], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+183], N[(N[(a * b), $MachinePrecision] * 27.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.99999999999999994e59

   1. Initial program 82.7%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 84.2

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

   5. Applied rewrites 84.2%

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

   7. Applied rewrites 77.6%

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

   if -1.99999999999999994e59 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 9.99999999999999947e182

   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 t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 90.2

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

   5. Applied rewrites 90.2%

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

   if 9.99999999999999947e182 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 79.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 2.5

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

   5. Applied rewrites 2.5%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 79.5

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

   8. Applied rewrites 79.5%

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

   10. Applied rewrites 90.8%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -2 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(t, z \cdot \left(y \cdot -9\right), x \cdot 2\right)\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot t\right) \cdot -9\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\left(z \cdot \left(y \cdot -9\right)\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot t\right) \cdot -9\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* 9.0 y) z) t)))
   (if (<= t_1 -1e+109)
     (* (* z (* y -9.0)) t)
     (if (<= t_1 1e+183)
       (fma (* a b) 27.0 (* x 2.0))
       (* (* (* z t) -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 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_1 <= -1e+109) {
		tmp = (z * (y * -9.0)) * t;
	} else if (t_1 <= 1e+183) {
		tmp = fma((a * b), 27.0, (x * 2.0));
	} else {
		tmp = ((z * t) * -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(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_1 <= -1e+109)
		tmp = Float64(Float64(z * Float64(y * -9.0)) * t);
	elseif (t_1 <= 1e+183)
		tmp = fma(Float64(a * b), 27.0, Float64(x * 2.0));
	else
		tmp = Float64(Float64(Float64(z * t) * -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[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+109], N[(N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 1e+183], N[(N[(a * b), $MachinePrecision] * 27.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -9.99999999999999982e108

   1. Initial program 81.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 4.9

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

   5. Applied rewrites 4.9%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 74.8

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

   8. Applied rewrites 74.8%

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

   10. Applied rewrites 74.8%

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

   if -9.99999999999999982e108 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 9.99999999999999947e182

   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 t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 89.3

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

   5. Applied rewrites 89.3%

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

   if 9.99999999999999947e182 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 79.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 2.5

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

   5. Applied rewrites 2.5%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 79.5

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

   8. Applied rewrites 79.5%

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

   10. Applied rewrites 90.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\left(z \cdot \left(y \cdot -9\right)\right) \cdot t\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot t\right) \cdot -9\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(9 \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\left(z \cdot \left(y \cdot -9\right)\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot t\right) \cdot -9\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* 9.0 y) z) t)))
   (if (<= t_1 -1e+109)
     (* (* z (* y -9.0)) t)
     (if (<= t_1 1e+183)
       (fma (* 27.0 b) a (* x 2.0))
       (* (* (* z t) -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 = ((9.0 * y) * z) * t;
	double tmp;
	if (t_1 <= -1e+109) {
		tmp = (z * (y * -9.0)) * t;
	} else if (t_1 <= 1e+183) {
		tmp = fma((27.0 * b), a, (x * 2.0));
	} else {
		tmp = ((z * t) * -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(9.0 * y) * z) * t)
	tmp = 0.0
	if (t_1 <= -1e+109)
		tmp = Float64(Float64(z * Float64(y * -9.0)) * t);
	elseif (t_1 <= 1e+183)
		tmp = fma(Float64(27.0 * b), a, Float64(x * 2.0));
	else
		tmp = Float64(Float64(Float64(z * t) * -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[(9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+109], N[(N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 1e+183], N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -9.99999999999999982e108

   1. Initial program 81.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 4.9

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

   5. Applied rewrites 4.9%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 74.8

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

   8. Applied rewrites 74.8%

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

   10. Applied rewrites 74.8%

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

   if -9.99999999999999982e108 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 9.99999999999999947e182

   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 t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 89.3

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

   5. Applied rewrites 89.3%

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

   7. Applied rewrites 89.3%

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

   if 9.99999999999999947e182 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 79.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 2.5

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

   5. Applied rewrites 2.5%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 79.5

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

   8. Applied rewrites 79.5%

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

   10. Applied rewrites 90.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\left(z \cdot \left(y \cdot -9\right)\right) \cdot t\\ \mathbf{elif}\;\left(\left(9 \cdot y\right) \cdot z\right) \cdot t \leq 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z \cdot t\right) \cdot -9\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{if}\;\left(9 \cdot y\right) \cdot z \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot -9, t, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (* 27.0 b) a (* x 2.0))))
   (if (<= (* (* 9.0 y) z) 2e+302)
     (fma (* (* z y) -9.0) t t_1)
     (fma (* (* y -9.0) t) z t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((27.0 * b), a, (x * 2.0));
	double tmp;
	if (((9.0 * y) * z) <= 2e+302) {
		tmp = fma(((z * y) * -9.0), t, t_1);
	} else {
		tmp = fma(((y * -9.0) * t), z, t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(Float64(27.0 * b), a, Float64(x * 2.0))
	tmp = 0.0
	if (Float64(Float64(9.0 * y) * z) <= 2e+302)
		tmp = fma(Float64(Float64(z * y) * -9.0), t, t_1);
	else
		tmp = fma(Float64(Float64(y * -9.0) * t), z, t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision], 2e+302], N[(N[(N[(z * y), $MachinePrecision] * -9.0), $MachinePrecision] * t + t$95$1), $MachinePrecision], N[(N[(N[(y * -9.0), $MachinePrecision] * t), $MachinePrecision] * z + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 2.0000000000000002e302

   1. Initial program 95.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval N/A

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

      18. lower-*.f64 N/A

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

   4. Applied rewrites 95.9%

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

   if 2.0000000000000002e302 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 50.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

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

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 99.7%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot y\right) \cdot z \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot -9, t, \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{if}\;\left(9 \cdot y\right) \cdot z \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot -9, t, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(y \cdot t\right) \cdot z, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (* 27.0 b) a (* x 2.0))))
   (if (<= (* (* 9.0 y) z) 2e+302)
     (fma (* (* z y) -9.0) t t_1)
     (fma -9.0 (* (* y t) z) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((27.0 * b), a, (x * 2.0));
	double tmp;
	if (((9.0 * y) * z) <= 2e+302) {
		tmp = fma(((z * y) * -9.0), t, t_1);
	} else {
		tmp = fma(-9.0, ((y * t) * z), t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(Float64(27.0 * b), a, Float64(x * 2.0))
	tmp = 0.0
	if (Float64(Float64(9.0 * y) * z) <= 2e+302)
		tmp = fma(Float64(Float64(z * y) * -9.0), t, t_1);
	else
		tmp = fma(-9.0, Float64(Float64(y * t) * z), t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(9.0 * y), $MachinePrecision] * z), $MachinePrecision], 2e+302], N[(N[(N[(z * y), $MachinePrecision] * -9.0), $MachinePrecision] * t + t$95$1), $MachinePrecision], N[(-9.0 * N[(N[(y * t), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 2.0000000000000002e302

   1. Initial program 95.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. +-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

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

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval N/A

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

      18. lower-*.f64 N/A

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

   4. Applied rewrites 95.9%

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

   if 2.0000000000000002e302 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 50.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

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

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. metadata-eval N/A

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

      16. *-commutative N/A

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

      17. associate-*r* N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. lower-*.f64 N/A

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

   4. Applied rewrites 99.6%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot y\right) \cdot z \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot -9, t, \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(y \cdot t\right) \cdot z, \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := \left(a \cdot b\right) \cdot 27\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+119}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)) (t_2 (* (* a b) 27.0)))
   (if (<= t_1 -2e+91) t_2 (if (<= t_1 1e+119) (* x 2.0) 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 = (a * 27.0) * b;
	double t_2 = (a * b) * 27.0;
	double tmp;
	if (t_1 <= -2e+91) {
		tmp = t_2;
	} else if (t_1 <= 1e+119) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    t_2 = (a * b) * 27.0d0
    if (t_1 <= (-2d+91)) then
        tmp = t_2
    else if (t_1 <= 1d+119) then
        tmp = x * 2.0d0
    else
        tmp = t_2
    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 t_2 = (a * b) * 27.0;
	double tmp;
	if (t_1 <= -2e+91) {
		tmp = t_2;
	} else if (t_1 <= 1e+119) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	t_2 = (a * b) * 27.0
	tmp = 0
	if t_1 <= -2e+91:
		tmp = t_2
	elif t_1 <= 1e+119:
		tmp = x * 2.0
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	t_2 = Float64(Float64(a * b) * 27.0)
	tmp = 0.0
	if (t_1 <= -2e+91)
		tmp = t_2;
	elseif (t_1 <= 1e+119)
		tmp = Float64(x * 2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	t_2 = (a * b) * 27.0;
	tmp = 0.0;
	if (t_1 <= -2e+91)
		tmp = t_2;
	elseif (t_1 <= 1e+119)
		tmp = x * 2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+91], t$95$2, If[LessEqual[t$95$1, 1e+119], N[(x * 2.0), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2.00000000000000016e91 or 9.99999999999999944e118 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 91.6%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 67.9

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

   5. Applied rewrites 67.9%

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

   if -2.00000000000000016e91 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.99999999999999944e118

   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 x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 42.1

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

   5. Applied rewrites 42.1%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 10^{+119}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := \left(27 \cdot b\right) \cdot a\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+119}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)) (t_2 (* (* 27.0 b) a)))
   (if (<= t_1 -2e+91) t_2 (if (<= t_1 1e+119) (* x 2.0) 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 = (a * 27.0) * b;
	double t_2 = (27.0 * b) * a;
	double tmp;
	if (t_1 <= -2e+91) {
		tmp = t_2;
	} else if (t_1 <= 1e+119) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    t_2 = (27.0d0 * b) * a
    if (t_1 <= (-2d+91)) then
        tmp = t_2
    else if (t_1 <= 1d+119) then
        tmp = x * 2.0d0
    else
        tmp = t_2
    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 t_2 = (27.0 * b) * a;
	double tmp;
	if (t_1 <= -2e+91) {
		tmp = t_2;
	} else if (t_1 <= 1e+119) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	t_2 = (27.0 * b) * a
	tmp = 0
	if t_1 <= -2e+91:
		tmp = t_2
	elif t_1 <= 1e+119:
		tmp = x * 2.0
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	t_2 = Float64(Float64(27.0 * b) * a)
	tmp = 0.0
	if (t_1 <= -2e+91)
		tmp = t_2;
	elseif (t_1 <= 1e+119)
		tmp = Float64(x * 2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	t_2 = (27.0 * b) * a;
	tmp = 0.0;
	if (t_1 <= -2e+91)
		tmp = t_2;
	elseif (t_1 <= 1e+119)
		tmp = x * 2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+91], t$95$2, If[LessEqual[t$95$1, 1e+119], N[(x * 2.0), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2.00000000000000016e91 or 9.99999999999999944e118 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 91.6%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 67.9

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

   5. Applied rewrites 67.9%

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

   7. Applied rewrites 67.8%

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

   if -2.00000000000000016e91 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.99999999999999944e118

   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 x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 42.1

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

   5. Applied rewrites 42.1%

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

Alternative 15: 30.7% accurate, 6.2× speedup

Math

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

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 (* 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) {
	return x * 2.0;
}

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 = x * 2.0d0
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 x * 2.0;
}

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 x * 2.0

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

Derivation

1. Initial program 92.5%

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

3. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 30.3

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

5. Applied rewrites 30.3%

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

Developer Target 1: 95.1% 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 2024273 
(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)))