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

Percentage Accurate: 95.8% → 98.6%

Time: 5.2s

Alternatives: 18

Speedup: 0.9×

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

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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: 95.8% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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: 98.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 10^{-93}:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot z\right) \cdot -9, y, \mathsf{fma}\left(b \cdot a, 27, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, \mathsf{fma}\left(-9 \cdot t, z \cdot y, 2 \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1e-93)
   (fma (* (* t z) -9.0) y (fma (* b a) 27.0 (* 2.0 x)))
   (fma (* b 27.0) a (fma (* -9.0 t) (* z y) (* 2.0 x)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1e-93) {
		tmp = fma(((t * z) * -9.0), y, fma((b * a), 27.0, (2.0 * x)));
	} else {
		tmp = fma((b * 27.0), a, fma((-9.0 * t), (z * y), (2.0 * x)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1e-93)
		tmp = fma(Float64(Float64(t * z) * -9.0), y, fma(Float64(b * a), 27.0, Float64(2.0 * x)));
	else
		tmp = fma(Float64(b * 27.0), a, fma(Float64(-9.0 * t), Float64(z * y), Float64(2.0 * x)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1e-93], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y + N[(N[(b * a), $MachinePrecision] * 27.0 + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * 27.0), $MachinePrecision] * a + N[(N[(-9.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 9.999999999999999e-94

   1. Initial program 94.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. associate-+l+ N/A

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

   4. Applied rewrites 98.1%

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

   if 9.999999999999999e-94 < t

   1. Initial program 96.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. *-commutative N/A

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

      17. associate-*r* N/A

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

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

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

   4. Applied rewrites 98.6%

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

Alternative 2: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+33} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot t\right) \cdot z, y, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (or (<= t_1 -5e+33) (not (<= t_1 5e+45)))
     (fma (* (* -9.0 t) z) y (+ x x))
     (fma a (* 27.0 b) (* x 2.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if ((t_1 <= -5e+33) || !(t_1 <= 5e+45)) {
		tmp = fma(((-9.0 * t) * z), y, (x + x));
	} else {
		tmp = fma(a, (27.0 * b), (x * 2.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if ((t_1 <= -5e+33) || !(t_1 <= 5e+45))
		tmp = fma(Float64(Float64(-9.0 * t) * z), y, Float64(x + x));
	else
		tmp = fma(a, Float64(27.0 * b), Float64(x * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+33], N[Not[LessEqual[t$95$1, 5e+45]], $MachinePrecision]], N[(N[(N[(-9.0 * t), $MachinePrecision] * z), $MachinePrecision] * y + N[(x + x), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999973e33 or 5e45 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.3%

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

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. associate-+l+ N/A

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

   4. Applied rewrites 89.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 89.9

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

   6. Applied rewrites 89.9%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 82.0

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

   9. Applied rewrites 82.0%

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

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. count-2-rev N/A

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

       4. lower-+.f64 82.0

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

   11. Applied rewrites 82.0%

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

   if -4.99999999999999973e33 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5e45

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 91.1

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

   5. Applied rewrites 91.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 91.0

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 91.0

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

   7. Applied rewrites 91.0%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+33} \lor \neg \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot t\right) \cdot z, y, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+33} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot t, -9, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (or (<= t_1 -5e+33) (not (<= t_1 5e+45)))
     (fma (* (* y z) t) -9.0 (+ x x))
     (fma a (* 27.0 b) (* x 2.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if ((t_1 <= -5e+33) || !(t_1 <= 5e+45)) {
		tmp = fma(((y * z) * t), -9.0, (x + x));
	} else {
		tmp = fma(a, (27.0 * b), (x * 2.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if ((t_1 <= -5e+33) || !(t_1 <= 5e+45))
		tmp = fma(Float64(Float64(y * z) * t), -9.0, Float64(x + x));
	else
		tmp = fma(a, Float64(27.0 * b), Float64(x * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+33], N[Not[LessEqual[t$95$1, 5e+45]], $MachinePrecision]], N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * -9.0 + N[(x + x), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999973e33 or 5e45 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.3%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 14.9

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

   5. Applied rewrites 14.9%

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

   6. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 81.5

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

   8. Applied rewrites 81.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 81.5

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

   10. Applied rewrites 81.5%

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

   if -4.99999999999999973e33 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5e45

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 91.1

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

   5. Applied rewrites 91.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 91.0

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 91.0

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

   7. Applied rewrites 91.0%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -5 \cdot 10^{+33} \lor \neg \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot t, -9, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot z\right) \cdot -9, y, x \cdot 2\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot t\right) \cdot z, y, x + x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -5e+33)
     (fma (* (* t z) -9.0) y (* x 2.0))
     (if (<= t_1 5e+45)
       (fma a (* 27.0 b) (* x 2.0))
       (fma (* (* -9.0 t) z) y (+ x x))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -5e+33) {
		tmp = fma(((t * z) * -9.0), y, (x * 2.0));
	} else if (t_1 <= 5e+45) {
		tmp = fma(a, (27.0 * b), (x * 2.0));
	} else {
		tmp = fma(((-9.0 * t) * z), y, (x + x));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -5e+33)
		tmp = fma(Float64(Float64(t * z) * -9.0), y, Float64(x * 2.0));
	elseif (t_1 <= 5e+45)
		tmp = fma(a, Float64(27.0 * b), Float64(x * 2.0));
	else
		tmp = fma(Float64(Float64(-9.0 * t) * z), y, Float64(x + x));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+33], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+45], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-9.0 * t), $MachinePrecision] * z), $MachinePrecision] * y + N[(x + x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999973e33

   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. 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. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. associate-+l+ N/A

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

   4. Applied rewrites 89.5%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 79.0

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

   7. Applied rewrites 79.0%

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

   if -4.99999999999999973e33 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5e45

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 91.1

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

   5. Applied rewrites 91.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 91.0

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 91.0

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

   7. Applied rewrites 91.0%

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

   if 5e45 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 82.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. associate-+l+ N/A

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

   4. Applied rewrites 90.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 90.5

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

   6. Applied rewrites 90.5%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 86.3

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

   9. Applied rewrites 86.3%

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

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. count-2-rev N/A

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

       4. lower-+.f64 86.3

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

   11. Applied rewrites 86.3%

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

Alternative 5: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+40} \lor \neg \left(t\_1 \leq 4\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot z\right) \cdot -9, y, \left(27 \cdot a\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(z \cdot t\right), -9, x \cdot 2\right)\\ \end{array} \end{array} \]

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 (* (* a 27.0) b)))
   (if (or (<= t_1 -5e+40) (not (<= t_1 4.0)))
     (fma (* (* t z) -9.0) y (* (* 27.0 a) b))
     (fma (* y (* z t)) -9.0 (* 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 = (a * 27.0) * b;
	double tmp;
	if ((t_1 <= -5e+40) || !(t_1 <= 4.0)) {
		tmp = fma(((t * z) * -9.0), y, ((27.0 * a) * b));
	} else {
		tmp = fma((y * (z * t)), -9.0, (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(a * 27.0) * b)
	tmp = 0.0
	if ((t_1 <= -5e+40) || !(t_1 <= 4.0))
		tmp = fma(Float64(Float64(t * z) * -9.0), y, Float64(Float64(27.0 * a) * b));
	else
		tmp = fma(Float64(y * Float64(z * t)), -9.0, 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[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+40], N[Not[LessEqual[t$95$1, 4.0]], $MachinePrecision]], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y + N[(N[(27.0 * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -5.00000000000000003e40 or 4 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 92.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. associate-+l+ N/A

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

   4. Applied rewrites 96.4%

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

   5. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 87.2

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

   7. Applied rewrites 87.2%

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

   if -5.00000000000000003e40 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 4

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 53.8

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

   5. Applied rewrites 53.8%

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

   6. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 88.9

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

   8. Applied rewrites 88.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 87.4

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

   10. Applied rewrites 87.4%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -5 \cdot 10^{+40} \lor \neg \left(\left(a \cdot 27\right) \cdot b \leq 4\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot z\right) \cdot -9, y, \left(27 \cdot a\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(z \cdot t\right), -9, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+209} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;\left(\left(z \cdot t\right) \cdot -9\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (or (<= t_1 -1e+209) (not (<= t_1 5e+45)))
     (* (* (* z t) -9.0) y)
     (fma a (* 27.0 b) (* x 2.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if ((t_1 <= -1e+209) || !(t_1 <= 5e+45)) {
		tmp = ((z * t) * -9.0) * y;
	} else {
		tmp = fma(a, (27.0 * b), (x * 2.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if ((t_1 <= -1e+209) || !(t_1 <= 5e+45))
		tmp = Float64(Float64(Float64(z * t) * -9.0) * y);
	else
		tmp = fma(a, Float64(27.0 * b), Float64(x * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+209], N[Not[LessEqual[t$95$1, 5e+45]], $MachinePrecision]], N[(N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.0000000000000001e209 or 5e45 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 85.4%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 77.3

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

   5. Applied rewrites 77.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 77.3

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

   7. Applied rewrites 77.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 78.4

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

   9. Applied rewrites 78.4%

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

   if -1.0000000000000001e209 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5e45

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 86.3

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

   5. Applied rewrites 86.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 86.3

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 86.3

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

   7. Applied rewrites 86.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -1 \cdot 10^{+209} \lor \neg \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;\left(\left(z \cdot t\right) \cdot -9\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+209} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;\left(\left(z \cdot t\right) \cdot -9\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a, 27, 2 \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (or (<= t_1 -1e+209) (not (<= t_1 5e+45)))
     (* (* (* z t) -9.0) y)
     (fma (* b a) 27.0 (* 2.0 x)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if ((t_1 <= -1e+209) || !(t_1 <= 5e+45)) {
		tmp = ((z * t) * -9.0) * y;
	} else {
		tmp = fma((b * a), 27.0, (2.0 * x));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if ((t_1 <= -1e+209) || !(t_1 <= 5e+45))
		tmp = Float64(Float64(Float64(z * t) * -9.0) * y);
	else
		tmp = fma(Float64(b * a), 27.0, Float64(2.0 * x));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+209], N[Not[LessEqual[t$95$1, 5e+45]], $MachinePrecision]], N[(N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision], N[(N[(b * a), $MachinePrecision] * 27.0 + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.0000000000000001e209 or 5e45 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 85.4%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 77.3

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

   5. Applied rewrites 77.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 77.3

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

   7. Applied rewrites 77.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 78.4

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

   9. Applied rewrites 78.4%

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

   if -1.0000000000000001e209 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5e45

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 86.3

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

   5. Applied rewrites 86.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -1 \cdot 10^{+209} \lor \neg \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;\left(\left(z \cdot t\right) \cdot -9\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a, 27, 2 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := \left(27 \cdot b\right) \cdot a\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-225}:\\ \;\;\;\;\left(\left(z \cdot t\right) \cdot -9\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq 4:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)) (t_2 (* (* 27.0 b) a)))
   (if (<= t_1 -4e+123)
     t_2
     (if (<= t_1 -2e-225)
       (* (* (* z t) -9.0) y)
       (if (<= t_1 4.0) (+ x x) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = (27.0 * b) * a;
	double tmp;
	if (t_1 <= -4e+123) {
		tmp = t_2;
	} else if (t_1 <= -2e-225) {
		tmp = ((z * t) * -9.0) * y;
	} else if (t_1 <= 4.0) {
		tmp = x + x;
	} 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.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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 <= (-4d+123)) then
        tmp = t_2
    else if (t_1 <= (-2d-225)) then
        tmp = ((z * t) * (-9.0d0)) * y
    else if (t_1 <= 4.0d0) then
        tmp = x + x
    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 <= -4e+123) {
		tmp = t_2;
	} else if (t_1 <= -2e-225) {
		tmp = ((z * t) * -9.0) * y;
	} else if (t_1 <= 4.0) {
		tmp = x + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	t_2 = (27.0 * b) * a
	tmp = 0
	if t_1 <= -4e+123:
		tmp = t_2
	elif t_1 <= -2e-225:
		tmp = ((z * t) * -9.0) * y
	elif t_1 <= 4.0:
		tmp = x + x
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	t_2 = Float64(Float64(27.0 * b) * a)
	tmp = 0.0
	if (t_1 <= -4e+123)
		tmp = t_2;
	elseif (t_1 <= -2e-225)
		tmp = Float64(Float64(Float64(z * t) * -9.0) * y);
	elseif (t_1 <= 4.0)
		tmp = Float64(x + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	t_2 = (27.0 * b) * a;
	tmp = 0.0;
	if (t_1 <= -4e+123)
		tmp = t_2;
	elseif (t_1 <= -2e-225)
		tmp = ((z * t) * -9.0) * y;
	elseif (t_1 <= 4.0)
		tmp = x + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+123], t$95$2, If[LessEqual[t$95$1, -2e-225], N[(N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 4.0], N[(x + x), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -3.99999999999999991e123 or 4 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 92.2%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 64.9

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

   5. Applied rewrites 64.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift-*.f64 65.1

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

   7. Applied rewrites 65.1%

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

   if -3.99999999999999991e123 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.9999999999999999e-225

   1. Initial program 96.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 55.1

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

   5. Applied rewrites 55.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 55.1

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

   7. Applied rewrites 55.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 51.6

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

   9. Applied rewrites 51.6%

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

   if -1.9999999999999999e-225 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 4

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 62.5

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

   5. Applied rewrites 62.5%

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

      1. lift-*.f64 N/A

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

      2. count-2-rev N/A

         \[\leadsto x + \color{blue}{x} \]

      3. lower-+.f64 62.5

         \[\leadsto x + \color{blue}{x} \]

   7. Applied rewrites 62.5%

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

Alternative 9: 54.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := \left(27 \cdot b\right) \cdot a\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-225}:\\ \;\;\;\;\left(\left(y \cdot z\right) \cdot -9\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 4:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)) (t_2 (* (* 27.0 b) a)))
   (if (<= t_1 -4e+123)
     t_2
     (if (<= t_1 -2e-225)
       (* (* (* y z) -9.0) t)
       (if (<= t_1 4.0) (+ x x) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = (27.0 * b) * a;
	double tmp;
	if (t_1 <= -4e+123) {
		tmp = t_2;
	} else if (t_1 <= -2e-225) {
		tmp = ((y * z) * -9.0) * t;
	} else if (t_1 <= 4.0) {
		tmp = x + x;
	} 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.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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 <= (-4d+123)) then
        tmp = t_2
    else if (t_1 <= (-2d-225)) then
        tmp = ((y * z) * (-9.0d0)) * t
    else if (t_1 <= 4.0d0) then
        tmp = x + x
    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 <= -4e+123) {
		tmp = t_2;
	} else if (t_1 <= -2e-225) {
		tmp = ((y * z) * -9.0) * t;
	} else if (t_1 <= 4.0) {
		tmp = x + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	t_2 = (27.0 * b) * a
	tmp = 0
	if t_1 <= -4e+123:
		tmp = t_2
	elif t_1 <= -2e-225:
		tmp = ((y * z) * -9.0) * t
	elif t_1 <= 4.0:
		tmp = x + x
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	t_2 = Float64(Float64(27.0 * b) * a)
	tmp = 0.0
	if (t_1 <= -4e+123)
		tmp = t_2;
	elseif (t_1 <= -2e-225)
		tmp = Float64(Float64(Float64(y * z) * -9.0) * t);
	elseif (t_1 <= 4.0)
		tmp = Float64(x + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	t_2 = (27.0 * b) * a;
	tmp = 0.0;
	if (t_1 <= -4e+123)
		tmp = t_2;
	elseif (t_1 <= -2e-225)
		tmp = ((y * z) * -9.0) * t;
	elseif (t_1 <= 4.0)
		tmp = x + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+123], t$95$2, If[LessEqual[t$95$1, -2e-225], N[(N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 4.0], N[(x + x), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -3.99999999999999991e123 or 4 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 92.2%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 64.9

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

   5. Applied rewrites 64.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift-*.f64 65.1

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

   7. Applied rewrites 65.1%

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

   if -3.99999999999999991e123 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.9999999999999999e-225

   1. Initial program 96.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 55.1

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

   5. Applied rewrites 55.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 55.2

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

   7. Applied rewrites 55.2%

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

   if -1.9999999999999999e-225 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 4

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 62.5

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

   5. Applied rewrites 62.5%

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

      1. lift-*.f64 N/A

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

      2. count-2-rev N/A

         \[\leadsto x + \color{blue}{x} \]

      3. lower-+.f64 62.5

         \[\leadsto x + \color{blue}{x} \]

   7. Applied rewrites 62.5%

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

Alternative 10: 54.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := \left(27 \cdot b\right) \cdot a\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-225}:\\ \;\;\;\;\left(-9 \cdot t\right) \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t\_1 \leq 4:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)) (t_2 (* (* 27.0 b) a)))
   (if (<= t_1 -4e+123)
     t_2
     (if (<= t_1 -2e-225)
       (* (* -9.0 t) (* y z))
       (if (<= t_1 4.0) (+ x x) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = (27.0 * b) * a;
	double tmp;
	if (t_1 <= -4e+123) {
		tmp = t_2;
	} else if (t_1 <= -2e-225) {
		tmp = (-9.0 * t) * (y * z);
	} else if (t_1 <= 4.0) {
		tmp = x + x;
	} 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.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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 <= (-4d+123)) then
        tmp = t_2
    else if (t_1 <= (-2d-225)) then
        tmp = ((-9.0d0) * t) * (y * z)
    else if (t_1 <= 4.0d0) then
        tmp = x + x
    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 <= -4e+123) {
		tmp = t_2;
	} else if (t_1 <= -2e-225) {
		tmp = (-9.0 * t) * (y * z);
	} else if (t_1 <= 4.0) {
		tmp = x + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	t_2 = (27.0 * b) * a
	tmp = 0
	if t_1 <= -4e+123:
		tmp = t_2
	elif t_1 <= -2e-225:
		tmp = (-9.0 * t) * (y * z)
	elif t_1 <= 4.0:
		tmp = x + x
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	t_2 = Float64(Float64(27.0 * b) * a)
	tmp = 0.0
	if (t_1 <= -4e+123)
		tmp = t_2;
	elseif (t_1 <= -2e-225)
		tmp = Float64(Float64(-9.0 * t) * Float64(y * z));
	elseif (t_1 <= 4.0)
		tmp = Float64(x + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	t_2 = (27.0 * b) * a;
	tmp = 0.0;
	if (t_1 <= -4e+123)
		tmp = t_2;
	elseif (t_1 <= -2e-225)
		tmp = (-9.0 * t) * (y * z);
	elseif (t_1 <= 4.0)
		tmp = x + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+123], t$95$2, If[LessEqual[t$95$1, -2e-225], N[(N[(-9.0 * t), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4.0], N[(x + x), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -3.99999999999999991e123 or 4 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 92.2%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 64.9

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

   5. Applied rewrites 64.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift-*.f64 65.1

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

   7. Applied rewrites 65.1%

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

   if -3.99999999999999991e123 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.9999999999999999e-225

   1. Initial program 96.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 55.1

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

   5. Applied rewrites 55.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 55.1

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

   7. Applied rewrites 55.1%

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

   if -1.9999999999999999e-225 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 4

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 62.5

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

   5. Applied rewrites 62.5%

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

      1. lift-*.f64 N/A

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

      2. count-2-rev N/A

         \[\leadsto x + \color{blue}{x} \]

      3. lower-+.f64 62.5

         \[\leadsto x + \color{blue}{x} \]

   7. Applied rewrites 62.5%

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

Alternative 11: 54.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := \left(27 \cdot b\right) \cdot a\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-225}:\\ \;\;\;\;-9 \cdot \left(\left(z \cdot y\right) \cdot t\right)\\ \mathbf{elif}\;t\_1 \leq 4:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)) (t_2 (* (* 27.0 b) a)))
   (if (<= t_1 -4e+123)
     t_2
     (if (<= t_1 -2e-225)
       (* -9.0 (* (* z y) t))
       (if (<= t_1 4.0) (+ x x) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = (27.0 * b) * a;
	double tmp;
	if (t_1 <= -4e+123) {
		tmp = t_2;
	} else if (t_1 <= -2e-225) {
		tmp = -9.0 * ((z * y) * t);
	} else if (t_1 <= 4.0) {
		tmp = x + x;
	} 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.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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 <= (-4d+123)) then
        tmp = t_2
    else if (t_1 <= (-2d-225)) then
        tmp = (-9.0d0) * ((z * y) * t)
    else if (t_1 <= 4.0d0) then
        tmp = x + x
    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 <= -4e+123) {
		tmp = t_2;
	} else if (t_1 <= -2e-225) {
		tmp = -9.0 * ((z * y) * t);
	} else if (t_1 <= 4.0) {
		tmp = x + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	t_2 = (27.0 * b) * a
	tmp = 0
	if t_1 <= -4e+123:
		tmp = t_2
	elif t_1 <= -2e-225:
		tmp = -9.0 * ((z * y) * t)
	elif t_1 <= 4.0:
		tmp = x + x
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	t_2 = Float64(Float64(27.0 * b) * a)
	tmp = 0.0
	if (t_1 <= -4e+123)
		tmp = t_2;
	elseif (t_1 <= -2e-225)
		tmp = Float64(-9.0 * Float64(Float64(z * y) * t));
	elseif (t_1 <= 4.0)
		tmp = Float64(x + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	t_2 = (27.0 * b) * a;
	tmp = 0.0;
	if (t_1 <= -4e+123)
		tmp = t_2;
	elseif (t_1 <= -2e-225)
		tmp = -9.0 * ((z * y) * t);
	elseif (t_1 <= 4.0)
		tmp = x + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+123], t$95$2, If[LessEqual[t$95$1, -2e-225], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4.0], N[(x + x), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -3.99999999999999991e123 or 4 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 92.2%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 64.9

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

   5. Applied rewrites 64.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift-*.f64 65.1

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

   7. Applied rewrites 65.1%

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

   if -3.99999999999999991e123 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.9999999999999999e-225

   1. Initial program 96.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 55.1

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

   5. Applied rewrites 55.1%

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

   if -1.9999999999999999e-225 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 4

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 62.5

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

   5. Applied rewrites 62.5%

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

      1. lift-*.f64 N/A

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

      2. count-2-rev N/A

         \[\leadsto x + \color{blue}{x} \]

      3. lower-+.f64 62.5

         \[\leadsto x + \color{blue}{x} \]

   7. Applied rewrites 62.5%

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

Alternative 12: 53.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := \left(27 \cdot b\right) \cdot a\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-225}:\\ \;\;\;\;-9 \cdot \left(\left(y \cdot t\right) \cdot z\right)\\ \mathbf{elif}\;t\_1 \leq 4:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)) (t_2 (* (* 27.0 b) a)))
   (if (<= t_1 -4e+123)
     t_2
     (if (<= t_1 -2e-225)
       (* -9.0 (* (* y t) z))
       (if (<= t_1 4.0) (+ x x) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = (27.0 * b) * a;
	double tmp;
	if (t_1 <= -4e+123) {
		tmp = t_2;
	} else if (t_1 <= -2e-225) {
		tmp = -9.0 * ((y * t) * z);
	} else if (t_1 <= 4.0) {
		tmp = x + x;
	} 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.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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 <= (-4d+123)) then
        tmp = t_2
    else if (t_1 <= (-2d-225)) then
        tmp = (-9.0d0) * ((y * t) * z)
    else if (t_1 <= 4.0d0) then
        tmp = x + x
    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 <= -4e+123) {
		tmp = t_2;
	} else if (t_1 <= -2e-225) {
		tmp = -9.0 * ((y * t) * z);
	} else if (t_1 <= 4.0) {
		tmp = x + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	t_2 = (27.0 * b) * a
	tmp = 0
	if t_1 <= -4e+123:
		tmp = t_2
	elif t_1 <= -2e-225:
		tmp = -9.0 * ((y * t) * z)
	elif t_1 <= 4.0:
		tmp = x + x
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	t_2 = Float64(Float64(27.0 * b) * a)
	tmp = 0.0
	if (t_1 <= -4e+123)
		tmp = t_2;
	elseif (t_1 <= -2e-225)
		tmp = Float64(-9.0 * Float64(Float64(y * t) * z));
	elseif (t_1 <= 4.0)
		tmp = Float64(x + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	t_2 = (27.0 * b) * a;
	tmp = 0.0;
	if (t_1 <= -4e+123)
		tmp = t_2;
	elseif (t_1 <= -2e-225)
		tmp = -9.0 * ((y * t) * z);
	elseif (t_1 <= 4.0)
		tmp = x + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+123], t$95$2, If[LessEqual[t$95$1, -2e-225], N[(-9.0 * N[(N[(y * t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4.0], N[(x + x), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -3.99999999999999991e123 or 4 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 92.2%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 64.9

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

   5. Applied rewrites 64.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift-*.f64 65.1

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

   7. Applied rewrites 65.1%

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

   if -3.99999999999999991e123 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.9999999999999999e-225

   1. Initial program 96.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 55.1

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

   5. Applied rewrites 55.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 56.6

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

   7. Applied rewrites 56.6%

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

   if -1.9999999999999999e-225 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 4

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 62.5

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

   5. Applied rewrites 62.5%

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

      1. lift-*.f64 N/A

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

      2. count-2-rev N/A

         \[\leadsto x + \color{blue}{x} \]

      3. lower-+.f64 62.5

         \[\leadsto x + \color{blue}{x} \]

   7. Applied rewrites 62.5%

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

Alternative 13: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, \mathsf{fma}\left(-9 \cdot t, z \cdot y, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot z\right) \cdot -9, y, \left(27 \cdot a\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (* y 9.0) z) 5e+288)
   (fma (* b 27.0) a (fma (* -9.0 t) (* z y) (* 2.0 x)))
   (fma (* (* t z) -9.0) y (* (* 27.0 a) b))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * 9.0) * z) <= 5e+288) {
		tmp = fma((b * 27.0), a, fma((-9.0 * t), (z * y), (2.0 * x)));
	} else {
		tmp = fma(((t * z) * -9.0), y, ((27.0 * a) * b));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 5e+288)
		tmp = fma(Float64(b * 27.0), a, fma(Float64(-9.0 * t), Float64(z * y), Float64(2.0 * x)));
	else
		tmp = fma(Float64(Float64(t * z) * -9.0), y, Float64(Float64(27.0 * a) * b));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 5.0000000000000003e288

   1. Initial program 97.5%

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

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. *-commutative N/A

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

      17. associate-*r* N/A

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

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

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

   4. Applied rewrites 97.0%

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

   if 5.0000000000000003e288 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 61.9%

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

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. associate-+l+ N/A

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

   4. Applied rewrites 89.9%

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

   5. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 80.8

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

   7. Applied rewrites 80.8%

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

Alternative 14: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+221}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \mathsf{fma}\left(b \cdot a, 27, 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(z \cdot t\right), -9, x \cdot 2\right)\\ \end{array} \end{array} \]

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
 (if (<= (* (* y 9.0) z) 5e+221)
   (fma (* -9.0 (* z y)) t (fma (* b a) 27.0 (* 2.0 x)))
   (fma (* y (* z t)) -9.0 (* x 2.0))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * 9.0) * z) <= 5e+221) {
		tmp = fma((-9.0 * (z * y)), t, fma((b * a), 27.0, (2.0 * x)));
	} else {
		tmp = fma((y * (z * t)), -9.0, (x * 2.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 5e+221)
		tmp = fma(Float64(-9.0 * Float64(z * y)), t, fma(Float64(b * a), 27.0, Float64(2.0 * x)));
	else
		tmp = fma(Float64(y * Float64(z * t)), -9.0, Float64(x * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 5e+221], N[(N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] * t + N[(N[(b * a), $MachinePrecision] * 27.0 + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 5.0000000000000002e221

   1. Initial program 97.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. associate-+l+ N/A

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

   4. Applied rewrites 97.4%

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

   if 5.0000000000000002e221 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 70.6%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 13.6

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

   5. Applied rewrites 13.6%

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

   6. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 78.3

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

   8. Applied rewrites 78.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 92.5

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

   10. Applied rewrites 92.5%

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

Alternative 15: 53.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+40} \lor \neg \left(t\_1 \leq 4\right):\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (or (<= t_1 -5e+40) (not (<= t_1 4.0))) (* (* 27.0 b) a) (+ x x))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if ((t_1 <= -5e+40) || !(t_1 <= 4.0)) {
		tmp = (27.0 * b) * a;
	} else {
		tmp = x + x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    if ((t_1 <= (-5d+40)) .or. (.not. (t_1 <= 4.0d0))) then
        tmp = (27.0d0 * b) * a
    else
        tmp = x + x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if ((t_1 <= -5e+40) || !(t_1 <= 4.0)) {
		tmp = (27.0 * b) * a;
	} else {
		tmp = x + x;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if (t_1 <= -5e+40) or not (t_1 <= 4.0):
		tmp = (27.0 * b) * a
	else:
		tmp = x + x
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if ((t_1 <= -5e+40) || !(t_1 <= 4.0))
		tmp = Float64(Float64(27.0 * b) * a);
	else
		tmp = Float64(x + x);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	tmp = 0.0;
	if ((t_1 <= -5e+40) || ~((t_1 <= 4.0)))
		tmp = (27.0 * b) * a;
	else
		tmp = x + x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+40], N[Not[LessEqual[t$95$1, 4.0]], $MachinePrecision]], N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision], N[(x + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -5.00000000000000003e40 or 4 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 92.6%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 59.0

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

   5. Applied rewrites 59.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift-*.f64 59.1

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

   7. Applied rewrites 59.1%

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

   if -5.00000000000000003e40 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 4

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 53.8

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

   5. Applied rewrites 53.8%

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

      1. lift-*.f64 N/A

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

      2. count-2-rev N/A

         \[\leadsto x + \color{blue}{x} \]

      3. lower-+.f64 53.8

         \[\leadsto x + \color{blue}{x} \]

   7. Applied rewrites 53.8%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -5 \cdot 10^{+40} \lor \neg \left(\left(a \cdot 27\right) \cdot b \leq 4\right):\\ \;\;\;\;\left(27 \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+40} \lor \neg \left(t\_1 \leq 4\right):\\ \;\;\;\;\left(27 \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (or (<= t_1 -5e+40) (not (<= t_1 4.0))) (* (* 27.0 a) b) (+ x x))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if ((t_1 <= -5e+40) || !(t_1 <= 4.0)) {
		tmp = (27.0 * a) * b;
	} else {
		tmp = x + x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    if ((t_1 <= (-5d+40)) .or. (.not. (t_1 <= 4.0d0))) then
        tmp = (27.0d0 * a) * b
    else
        tmp = x + x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if ((t_1 <= -5e+40) || !(t_1 <= 4.0)) {
		tmp = (27.0 * a) * b;
	} else {
		tmp = x + x;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if (t_1 <= -5e+40) or not (t_1 <= 4.0):
		tmp = (27.0 * a) * b
	else:
		tmp = x + x
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if ((t_1 <= -5e+40) || !(t_1 <= 4.0))
		tmp = Float64(Float64(27.0 * a) * b);
	else
		tmp = Float64(x + x);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	tmp = 0.0;
	if ((t_1 <= -5e+40) || ~((t_1 <= 4.0)))
		tmp = (27.0 * a) * b;
	else
		tmp = x + x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+40], N[Not[LessEqual[t$95$1, 4.0]], $MachinePrecision]], N[(N[(27.0 * a), $MachinePrecision] * b), $MachinePrecision], N[(x + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -5.00000000000000003e40 or 4 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 92.6%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 11.1

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

   5. Applied rewrites 11.1%

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

   6. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.1

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

   8. Applied rewrites 59.1%

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

   if -5.00000000000000003e40 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 4

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 53.8

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

   5. Applied rewrites 53.8%

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

      1. lift-*.f64 N/A

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

      2. count-2-rev N/A

         \[\leadsto x + \color{blue}{x} \]

      3. lower-+.f64 53.8

         \[\leadsto x + \color{blue}{x} \]

   7. Applied rewrites 53.8%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -5 \cdot 10^{+40} \lor \neg \left(\left(a \cdot 27\right) \cdot b \leq 4\right):\\ \;\;\;\;\left(27 \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 98.6% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if t < 5.00000000000000018e-98

   1. Initial program 94.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. associate-+l+ N/A

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

   4. Applied rewrites 98.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 98.1

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

   6. Applied rewrites 98.1%

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

   if 5.00000000000000018e-98 < t

   1. Initial program 96.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. *-commutative N/A

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

      17. associate-*r* N/A

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

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

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

   4. Applied rewrites 98.6%

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

Alternative 18: 30.7% accurate, 9.3× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (+ x x))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return x + x;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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 + x
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return x + x;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return x + x

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(x + x)
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = x + x;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(x + x), $MachinePrecision]

Derivation

1. Initial program 94.7%

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

3. Taylor expanded in x around inf

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

   1. lower-*.f64 33.9

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

5. Applied rewrites 33.9%

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

   1. lift-*.f64 N/A

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

   2. count-2-rev N/A

      \[\leadsto x + \color{blue}{x} \]

   3. lower-+.f64 33.9

      \[\leadsto x + \color{blue}{x} \]

7. Applied rewrites 33.9%

   \[\leadsto x + \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 95.3% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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 2025057 
(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)))