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

Percentage Accurate: 95.4% → 97.4%

Time: 8.4s

Alternatives: 15

Speedup: 0.9×

• 27.0% 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: 95.4% 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: 97.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot t\right) \cdot -9, y, \left(a \cdot b\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, \mathsf{fma}\left(-9 \cdot t, z \cdot y, x + x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.5e+15)
   (fma (* (* z t) -9.0) y (* (* a b) 27.0))
   (fma (* b 27.0) a (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 tmp;
	if (z <= -1.5e+15) {
		tmp = fma(((z * t) * -9.0), y, ((a * b) * 27.0));
	} else {
		tmp = fma((b * 27.0), a, 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)
	tmp = 0.0
	if (z <= -1.5e+15)
		tmp = fma(Float64(Float64(z * t) * -9.0), y, Float64(Float64(a * b) * 27.0));
	else
		tmp = fma(Float64(b * 27.0), a, fma(Float64(-9.0 * t), Float64(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_] := If[LessEqual[z, -1.5e+15], N[(N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision] * y + N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], N[(N[(b * 27.0), $MachinePrecision] * a + N[(N[(-9.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e15

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 74.9

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

   5. Applied rewrites 74.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. associate-*r* N/A

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 N/A

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

      21. lower-*.f64 71.7

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

   7. Applied rewrites 71.7%

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

   if -1.5e15 < z

   1. Initial program 94.6%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      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. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

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

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

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

      18. *-commutative N/A

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

      19. +-commutative N/A

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

   4. Applied rewrites 96.2%

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

Alternative 2: 96.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+60}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot t\right) \cdot -9, y, \left(a \cdot b\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot \left(z \cdot y\right), t, \mathsf{fma}\left(b \cdot a, 27, x + x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2e+60)
   (fma (* (* z t) -9.0) y (* (* a b) 27.0))
   (fma (* -9.0 (* z y)) t (fma (* b a) 27.0 (+ 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 tmp;
	if (z <= -2e+60) {
		tmp = fma(((z * t) * -9.0), y, ((a * b) * 27.0));
	} else {
		tmp = fma((-9.0 * (z * y)), t, fma((b * a), 27.0, (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)
	tmp = 0.0
	if (z <= -2e+60)
		tmp = fma(Float64(Float64(z * t) * -9.0), y, Float64(Float64(a * b) * 27.0));
	else
		tmp = fma(Float64(-9.0 * Float64(z * y)), t, fma(Float64(b * a), 27.0, 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_] := If[LessEqual[z, -2e+60], N[(N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision] * y + N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], N[(N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] * t + N[(N[(b * a), $MachinePrecision] * 27.0 + N[(x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9999999999999999e60

   1. Initial program 88.4%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 75.2

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

   5. Applied rewrites 75.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. associate-*r* N/A

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 N/A

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

      21. lower-*.f64 73.3

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

   7. Applied rewrites 73.3%

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

   if -1.9999999999999999e60 < z

   1. Initial program 94.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. associate-+l- N/A

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

   4. Applied rewrites 95.4%

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

Alternative 3: 87.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot y\right) \cdot t, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{elif}\;t\_1 \leq 200:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot t, -9, x + x\right)\\ \end{array} \end{array} \]

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 (- INFINITY))
     (* (* t z) (* -9.0 y))
     (if (<= t_1 -5e-22)
       (fma -9.0 (* (* z y) t) (* (* b a) 27.0))
       (if (<= t_1 200.0)
         (fma (* b 27.0) a (+ x x))
         (fma (* (* y z) t) -9.0 (+ 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 <= -((double) INFINITY)) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t_1 <= -5e-22) {
		tmp = fma(-9.0, ((z * y) * t), ((b * a) * 27.0));
	} else if (t_1 <= 200.0) {
		tmp = fma((b * 27.0), a, (x + x));
	} else {
		tmp = fma(((y * z) * t), -9.0, (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 <= Float64(-Inf))
		tmp = Float64(Float64(t * z) * Float64(-9.0 * y));
	elseif (t_1 <= -5e-22)
		tmp = fma(-9.0, Float64(Float64(z * y) * t), Float64(Float64(b * a) * 27.0));
	elseif (t_1 <= 200.0)
		tmp = fma(Float64(b * 27.0), a, Float64(x + x));
	else
		tmp = fma(Float64(Float64(y * z) * t), -9.0, 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, (-Infinity)], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-22], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] + N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 200.0], N[(N[(b * 27.0), $MachinePrecision] * a + N[(x + x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * -9.0 + N[(x + x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 65.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      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 15.9

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

   5. Applied rewrites 15.9%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 72.9

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

   8. Applied rewrites 72.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      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. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 92.8

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

   10. Applied rewrites 92.8%

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

   if -inf.0 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999954e-22

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 87.5

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

   5. Applied rewrites 87.5%

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

   if -4.99999999999999954e-22 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 200

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      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. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

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

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

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

      18. *-commutative N/A

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

      19. +-commutative N/A

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. count-2-rev N/A

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

      2. lift-+.f64 95.4

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

   7. Applied rewrites 95.4%

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

   if 200 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 89.2%

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

   3. Taylor expanded in a around 0

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

      1. 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. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. count-2-rev N/A

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

      10. lower-+.f64 79.8

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

   5. Applied rewrites 79.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. count-2-rev N/A

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

      8. lower-fma.f64 N/A

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

      9. associate-*r* N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. count-2-rev N/A

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

      14. lift-+.f64 76.9

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

   7. Applied rewrites 76.9%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. count-2-rev N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. count-2-rev N/A

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

      16. lift-+.f64 79.9

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

   9. Applied rewrites 79.9%

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

Alternative 4: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+303}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot -9, t, x + x\right)\\ \mathbf{elif}\;t\_1 \leq 200:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot t, -9, x + x\right)\\ \end{array} \end{array} \]

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 -1e+303)
     (* (* t z) (* -9.0 y))
     (if (<= t_1 -5e+139)
       (fma (* (* y z) -9.0) t (+ x x))
       (if (<= t_1 200.0)
         (fma (* b 27.0) a (+ x x))
         (fma (* (* y z) t) -9.0 (+ 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 <= -1e+303) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t_1 <= -5e+139) {
		tmp = fma(((y * z) * -9.0), t, (x + x));
	} else if (t_1 <= 200.0) {
		tmp = fma((b * 27.0), a, (x + x));
	} else {
		tmp = fma(((y * z) * t), -9.0, (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 <= -1e+303)
		tmp = Float64(Float64(t * z) * Float64(-9.0 * y));
	elseif (t_1 <= -5e+139)
		tmp = fma(Float64(Float64(y * z) * -9.0), t, Float64(x + x));
	elseif (t_1 <= 200.0)
		tmp = fma(Float64(b * 27.0), a, Float64(x + x));
	else
		tmp = fma(Float64(Float64(y * z) * t), -9.0, 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, -1e+303], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+139], N[(N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision] * t + N[(x + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 200.0], N[(N[(b * 27.0), $MachinePrecision] * a + N[(x + x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * -9.0 + N[(x + x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1e303

   1. Initial program 66.9%

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

   3. Taylor expanded in a around 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 18.8

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

   5. Applied rewrites 18.8%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 70.8

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

   8. Applied rewrites 70.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      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. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 93.1

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

   10. Applied rewrites 93.1%

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

   if -1e303 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000003e139

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. count-2-rev N/A

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

      2. lower-+.f64 3.8

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

   5. Applied rewrites 3.8%

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

   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. *-commutative N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. count-2-rev N/A

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

      15. lift-+.f64 73.7

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

   8. Applied rewrites 73.7%

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

   if -5.0000000000000003e139 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 200

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      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. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

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

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

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

      18. *-commutative N/A

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

      19. +-commutative N/A

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. count-2-rev N/A

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

      2. lift-+.f64 92.0

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

   7. Applied rewrites 92.0%

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

   if 200 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 89.2%

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

   3. Taylor expanded in a around 0

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

      1. 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. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. count-2-rev N/A

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

      10. lower-+.f64 79.8

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

   5. Applied rewrites 79.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. count-2-rev N/A

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

      8. lower-fma.f64 N/A

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

      9. associate-*r* N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. count-2-rev N/A

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

      14. lift-+.f64 76.9

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

   7. Applied rewrites 76.9%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. count-2-rev N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. count-2-rev N/A

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

      16. lift-+.f64 79.9

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

   9. Applied rewrites 79.9%

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

Alternative 5: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(y \cdot z\right) \cdot -9, t, x + x\right)\\ t_2 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+303}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 200:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (* (* y z) -9.0) t (+ x x))) (t_2 (* (* (* y 9.0) z) t)))
   (if (<= t_2 -1e+303)
     (* (* t z) (* -9.0 y))
     (if (<= t_2 -5e+139)
       t_1
       (if (<= t_2 200.0) (fma (* b 27.0) a (+ x x)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((y * z) * -9.0), t, (x + x));
	double t_2 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_2 <= -1e+303) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t_2 <= -5e+139) {
		tmp = t_1;
	} else if (t_2 <= 200.0) {
		tmp = fma((b * 27.0), a, (x + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(y * z) * -9.0), t, Float64(x + x))
	t_2 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_2 <= -1e+303)
		tmp = Float64(Float64(t * z) * Float64(-9.0 * y));
	elseif (t_2 <= -5e+139)
		tmp = t_1;
	elseif (t_2 <= 200.0)
		tmp = fma(Float64(b * 27.0), a, Float64(x + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision] * t + N[(x + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+303], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e+139], t$95$1, If[LessEqual[t$95$2, 200.0], N[(N[(b * 27.0), $MachinePrecision] * a + N[(x + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1e303

   1. Initial program 66.9%

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

   3. Taylor expanded in a around 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 18.8

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

   5. Applied rewrites 18.8%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 70.8

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

   8. Applied rewrites 70.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      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. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 93.1

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

   10. Applied rewrites 93.1%

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

   if -1e303 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000003e139 or 200 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 92.1%

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

   3. Taylor expanded in x around inf

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

      1. count-2-rev N/A

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

      2. lower-+.f64 13.0

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

   5. Applied rewrites 13.0%

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

   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. *-commutative N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. count-2-rev N/A

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

      15. lift-+.f64 78.2

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

   8. Applied rewrites 78.2%

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

   if -5.0000000000000003e139 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 200

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      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. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

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

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

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

      18. *-commutative N/A

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

      19. +-commutative N/A

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. count-2-rev N/A

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

      2. lift-+.f64 92.0

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

   7. Applied rewrites 92.0%

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

Alternative 6: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-9 \cdot t, z \cdot y, x + x\right)\\ t_2 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+303}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 200:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (* -9.0 t) (* z y) (+ x x))) (t_2 (* (* (* y 9.0) z) t)))
   (if (<= t_2 -1e+303)
     (* (* t z) (* -9.0 y))
     (if (<= t_2 -5e+139)
       t_1
       (if (<= t_2 200.0) (fma (* b 27.0) a (+ x x)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((-9.0 * t), (z * y), (x + x));
	double t_2 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_2 <= -1e+303) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t_2 <= -5e+139) {
		tmp = t_1;
	} else if (t_2 <= 200.0) {
		tmp = fma((b * 27.0), a, (x + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-9.0 * t), Float64(z * y), Float64(x + x))
	t_2 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_2 <= -1e+303)
		tmp = Float64(Float64(t * z) * Float64(-9.0 * y));
	elseif (t_2 <= -5e+139)
		tmp = t_1;
	elseif (t_2 <= 200.0)
		tmp = fma(Float64(b * 27.0), a, Float64(x + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(-9.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(x + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+303], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e+139], t$95$1, If[LessEqual[t$95$2, 200.0], N[(N[(b * 27.0), $MachinePrecision] * a + N[(x + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1e303

   1. Initial program 66.9%

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

   3. Taylor expanded in a around 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 18.8

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

   5. Applied rewrites 18.8%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 70.8

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

   8. Applied rewrites 70.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      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. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 93.1

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

   10. Applied rewrites 93.1%

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

   if -1e303 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000003e139 or 200 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 92.1%

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

   3. Taylor expanded in a around 0

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

      1. 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. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. count-2-rev N/A

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

      10. lower-+.f64 78.1

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

   5. Applied rewrites 78.1%

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

   if -5.0000000000000003e139 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 200

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      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. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

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

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

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

      18. *-commutative N/A

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

      19. +-commutative N/A

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. count-2-rev N/A

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

      2. lift-+.f64 92.0

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

   7. Applied rewrites 92.0%

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

Alternative 7: 82.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\left(\left(y \cdot t\right) \cdot -9\right) \cdot z\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(\left(z \cdot y\right) \cdot t\right)\\ \end{array} \end{array} \]

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+139)
     (* (* (* y t) -9.0) z)
     (if (<= t_1 2e+153) (fma (* b 27.0) a (+ x x)) (* -9.0 (* (* z y) t))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -5e+139) {
		tmp = ((y * t) * -9.0) * z;
	} else if (t_1 <= 2e+153) {
		tmp = fma((b * 27.0), a, (x + x));
	} else {
		tmp = -9.0 * ((z * y) * t);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -5e+139)
		tmp = Float64(Float64(Float64(y * t) * -9.0) * z);
	elseif (t_1 <= 2e+153)
		tmp = fma(Float64(b * 27.0), a, Float64(x + x));
	else
		tmp = Float64(-9.0 * Float64(Float64(z * y) * t));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+139], N[(N[(N[(y * t), $MachinePrecision] * -9.0), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 2e+153], N[(N[(b * 27.0), $MachinePrecision] * a + N[(x + x), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000003e139

   1. Initial program 81.8%

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

   3. Taylor expanded in 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 22.7

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

   5. Applied rewrites 22.7%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 70.2

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

   8. Applied rewrites 70.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      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. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

      18. associate-*l* N/A

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

      19. *-commutative N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lift-*.f64 N/A

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

      24. *-commutative N/A

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

      25. lower-*.f64 69.6

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

   10. Applied rewrites 69.6%

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

   if -5.0000000000000003e139 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2e153

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      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. lift-*.f64 N/A

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

      16. lift-*.f64 N/A

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

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

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

      18. *-commutative N/A

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

      19. +-commutative N/A

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. count-2-rev N/A

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

      2. lift-+.f64 87.1

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

   7. Applied rewrites 87.1%

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

   if 2e153 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      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 79.9

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

   5. Applied rewrites 79.9%

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

Alternative 8: 82.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\left(\left(y \cdot t\right) \cdot -9\right) \cdot z\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a, 27, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(\left(z \cdot y\right) \cdot t\right)\\ \end{array} \end{array} \]

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+139)
     (* (* (* y t) -9.0) z)
     (if (<= t_1 2e+153) (fma (* b a) 27.0 (+ x x)) (* -9.0 (* (* z y) t))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -5e+139) {
		tmp = ((y * t) * -9.0) * z;
	} else if (t_1 <= 2e+153) {
		tmp = fma((b * a), 27.0, (x + x));
	} else {
		tmp = -9.0 * ((z * y) * t);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -5e+139)
		tmp = Float64(Float64(Float64(y * t) * -9.0) * z);
	elseif (t_1 <= 2e+153)
		tmp = fma(Float64(b * a), 27.0, Float64(x + x));
	else
		tmp = Float64(-9.0 * Float64(Float64(z * y) * t));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+139], N[(N[(N[(y * t), $MachinePrecision] * -9.0), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 2e+153], N[(N[(b * a), $MachinePrecision] * 27.0 + N[(x + x), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000003e139

   1. Initial program 81.8%

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

   3. Taylor expanded in 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 22.7

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

   5. Applied rewrites 22.7%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 70.2

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

   8. Applied rewrites 70.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      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. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

      18. associate-*l* N/A

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

      19. *-commutative N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lift-*.f64 N/A

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

      24. *-commutative N/A

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

      25. lower-*.f64 69.6

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

   10. Applied rewrites 69.6%

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

   if -5.0000000000000003e139 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2e153

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. +-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. count-2-rev N/A

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

      7. lower-+.f64 87.1

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

   5. Applied rewrites 87.1%

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

   if 2e153 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      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 79.9

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

   5. Applied rewrites 79.9%

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

Alternative 9: 82.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\left(\left(y \cdot t\right) \cdot -9\right) \cdot z\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(\left(z \cdot y\right) \cdot t\right)\\ \end{array} \end{array} \]

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+139)
     (* (* (* y t) -9.0) z)
     (if (<= t_1 2e+153) (fma (* a 27.0) b (+ x x)) (* -9.0 (* (* z y) t))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -5e+139) {
		tmp = ((y * t) * -9.0) * z;
	} else if (t_1 <= 2e+153) {
		tmp = fma((a * 27.0), b, (x + x));
	} else {
		tmp = -9.0 * ((z * y) * t);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -5e+139)
		tmp = Float64(Float64(Float64(y * t) * -9.0) * z);
	elseif (t_1 <= 2e+153)
		tmp = fma(Float64(a * 27.0), b, Float64(x + x));
	else
		tmp = Float64(-9.0 * Float64(Float64(z * y) * t));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+139], N[(N[(N[(y * t), $MachinePrecision] * -9.0), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 2e+153], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x + x), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000003e139

   1. Initial program 81.8%

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

   3. Taylor expanded in 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 22.7

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

   5. Applied rewrites 22.7%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 70.2

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

   8. Applied rewrites 70.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      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. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

      18. associate-*l* N/A

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

      19. *-commutative N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lift-*.f64 N/A

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

      24. *-commutative N/A

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

      25. lower-*.f64 69.6

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

   10. Applied rewrites 69.6%

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

   if -5.0000000000000003e139 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2e153

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. +-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. count-2-rev N/A

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

      7. lower-+.f64 87.1

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

   5. Applied rewrites 87.1%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lift-+.f64 N/A

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

      7. count-2-rev N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. count-2-rev N/A

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

      12. lift-+.f64 87.1

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

   7. Applied rewrites 87.1%

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

   if 2e153 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      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 79.9

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

   5. Applied rewrites 79.9%

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

Alternative 10: 57.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+303}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t\_1 \leq -3 \cdot 10^{+96}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-9 \cdot t\right)\\ \mathbf{elif}\;t\_1 \leq 200:\\ \;\;\;\;\left(b \cdot a\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(\left(z \cdot y\right) \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -1e+303)
     (* (* t z) (* -9.0 y))
     (if (<= t_1 -3e+96)
       (* (* y z) (* -9.0 t))
       (if (<= t_1 200.0) (* (* b a) 27.0) (* -9.0 (* (* z y) t)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -1e+303) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t_1 <= -3e+96) {
		tmp = (y * z) * (-9.0 * t);
	} else if (t_1 <= 200.0) {
		tmp = (b * a) * 27.0;
	} else {
		tmp = -9.0 * ((z * y) * t);
	}
	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 = ((y * 9.0d0) * z) * t
    if (t_1 <= (-1d+303)) then
        tmp = (t * z) * ((-9.0d0) * y)
    else if (t_1 <= (-3d+96)) then
        tmp = (y * z) * ((-9.0d0) * t)
    else if (t_1 <= 200.0d0) then
        tmp = (b * a) * 27.0d0
    else
        tmp = (-9.0d0) * ((z * y) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -1e+303) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t_1 <= -3e+96) {
		tmp = (y * z) * (-9.0 * t);
	} else if (t_1 <= 200.0) {
		tmp = (b * a) * 27.0;
	} else {
		tmp = -9.0 * ((z * y) * t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = ((y * 9.0) * z) * t
	tmp = 0
	if t_1 <= -1e+303:
		tmp = (t * z) * (-9.0 * y)
	elif t_1 <= -3e+96:
		tmp = (y * z) * (-9.0 * t)
	elif t_1 <= 200.0:
		tmp = (b * a) * 27.0
	else:
		tmp = -9.0 * ((z * y) * t)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -1e+303)
		tmp = Float64(Float64(t * z) * Float64(-9.0 * y));
	elseif (t_1 <= -3e+96)
		tmp = Float64(Float64(y * z) * Float64(-9.0 * t));
	elseif (t_1 <= 200.0)
		tmp = Float64(Float64(b * a) * 27.0);
	else
		tmp = Float64(-9.0 * Float64(Float64(z * y) * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * 9.0) * z) * t;
	tmp = 0.0;
	if (t_1 <= -1e+303)
		tmp = (t * z) * (-9.0 * y);
	elseif (t_1 <= -3e+96)
		tmp = (y * z) * (-9.0 * t);
	elseif (t_1 <= 200.0)
		tmp = (b * a) * 27.0;
	else
		tmp = -9.0 * ((z * y) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+303], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -3e+96], N[(N[(y * z), $MachinePrecision] * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 200.0], N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1e303

   1. Initial program 66.9%

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

   3. Taylor expanded in a around 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 18.8

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

   5. Applied rewrites 18.8%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 70.8

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

   8. Applied rewrites 70.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      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. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 93.1

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

   10. Applied rewrites 93.1%

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

   if -1e303 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -3e96

   1. Initial program 99.8%

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

   3. Taylor expanded in 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 29.8

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

   5. Applied rewrites 29.8%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 64.6

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

   8. Applied rewrites 64.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 64.5

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 64.5

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

   10. Applied rewrites 64.5%

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

   if -3e96 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 200

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      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 52.6

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

   5. Applied rewrites 52.6%

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

   if 200 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 89.2%

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

   3. 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 67.8

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

   5. Applied rewrites 67.8%

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

Alternative 11: 57.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(\left(z \cdot y\right) \cdot t\right)\\ t_2 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+303}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(-9 \cdot y\right)\\ \mathbf{elif}\;t\_2 \leq -3 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 200:\\ \;\;\;\;\left(b \cdot a\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* (* z y) t))) (t_2 (* (* (* y 9.0) z) t)))
   (if (<= t_2 -1e+303)
     (* (* t z) (* -9.0 y))
     (if (<= t_2 -3e+96) t_1 (if (<= t_2 200.0) (* (* b a) 27.0) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * ((z * y) * t);
	double t_2 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_2 <= -1e+303) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t_2 <= -3e+96) {
		tmp = t_1;
	} else if (t_2 <= 200.0) {
		tmp = (b * a) * 27.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 = (-9.0d0) * ((z * y) * t)
    t_2 = ((y * 9.0d0) * z) * t
    if (t_2 <= (-1d+303)) then
        tmp = (t * z) * ((-9.0d0) * y)
    else if (t_2 <= (-3d+96)) then
        tmp = t_1
    else if (t_2 <= 200.0d0) then
        tmp = (b * a) * 27.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * ((z * y) * t);
	double t_2 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_2 <= -1e+303) {
		tmp = (t * z) * (-9.0 * y);
	} else if (t_2 <= -3e+96) {
		tmp = t_1;
	} else if (t_2 <= 200.0) {
		tmp = (b * a) * 27.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * ((z * y) * t)
	t_2 = ((y * 9.0) * z) * t
	tmp = 0
	if t_2 <= -1e+303:
		tmp = (t * z) * (-9.0 * y)
	elif t_2 <= -3e+96:
		tmp = t_1
	elif t_2 <= 200.0:
		tmp = (b * a) * 27.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(Float64(z * y) * t))
	t_2 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_2 <= -1e+303)
		tmp = Float64(Float64(t * z) * Float64(-9.0 * y));
	elseif (t_2 <= -3e+96)
		tmp = t_1;
	elseif (t_2 <= 200.0)
		tmp = Float64(Float64(b * a) * 27.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * ((z * y) * t);
	t_2 = ((y * 9.0) * z) * t;
	tmp = 0.0;
	if (t_2 <= -1e+303)
		tmp = (t * z) * (-9.0 * y);
	elseif (t_2 <= -3e+96)
		tmp = t_1;
	elseif (t_2 <= 200.0)
		tmp = (b * a) * 27.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+303], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -3e+96], t$95$1, If[LessEqual[t$95$2, 200.0], N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1e303

   1. Initial program 66.9%

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

   3. Taylor expanded in a around 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 18.8

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

   5. Applied rewrites 18.8%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 70.8

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

   8. Applied rewrites 70.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      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. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 93.1

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

   10. Applied rewrites 93.1%

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

   if -1e303 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -3e96 or 200 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 92.5%

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

   3. Taylor expanded in 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 66.8

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

   5. Applied rewrites 66.8%

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

   if -3e96 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 200

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      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 52.6

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

   5. Applied rewrites 52.6%

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

Alternative 12: 57.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\left(\left(y \cdot t\right) \cdot -9\right) \cdot z\\ \mathbf{elif}\;t\_1 \leq 200:\\ \;\;\;\;\left(b \cdot a\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(\left(z \cdot y\right) \cdot t\right)\\ \end{array} \end{array} \]

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+139)
     (* (* (* y t) -9.0) z)
     (if (<= t_1 200.0) (* (* b a) 27.0) (* -9.0 (* (* z y) t))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -5e+139) {
		tmp = ((y * t) * -9.0) * z;
	} else if (t_1 <= 200.0) {
		tmp = (b * a) * 27.0;
	} else {
		tmp = -9.0 * ((z * y) * t);
	}
	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 = ((y * 9.0d0) * z) * t
    if (t_1 <= (-5d+139)) then
        tmp = ((y * t) * (-9.0d0)) * z
    else if (t_1 <= 200.0d0) then
        tmp = (b * a) * 27.0d0
    else
        tmp = (-9.0d0) * ((z * y) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -5e+139) {
		tmp = ((y * t) * -9.0) * z;
	} else if (t_1 <= 200.0) {
		tmp = (b * a) * 27.0;
	} else {
		tmp = -9.0 * ((z * y) * t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = ((y * 9.0) * z) * t
	tmp = 0
	if t_1 <= -5e+139:
		tmp = ((y * t) * -9.0) * z
	elif t_1 <= 200.0:
		tmp = (b * a) * 27.0
	else:
		tmp = -9.0 * ((z * y) * t)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -5e+139)
		tmp = Float64(Float64(Float64(y * t) * -9.0) * z);
	elseif (t_1 <= 200.0)
		tmp = Float64(Float64(b * a) * 27.0);
	else
		tmp = Float64(-9.0 * Float64(Float64(z * y) * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * 9.0) * z) * t;
	tmp = 0.0;
	if (t_1 <= -5e+139)
		tmp = ((y * t) * -9.0) * z;
	elseif (t_1 <= 200.0)
		tmp = (b * a) * 27.0;
	else
		tmp = -9.0 * ((z * y) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+139], N[(N[(N[(y * t), $MachinePrecision] * -9.0), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 200.0], N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000003e139

   1. Initial program 81.8%

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

   3. Taylor expanded in 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 22.7

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

   5. Applied rewrites 22.7%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 70.2

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

   8. Applied rewrites 70.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      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. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

      18. associate-*l* N/A

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

      19. *-commutative N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lift-*.f64 N/A

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

      24. *-commutative N/A

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

      25. lower-*.f64 69.6

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

   10. Applied rewrites 69.6%

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

   if -5.0000000000000003e139 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 200

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      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 52.2

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

   5. Applied rewrites 52.2%

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

   if 200 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 89.2%

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

   3. 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 67.8

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

   5. Applied rewrites 67.8%

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

Alternative 13: 56.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(\left(z \cdot y\right) \cdot t\right)\\ t_2 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -3 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 200:\\ \;\;\;\;\left(b \cdot a\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* (* z y) t))) (t_2 (* (* (* y 9.0) z) t)))
   (if (<= t_2 -3e+96) t_1 (if (<= t_2 200.0) (* (* b a) 27.0) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * ((z * y) * t);
	double t_2 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_2 <= -3e+96) {
		tmp = t_1;
	} else if (t_2 <= 200.0) {
		tmp = (b * a) * 27.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 = (-9.0d0) * ((z * y) * t)
    t_2 = ((y * 9.0d0) * z) * t
    if (t_2 <= (-3d+96)) then
        tmp = t_1
    else if (t_2 <= 200.0d0) then
        tmp = (b * a) * 27.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * ((z * y) * t);
	double t_2 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_2 <= -3e+96) {
		tmp = t_1;
	} else if (t_2 <= 200.0) {
		tmp = (b * a) * 27.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * ((z * y) * t)
	t_2 = ((y * 9.0) * z) * t
	tmp = 0
	if t_2 <= -3e+96:
		tmp = t_1
	elif t_2 <= 200.0:
		tmp = (b * a) * 27.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(Float64(z * y) * t))
	t_2 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_2 <= -3e+96)
		tmp = t_1;
	elseif (t_2 <= 200.0)
		tmp = Float64(Float64(b * a) * 27.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * ((z * y) * t);
	t_2 = ((y * 9.0) * z) * t;
	tmp = 0.0;
	if (t_2 <= -3e+96)
		tmp = t_1;
	elseif (t_2 <= 200.0)
		tmp = (b * a) * 27.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -3e+96], t$95$1, If[LessEqual[t$95$2, 200.0], N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -3e96 or 200 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 86.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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 67.8

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

   5. Applied rewrites 67.8%

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

   if -3e96 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 200

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      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 52.6

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

   5. Applied rewrites 52.6%

      \[\leadsto \color{blue}{\left(b \cdot a\right) \cdot 27} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 53.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := \left(b \cdot a\right) \cdot 27\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-79}:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* (* b a) 27.0)))
   (if (<= t_1 -5e+65) t_2 (if (<= t_1 1e-79) (+ 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 = (b * a) * 27.0;
	double tmp;
	if (t_1 <= -5e+65) {
		tmp = t_2;
	} else if (t_1 <= 1e-79) {
		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 = (b * a) * 27.0d0
    if (t_1 <= (-5d+65)) then
        tmp = t_2
    else if (t_1 <= 1d-79) 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 = (b * a) * 27.0;
	double tmp;
	if (t_1 <= -5e+65) {
		tmp = t_2;
	} else if (t_1 <= 1e-79) {
		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 = (b * a) * 27.0
	tmp = 0
	if t_1 <= -5e+65:
		tmp = t_2
	elif t_1 <= 1e-79:
		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(b * a) * 27.0)
	tmp = 0.0
	if (t_1 <= -5e+65)
		tmp = t_2;
	elseif (t_1 <= 1e-79)
		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 = (b * a) * 27.0;
	tmp = 0.0;
	if (t_1 <= -5e+65)
		tmp = t_2;
	elseif (t_1 <= 1e-79)
		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[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+65], t$95$2, If[LessEqual[t$95$1, 1e-79], N[(x + x), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.99999999999999973e65 or 1e-79 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 91.9%

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

   3. 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 66.5

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

   5. Applied rewrites 66.5%

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

   if -4.99999999999999973e65 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1e-79

   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. count-2-rev N/A

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

      2. lower-+.f64 44.1

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

   5. Applied rewrites 44.1%

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

Alternative 15: 30.9% accurate, 6.4× 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 93.4%

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

3. Taylor expanded in x around inf

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

   1. count-2-rev N/A

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

   2. lower-+.f64 27.7

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

5. Applied rewrites 27.7%

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

Reproduce

herbie shell --seed 2025064 
(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)))