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

Percentage Accurate: 95.4% → 95.9%

Time: 4.2s

Alternatives: 10

Speedup: 1.1×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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: 95.9% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return fma(Float64(b * 27.0), a, fma(Float64(-9.0 * t), Float64(z * y), Float64(x + x)))
end

Wolfram

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

Derivation

1. Initial program 95.4%

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

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

   11. associate-*r* N/A

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

   12. *-commutative N/A

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

   13. associate-*r* N/A

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

   14. lower-fma.f64 N/A

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

   15. *-commutative N/A

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

   16. lower-*.f64 N/A

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

   17. *-commutative N/A

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

3. Applied rewrites 95.9%

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

Alternative 2: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot y\right) \cdot t, \left(a \cdot 27\right) \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-74}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot t, z \cdot y, x + x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -5e+46)
     (fma -9.0 (* (* z y) t) (* (* a 27.0) b))
     (if (<= t_1 5e-74)
       (fma (* a 27.0) b (+ x x))
       (fma (* -9.0 t) (* z y) (+ x x))))))

C

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+46) {
		tmp = fma(-9.0, ((z * y) * t), ((a * 27.0) * b));
	} else if (t_1 <= 5e-74) {
		tmp = fma((a * 27.0), b, (x + x));
	} else {
		tmp = fma((-9.0 * t), (z * y), (x + x));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
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+46)
		tmp = fma(-9.0, Float64(Float64(z * y) * t), Float64(Float64(a * 27.0) * b));
	elseif (t_1 <= 5e-74)
		tmp = fma(Float64(a * 27.0), b, Float64(x + x));
	else
		tmp = 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.
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+46], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-74], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x + x), $MachinePrecision]), $MachinePrecision], N[(N[(-9.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(x + x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000002e46

   1. Initial program 90.6%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   3. 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 80.6

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

   4. Applied rewrites 80.6%

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

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 80.6

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

   6. Applied rewrites 80.6%

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

   if -5.0000000000000002e46 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 4.99999999999999998e-74

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. 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 92.7

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

   4. Applied rewrites 92.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a, 27, x + x\right)} \]
   5. 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 92.6

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

   6. Applied rewrites 92.6%

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

   if 4.99999999999999998e-74 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 92.8%

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

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   3. 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 73.2

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

   4. Applied rewrites 73.2%

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

Alternative 3: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot z\right) \cdot t, y, x + x\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-74}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot t, z \cdot y, x + x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -1e+52)
     (fma (* (* -9.0 z) t) y (+ x x))
     (if (<= t_1 5e-74)
       (fma (* a 27.0) b (+ x x))
       (fma (* -9.0 t) (* z y) (+ x x))))))

C

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+52) {
		tmp = fma(((-9.0 * z) * t), y, (x + x));
	} else if (t_1 <= 5e-74) {
		tmp = fma((a * 27.0), b, (x + x));
	} else {
		tmp = fma((-9.0 * t), (z * y), (x + x));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
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+52)
		tmp = fma(Float64(Float64(-9.0 * z) * t), y, Float64(x + x));
	elseif (t_1 <= 5e-74)
		tmp = fma(Float64(a * 27.0), b, Float64(x + x));
	else
		tmp = 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.
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+52], N[(N[(N[(-9.0 * z), $MachinePrecision] * t), $MachinePrecision] * y + N[(x + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-74], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x + x), $MachinePrecision]), $MachinePrecision], N[(N[(-9.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(x + x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -9.9999999999999999e51

   1. Initial program 90.4%

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

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

   3. Applied rewrites 85.8%

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

   4. Taylor expanded in x around inf

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

      1. count-2-rev N/A

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

      2. lift-+.f64 74.0

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

   6. Applied rewrites 74.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 74.1

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

      10. *-commutative 74.1

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

   8. Applied rewrites 74.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 79.1

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

      9. *-commutative 79.1

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

   10. Applied rewrites 79.1%

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

   if -9.9999999999999999e51 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 4.99999999999999998e-74

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. 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 92.6

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

   4. Applied rewrites 92.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a, 27, x + x\right)} \]
   5. 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 92.5

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

   6. Applied rewrites 92.5%

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

   if 4.99999999999999998e-74 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 92.8%

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

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   3. 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 73.2

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

   4. Applied rewrites 73.2%

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

Alternative 4: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot t\right) \cdot -9, y, x + x\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-74}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9 \cdot t, z \cdot y, x + x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -1e+52)
     (fma (* (* z t) -9.0) y (+ x x))
     (if (<= t_1 5e-74)
       (fma (* a 27.0) b (+ x x))
       (fma (* -9.0 t) (* z y) (+ x x))))))

C

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+52) {
		tmp = fma(((z * t) * -9.0), y, (x + x));
	} else if (t_1 <= 5e-74) {
		tmp = fma((a * 27.0), b, (x + x));
	} else {
		tmp = fma((-9.0 * t), (z * y), (x + x));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
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+52)
		tmp = fma(Float64(Float64(z * t) * -9.0), y, Float64(x + x));
	elseif (t_1 <= 5e-74)
		tmp = fma(Float64(a * 27.0), b, Float64(x + x));
	else
		tmp = 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.
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+52], N[(N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision] * y + N[(x + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-74], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x + x), $MachinePrecision]), $MachinePrecision], N[(N[(-9.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(x + x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -9.9999999999999999e51

   1. Initial program 90.4%

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

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   3. 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 19.6

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

   4. Applied rewrites 19.6%

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

   5. Taylor expanded in a around 0

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   6. 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. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      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. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. count-2-rev N/A

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

      14. lift-+.f64 79.1

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

   7. Applied rewrites 79.1%

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

   if -9.9999999999999999e51 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 4.99999999999999998e-74

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. 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 92.6

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

   4. Applied rewrites 92.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a, 27, x + x\right)} \]
   5. 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 92.5

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

   6. Applied rewrites 92.5%

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

   if 4.99999999999999998e-74 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 92.8%

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

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   3. 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 73.2

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

   4. Applied rewrites 73.2%

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

Alternative 5: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-9 \cdot t, z \cdot y, x + x\right)\\ t_2 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-74}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(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+52)
     t_1
     (if (<= t_2 5e-74) (fma (* a 27.0) b (+ x x)) t_1))))

C

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+52) {
		tmp = t_1;
	} else if (t_2 <= 5e-74) {
		tmp = fma((a * 27.0), b, (x + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

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+52)
		tmp = t_1;
	elseif (t_2 <= 5e-74)
		tmp = fma(Float64(a * 27.0), b, 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.
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+52], t$95$1, If[LessEqual[t$95$2, 5e-74], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -9.9999999999999999e51 or 4.99999999999999998e-74 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 91.8%

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

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   3. 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 75.3

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

   4. Applied rewrites 75.3%

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

   if -9.9999999999999999e51 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 4.99999999999999998e-74

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. 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 92.6

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

   4. Applied rewrites 92.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a, 27, x + x\right)} \]
   5. 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 92.5

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

   6. Applied rewrites 92.5%

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

Alternative 6: 81.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+46}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(t \cdot -9\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(\left(z \cdot y\right) \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -5e+46)
     (* (* z y) (* t -9.0))
     (if (<= t_1 2e+88) (fma (* a 27.0) b (+ x x)) (* -9.0 (* (* z y) t))))))

C

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+46) {
		tmp = (z * y) * (t * -9.0);
	} else if (t_1 <= 2e+88) {
		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])
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+46)
		tmp = Float64(Float64(z * y) * Float64(t * -9.0));
	elseif (t_1 <= 2e+88)
		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.
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+46], N[(N[(z * y), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+88], 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) < -5.0000000000000002e46

   1. Initial program 90.6%

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

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   3. 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 20.0

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

   4. Applied rewrites 20.0%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   6. 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. lower-*.f64 67.7

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

   7. Applied rewrites 67.7%

      \[\leadsto \color{blue}{\left(\left(z \cdot y\right) \cdot t\right) \cdot -9} \]
   8. 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. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-*.f64 67.6

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

   9. Applied rewrites 67.6%

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

   if -5.0000000000000002e46 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1.99999999999999992e88

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. 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 89.5

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

   4. Applied rewrites 89.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a, 27, x + x\right)} \]
   5. 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 89.4

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

   6. Applied rewrites 89.4%

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

   if 1.99999999999999992e88 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 89.3%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   3. 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 72.0

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

   4. Applied rewrites 72.0%

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

Alternative 7: 59.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+299}:\\ \;\;\;\;-9 \cdot \left(\left(z \cdot y\right) \cdot t\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+78}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+81}:\\ \;\;\;\;\left(27 \cdot a\right) \cdot b\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot y\right) \cdot z\right) \cdot -9\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* x 2.0) (* (* (* y 9.0) z) t))))
   (if (<= t_1 -1e+299)
     (* -9.0 (* (* z y) t))
     (if (<= t_1 -5e+78)
       (+ x x)
       (if (<= t_1 5e+81)
         (* (* 27.0 a) b)
         (if (<= t_1 2e+305) (+ x x) (* (* (* t y) z) -9.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_1 <= -1e+299) {
		tmp = -9.0 * ((z * y) * t);
	} else if (t_1 <= -5e+78) {
		tmp = x + x;
	} else if (t_1 <= 5e+81) {
		tmp = (27.0 * a) * b;
	} else if (t_1 <= 2e+305) {
		tmp = x + x;
	} else {
		tmp = ((t * y) * z) * -9.0;
	}
	return tmp;
}

Fortran

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 = (x * 2.0d0) - (((y * 9.0d0) * z) * t)
    if (t_1 <= (-1d+299)) then
        tmp = (-9.0d0) * ((z * y) * t)
    else if (t_1 <= (-5d+78)) then
        tmp = x + x
    else if (t_1 <= 5d+81) then
        tmp = (27.0d0 * a) * b
    else if (t_1 <= 2d+305) then
        tmp = x + x
    else
        tmp = ((t * y) * z) * (-9.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_1 <= -1e+299) {
		tmp = -9.0 * ((z * y) * t);
	} else if (t_1 <= -5e+78) {
		tmp = x + x;
	} else if (t_1 <= 5e+81) {
		tmp = (27.0 * a) * b;
	} else if (t_1 <= 2e+305) {
		tmp = x + x;
	} else {
		tmp = ((t * y) * z) * -9.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (((y * 9.0) * z) * t)
	tmp = 0
	if t_1 <= -1e+299:
		tmp = -9.0 * ((z * y) * t)
	elif t_1 <= -5e+78:
		tmp = x + x
	elif t_1 <= 5e+81:
		tmp = (27.0 * a) * b
	elif t_1 <= 2e+305:
		tmp = x + x
	else:
		tmp = ((t * y) * z) * -9.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t))
	tmp = 0.0
	if (t_1 <= -1e+299)
		tmp = Float64(-9.0 * Float64(Float64(z * y) * t));
	elseif (t_1 <= -5e+78)
		tmp = Float64(x + x);
	elseif (t_1 <= 5e+81)
		tmp = Float64(Float64(27.0 * a) * b);
	elseif (t_1 <= 2e+305)
		tmp = Float64(x + x);
	else
		tmp = Float64(Float64(Float64(t * y) * z) * -9.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (((y * 9.0) * z) * t);
	tmp = 0.0;
	if (t_1 <= -1e+299)
		tmp = -9.0 * ((z * y) * t);
	elseif (t_1 <= -5e+78)
		tmp = x + x;
	elseif (t_1 <= 5e+81)
		tmp = (27.0 * a) * b;
	elseif (t_1 <= 2e+305)
		tmp = x + x;
	else
		tmp = ((t * y) * z) * -9.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+299], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+78], N[(x + x), $MachinePrecision], If[LessEqual[t$95$1, 5e+81], N[(N[(27.0 * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t$95$1, 2e+305], N[(x + x), $MachinePrecision], N[(N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision] * -9.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -1.0000000000000001e299

   1. Initial program 81.7%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 77.2

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

   4. Applied rewrites 77.2%

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

   if -1.0000000000000001e299 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.99999999999999984e78 or 4.9999999999999998e81 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 1.9999999999999999e305

   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. Taylor expanded in x around inf

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

      1. count-2-rev N/A

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

      2. lower-+.f64 48.0

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

   4. Applied rewrites 48.0%

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

   if -4.99999999999999984e78 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 4.9999999999999998e81

   1. Initial program 98.9%

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

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   3. 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 58.4

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

   4. Applied rewrites 58.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 58.3

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

   6. Applied rewrites 58.3%

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

   if 1.9999999999999999e305 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   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. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   3. 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 25.8

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

   4. Applied rewrites 25.8%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   6. 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. lower-*.f64 29.3

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

   7. Applied rewrites 29.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lift-*.f64 22.2

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

   9. Applied rewrites 22.2%

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

Alternative 8: 58.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(\left(z \cdot y\right) \cdot t\right)\\ t_2 := x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+78}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+81}:\\ \;\;\;\;\left(27 \cdot a\right) \cdot b\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* (* z y) t))) (t_2 (- (* x 2.0) (* (* (* y 9.0) z) t))))
   (if (<= t_2 -1e+299)
     t_1
     (if (<= t_2 -5e+78)
       (+ x x)
       (if (<= t_2 5e+81)
         (* (* 27.0 a) b)
         (if (<= t_2 2e+305) (+ x x) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * ((z * y) * t);
	double t_2 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_2 <= -1e+299) {
		tmp = t_1;
	} else if (t_2 <= -5e+78) {
		tmp = x + x;
	} else if (t_2 <= 5e+81) {
		tmp = (27.0 * a) * b;
	} else if (t_2 <= 2e+305) {
		tmp = x + x;
	} 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.
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 = (x * 2.0d0) - (((y * 9.0d0) * z) * t)
    if (t_2 <= (-1d+299)) then
        tmp = t_1
    else if (t_2 <= (-5d+78)) then
        tmp = x + x
    else if (t_2 <= 5d+81) then
        tmp = (27.0d0 * a) * b
    else if (t_2 <= 2d+305) then
        tmp = x + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * ((z * y) * t);
	double t_2 = (x * 2.0) - (((y * 9.0) * z) * t);
	double tmp;
	if (t_2 <= -1e+299) {
		tmp = t_1;
	} else if (t_2 <= -5e+78) {
		tmp = x + x;
	} else if (t_2 <= 5e+81) {
		tmp = (27.0 * a) * b;
	} else if (t_2 <= 2e+305) {
		tmp = x + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * ((z * y) * t)
	t_2 = (x * 2.0) - (((y * 9.0) * z) * t)
	tmp = 0
	if t_2 <= -1e+299:
		tmp = t_1
	elif t_2 <= -5e+78:
		tmp = x + x
	elif t_2 <= 5e+81:
		tmp = (27.0 * a) * b
	elif t_2 <= 2e+305:
		tmp = x + x
	else:
		tmp = t_1
	return tmp

Julia

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(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t))
	tmp = 0.0
	if (t_2 <= -1e+299)
		tmp = t_1;
	elseif (t_2 <= -5e+78)
		tmp = Float64(x + x);
	elseif (t_2 <= 5e+81)
		tmp = Float64(Float64(27.0 * a) * b);
	elseif (t_2 <= 2e+305)
		tmp = Float64(x + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * ((z * y) * t);
	t_2 = (x * 2.0) - (((y * 9.0) * z) * t);
	tmp = 0.0;
	if (t_2 <= -1e+299)
		tmp = t_1;
	elseif (t_2 <= -5e+78)
		tmp = x + x;
	elseif (t_2 <= 5e+81)
		tmp = (27.0 * a) * b;
	elseif (t_2 <= 2e+305)
		tmp = x + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+299], t$95$1, If[LessEqual[t$95$2, -5e+78], N[(x + x), $MachinePrecision], If[LessEqual[t$95$2, 5e+81], N[(N[(27.0 * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t$95$2, 2e+305], N[(x + x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -1.0000000000000001e299 or 1.9999999999999999e305 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t))

   1. Initial program 80.9%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   3. 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 78.9

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

   4. Applied rewrites 78.9%

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

   if -1.0000000000000001e299 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < -4.99999999999999984e78 or 4.9999999999999998e81 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 1.9999999999999999e305

   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. Taylor expanded in x around inf

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

      1. count-2-rev N/A

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

      2. lower-+.f64 48.0

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

   4. Applied rewrites 48.0%

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

   if -4.99999999999999984e78 < (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) < 4.9999999999999998e81

   1. Initial program 98.9%

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

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   3. 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 58.4

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

   4. Applied rewrites 58.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 58.3

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

   6. Applied rewrites 58.3%

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

Alternative 9: 52.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := \left(27 \cdot a\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 100000:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)) (t_2 (* (* 27.0 a) b)))
   (if (<= t_1 -5e-20) t_2 (if (<= t_1 100000.0) (+ x x) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = (27.0 * a) * b;
	double tmp;
	if (t_1 <= -5e-20) {
		tmp = t_2;
	} else if (t_1 <= 100000.0) {
		tmp = x + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    t_2 = (27.0d0 * a) * b
    if (t_1 <= (-5d-20)) then
        tmp = t_2
    else if (t_1 <= 100000.0d0) then
        tmp = x + x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = (27.0 * a) * b;
	double tmp;
	if (t_1 <= -5e-20) {
		tmp = t_2;
	} else if (t_1 <= 100000.0) {
		tmp = x + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	t_2 = (27.0 * a) * b
	tmp = 0
	if t_1 <= -5e-20:
		tmp = t_2
	elif t_1 <= 100000.0:
		tmp = x + x
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	t_2 = Float64(Float64(27.0 * a) * b)
	tmp = 0.0
	if (t_1 <= -5e-20)
		tmp = t_2;
	elseif (t_1 <= 100000.0)
		tmp = Float64(x + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	t_2 = (27.0 * a) * b;
	tmp = 0.0;
	if (t_1 <= -5e-20)
		tmp = t_2;
	elseif (t_1 <= 100000.0)
		tmp = x + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-20], t$95$2, If[LessEqual[t$95$1, 100000.0], N[(x + x), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.9999999999999999e-20 or 1e5 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 59.7

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

   4. Applied rewrites 59.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 59.7

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

   6. Applied rewrites 59.7%

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

   if -4.9999999999999999e-20 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1e5

   1. Initial program 95.5%

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

   2. Taylor expanded in x around inf

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

      1. count-2-rev N/A

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

      2. lower-+.f64 45.5

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

   4. Applied rewrites 45.5%

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

Alternative 10: 31.3% accurate, 6.4× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (+ x x))

C

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.
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;
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])
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])
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])){:}
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.
code[x_, y_, z_, t_, a_, b_] := N[(x + x), $MachinePrecision]

Derivation

1. Initial program 95.4%

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

2. Taylor expanded in x around inf

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

   1. count-2-rev N/A

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

   2. lower-+.f64 31.3

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

4. Applied rewrites 31.3%

   \[\leadsto \color{blue}{x + x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025134 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64
  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))