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

Percentage Accurate: 95.5% → 97.9%

Time: 26.6s

Alternatives: 14

Speedup: 0.9×

• 27.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(y \cdot 9\right) \cdot z\\ \mathbf{if}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;\left(x \cdot 2 - t\_1 \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* y 9.0) z)))
   (if (<= t_1 1e+308)
     (+ (- (* x 2.0) (* t_1 t)) (* (* a 27.0) b))
     (fma (* 27.0 b) a (* z (* t (* y -9.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 1e+308) {
		tmp = ((x * 2.0) - (t_1 * t)) + ((a * 27.0) * b);
	} else {
		tmp = fma((27.0 * b), a, (z * (t * (y * -9.0))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * 9.0) * z)
	tmp = 0.0
	if (t_1 <= 1e+308)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t_1 * t)) + Float64(Float64(a * 27.0) * b));
	else
		tmp = fma(Float64(27.0 * b), a, Float64(z * Float64(t * Float64(y * -9.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+308], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t$95$1 * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * b), $MachinePrecision] * a + N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 1e308

   1. Initial program 96.8%

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

   if 1e308 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 84.1%

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

   3. Taylor expanded in x around 0

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

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

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

      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. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)}, \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      8. +-lft-identity N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 + \color{blue}{-9 \cdot \left(y \cdot z\right)}\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(-9 \cdot \left(y \cdot z\right) + \color{blue}{0}\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(\left(y \cdot z\right) \cdot -9 + 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      11. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\left(y \cdot z\right), \color{blue}{-9}, 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      13. +-rgt-identity N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, \color{blue}{0}\right), \left(27 \cdot \left(a \cdot b\right) + 0\right)\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, \color{blue}{0}\right), \mathsf{fma.f64}\left(27, \left(a \cdot b\right), 0\right)\right) \]

      15. *-lowering-*.f64 84.1%

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), 0\right)\right) \]

   5. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(y \cdot z, -9, 0\right), \mathsf{fma}\left(27, a \cdot b, 0\right)\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + \left(27 \cdot \color{blue}{\left(a \cdot b\right)} + 0\right) \]

      2. +-rgt-identity N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(27 \cdot b\right), \color{blue}{a}, \left(\left(y \cdot \left(z \cdot -9\right)\right) \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(y \cdot \left(z \cdot -9\right)\right) \cdot t\right)\right) \]

      10. +-rgt-identity N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(y \cdot \left(z \cdot -9\right)\right) \cdot t + 0\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(\left(y \cdot z\right) \cdot -9\right) \cdot t + 0\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(-9 \cdot \left(y \cdot z\right)\right) \cdot t + 0\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(-9 \cdot \left(\left(y \cdot z\right) \cdot t\right) + 0\right)\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{fma.f64}\left(-9, \left(\left(y \cdot z\right) \cdot t\right), 0\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{fma.f64}\left(-9, \mathsf{*.f64}\left(\left(y \cdot z\right), t\right), 0\right)\right) \]

      16. *-lowering-*.f64 84.1%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{fma.f64}\left(-9, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right), 0\right)\right) \]

   7. Applied egg-rr 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, \mathsf{fma}\left(-9, \left(y \cdot z\right) \cdot t, 0\right)\right)} \]
   8. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(-9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(-9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(y \cdot -9\right) \cdot \left(z \cdot t\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(t \cdot \left(y \cdot -9\right)\right) \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot -9\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot -9\right)\right), z\right)\right) \]

      10. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, -9\right)\right), z\right)\right) \]

   9. Applied egg-rr 99.9%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 10^{+308}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+100}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-222}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+111}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= t_1 -4e+100)
     (* 27.0 (* a b))
     (if (<= t_1 2e-222)
       (* t (* z (* y -9.0)))
       (if (<= t_1 2e+111) (* x 2.0) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -4e+100) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= 2e-222) {
		tmp = t * (z * (y * -9.0));
	} else if (t_1 <= 2e+111) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    if (t_1 <= (-4d+100)) then
        tmp = 27.0d0 * (a * b)
    else if (t_1 <= 2d-222) then
        tmp = t * (z * (y * (-9.0d0)))
    else if (t_1 <= 2d+111) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -4e+100) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= 2e-222) {
		tmp = t * (z * (y * -9.0));
	} else if (t_1 <= 2e+111) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -4e+100:
		tmp = 27.0 * (a * b)
	elif t_1 <= 2e-222:
		tmp = t * (z * (y * -9.0))
	elif t_1 <= 2e+111:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -4e+100)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t_1 <= 2e-222)
		tmp = Float64(t * Float64(z * Float64(y * -9.0)));
	elseif (t_1 <= 2e+111)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -4e+100)
		tmp = 27.0 * (a * b);
	elseif (t_1 <= 2e-222)
		tmp = t * (z * (y * -9.0));
	elseif (t_1 <= 2e+111)
		tmp = x * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+100], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-222], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+111], N[(x * 2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.00000000000000006e100

   1. Initial program 97.4%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 97.4%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 97.4%

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

   5. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 85.4%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 85.4%

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

   if -4.00000000000000006e100 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2.0000000000000001e-222

   1. Initial program 97.1%

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

   3. Taylor expanded in y around inf

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

      1. +-lft-identity N/A

         \[\leadsto 0 + \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{0} \]

      3. *-commutative N/A

         \[\leadsto \left(t \cdot \left(y \cdot z\right)\right) \cdot -9 + 0 \]

      4. associate-*l* N/A

         \[\leadsto t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + 0 \]

      5. *-commutative N/A

         \[\leadsto t \cdot \left(-9 \cdot \left(y \cdot z\right)\right) + 0 \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)}, 0\right) \]

      7. +-lft-identity N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 + \color{blue}{-9 \cdot \left(y \cdot z\right)}\right), 0\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(-9 \cdot \left(y \cdot z\right) + \color{blue}{0}\right), 0\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(\left(y \cdot z\right) \cdot -9 + 0\right), 0\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\left(y \cdot z\right), \color{blue}{-9}, 0\right), 0\right) \]

      11. *-lowering-*.f64 52.0%

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), 0\right) \]

   5. Simplified 52.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(y \cdot z, -9, 0\right), 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + 0 \]

      2. *-commutative N/A

         \[\leadsto \left(\left(y \cdot z\right) \cdot -9\right) \cdot t + 0 \]

      3. associate-*r* N/A

         \[\leadsto \left(y \cdot \left(z \cdot -9\right)\right) \cdot t + 0 \]

      4. +-rgt-identity N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-lowering-*.f64 48.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -9\right), \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right) \]

   7. Applied egg-rr 48.8%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-9 \cdot \left(z \cdot y\right)\right), t\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(-9 \cdot z\right) \cdot y\right), t\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(z \cdot -9\right) \cdot y\right), t\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot \left(-9 \cdot y\right)\right), t\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(z \cdot \left(y \cdot -9\right)\right), t\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot -9\right)\right), t\right) \]

      12. *-lowering-*.f64 52.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, -9\right)\right), t\right) \]

   9. Applied egg-rr 52.1%

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

   if 2.0000000000000001e-222 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.99999999999999991e111

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf

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

      1. +-rgt-identity N/A

         \[\leadsto 2 \cdot x + \color{blue}{0} \]

      2. accelerator-lowering-fma.f64 52.9%

         \[\leadsto \mathsf{fma.f64}\left(2, \color{blue}{x}, 0\right) \]

   5. Simplified 52.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 52.9%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{2}\right) \]

   7. Applied egg-rr 52.9%

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

   if 1.99999999999999991e111 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 88.1%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 88.0%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 88.0%

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

   5. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 64.8%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 64.8%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot 27\right), \color{blue}{b}\right) \]

      4. *-lowering-*.f64 64.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right) \]

   9. Applied egg-rr 64.7%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -4 \cdot 10^{+100}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{-222}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+111}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+100}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-222}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+111}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= t_1 -4e+100)
     (* 27.0 (* a b))
     (if (<= t_1 2e-222)
       (* -9.0 (* t (* y z)))
       (if (<= t_1 2e+111) (* x 2.0) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -4e+100) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= 2e-222) {
		tmp = -9.0 * (t * (y * z));
	} else if (t_1 <= 2e+111) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    if (t_1 <= (-4d+100)) then
        tmp = 27.0d0 * (a * b)
    else if (t_1 <= 2d-222) then
        tmp = (-9.0d0) * (t * (y * z))
    else if (t_1 <= 2d+111) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -4e+100) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= 2e-222) {
		tmp = -9.0 * (t * (y * z));
	} else if (t_1 <= 2e+111) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -4e+100:
		tmp = 27.0 * (a * b)
	elif t_1 <= 2e-222:
		tmp = -9.0 * (t * (y * z))
	elif t_1 <= 2e+111:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -4e+100)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t_1 <= 2e-222)
		tmp = Float64(-9.0 * Float64(t * Float64(y * z)));
	elseif (t_1 <= 2e+111)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -4e+100)
		tmp = 27.0 * (a * b);
	elseif (t_1 <= 2e-222)
		tmp = -9.0 * (t * (y * z));
	elseif (t_1 <= 2e+111)
		tmp = x * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+100], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-222], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+111], N[(x * 2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.00000000000000006e100

   1. Initial program 97.4%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 97.4%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 97.4%

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

   5. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 85.4%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 85.4%

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

   if -4.00000000000000006e100 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2.0000000000000001e-222

   1. Initial program 97.1%

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

   3. Taylor expanded in y around inf

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

      1. +-lft-identity N/A

         \[\leadsto 0 + \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{0} \]

      3. *-commutative N/A

         \[\leadsto \left(t \cdot \left(y \cdot z\right)\right) \cdot -9 + 0 \]

      4. associate-*l* N/A

         \[\leadsto t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + 0 \]

      5. *-commutative N/A

         \[\leadsto t \cdot \left(-9 \cdot \left(y \cdot z\right)\right) + 0 \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)}, 0\right) \]

      7. +-lft-identity N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 + \color{blue}{-9 \cdot \left(y \cdot z\right)}\right), 0\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(-9 \cdot \left(y \cdot z\right) + \color{blue}{0}\right), 0\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(\left(y \cdot z\right) \cdot -9 + 0\right), 0\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\left(y \cdot z\right), \color{blue}{-9}, 0\right), 0\right) \]

      11. *-lowering-*.f64 52.0%

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), 0\right) \]

   5. Simplified 52.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(y \cdot z, -9, 0\right), 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + 0 \]

      2. mul0-rgt N/A

         \[\leadsto t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + t \cdot \color{blue}{0} \]

      3. distribute-lft-in N/A

         \[\leadsto t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot -9 + 0\right)} \]

      4. +-rgt-identity N/A

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

      5. associate-*r* N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), -9\right) \]

      8. *-lowering-*.f64 52.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), -9\right) \]

   7. Applied egg-rr 52.0%

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

   if 2.0000000000000001e-222 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.99999999999999991e111

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf

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

      1. +-rgt-identity N/A

         \[\leadsto 2 \cdot x + \color{blue}{0} \]

      2. accelerator-lowering-fma.f64 52.9%

         \[\leadsto \mathsf{fma.f64}\left(2, \color{blue}{x}, 0\right) \]

   5. Simplified 52.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 52.9%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{2}\right) \]

   7. Applied egg-rr 52.9%

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

   if 1.99999999999999991e111 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 88.1%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 88.0%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 88.0%

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

   5. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 64.8%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 64.8%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot 27\right), \color{blue}{b}\right) \]

      4. *-lowering-*.f64 64.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right) \]

   9. Applied egg-rr 64.7%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -4 \cdot 10^{+100}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{-222}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+111}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(t \cdot -9\right), y, \mathsf{fma}\left(27, a \cdot b, 0\right)\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+89}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(z \cdot -9\right), t, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= t_1 -1e+41)
     (fma (* z (* t -9.0)) y (fma 27.0 (* a b) 0.0))
     (if (<= t_1 2e+89)
       (fma (* y (* z -9.0)) t (* x 2.0))
       (fma (* 27.0 b) a (* z (* t (* y -9.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -1e+41) {
		tmp = fma((z * (t * -9.0)), y, fma(27.0, (a * b), 0.0));
	} else if (t_1 <= 2e+89) {
		tmp = fma((y * (z * -9.0)), t, (x * 2.0));
	} else {
		tmp = fma((27.0 * b), a, (z * (t * (y * -9.0))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -1e+41)
		tmp = fma(Float64(z * Float64(t * -9.0)), y, fma(27.0, Float64(a * b), 0.0));
	elseif (t_1 <= 2e+89)
		tmp = fma(Float64(y * Float64(z * -9.0)), t, Float64(x * 2.0));
	else
		tmp = fma(Float64(27.0 * b), a, Float64(z * Float64(t * Float64(y * -9.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+41], N[(N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision] * y + N[(27.0 * N[(a * b), $MachinePrecision] + 0.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+89], N[(N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * b), $MachinePrecision] * a + N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.00000000000000001e41

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0

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

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

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

      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. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)}, \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      8. +-lft-identity N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 + \color{blue}{-9 \cdot \left(y \cdot z\right)}\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(-9 \cdot \left(y \cdot z\right) + \color{blue}{0}\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(\left(y \cdot z\right) \cdot -9 + 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      11. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\left(y \cdot z\right), \color{blue}{-9}, 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      13. +-rgt-identity N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, \color{blue}{0}\right), \left(27 \cdot \left(a \cdot b\right) + 0\right)\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, \color{blue}{0}\right), \mathsf{fma.f64}\left(27, \left(a \cdot b\right), 0\right)\right) \]

      15. *-lowering-*.f64 84.5%

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), 0\right)\right) \]

   5. Simplified 84.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(y \cdot z, -9, 0\right), \mathsf{fma}\left(27, a \cdot b, 0\right)\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + \left(27 \cdot \color{blue}{\left(a \cdot b\right)} + 0\right) \]

      2. *-commutative N/A

         \[\leadsto \left(\left(y \cdot z\right) \cdot -9\right) \cdot t + \left(\color{blue}{27 \cdot \left(a \cdot b\right)} + 0\right) \]

      3. +-rgt-identity N/A

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

      4. associate-*r* N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\left(z \cdot -9\right) \cdot t\right), \color{blue}{y}, \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(z \cdot \left(-9 \cdot t\right)\right), y, \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \left(-9 \cdot t\right)\right), y, \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(-9, t\right)\right), y, \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      11. +-rgt-identity N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(-9, t\right)\right), y, \left(27 \cdot \left(a \cdot b\right) + 0\right)\right) \]

      12. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(-9, t\right)\right), y, \mathsf{fma.f64}\left(27, \left(a \cdot b\right), 0\right)\right) \]

      13. *-lowering-*.f64 87.9%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(-9, t\right)\right), y, \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), 0\right)\right) \]

   7. Applied egg-rr 87.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(-9 \cdot t\right), y, \mathsf{fma}\left(27, a \cdot b, 0\right)\right)} \]

   if -1.00000000000000001e41 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.99999999999999999e89

   1. Initial program 97.7%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 97.7%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \color{blue}{\left(2 \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 90.7%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{*.f64}\left(2, x\right)\right) \]

   7. Simplified 90.7%

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

   if 1.99999999999999999e89 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   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. Add Preprocessing

   3. Taylor expanded in x around 0

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

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

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

      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. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)}, \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      8. +-lft-identity N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 + \color{blue}{-9 \cdot \left(y \cdot z\right)}\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(-9 \cdot \left(y \cdot z\right) + \color{blue}{0}\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(\left(y \cdot z\right) \cdot -9 + 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      11. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\left(y \cdot z\right), \color{blue}{-9}, 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      13. +-rgt-identity N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, \color{blue}{0}\right), \left(27 \cdot \left(a \cdot b\right) + 0\right)\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, \color{blue}{0}\right), \mathsf{fma.f64}\left(27, \left(a \cdot b\right), 0\right)\right) \]

      15. *-lowering-*.f64 80.6%

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), 0\right)\right) \]

   5. Simplified 80.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(y \cdot z, -9, 0\right), \mathsf{fma}\left(27, a \cdot b, 0\right)\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + \left(27 \cdot \color{blue}{\left(a \cdot b\right)} + 0\right) \]

      2. +-rgt-identity N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(27 \cdot b\right), \color{blue}{a}, \left(\left(y \cdot \left(z \cdot -9\right)\right) \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(y \cdot \left(z \cdot -9\right)\right) \cdot t\right)\right) \]

      10. +-rgt-identity N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(y \cdot \left(z \cdot -9\right)\right) \cdot t + 0\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(\left(y \cdot z\right) \cdot -9\right) \cdot t + 0\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(-9 \cdot \left(y \cdot z\right)\right) \cdot t + 0\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(-9 \cdot \left(\left(y \cdot z\right) \cdot t\right) + 0\right)\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{fma.f64}\left(-9, \left(\left(y \cdot z\right) \cdot t\right), 0\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{fma.f64}\left(-9, \mathsf{*.f64}\left(\left(y \cdot z\right), t\right), 0\right)\right) \]

      16. *-lowering-*.f64 86.0%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{fma.f64}\left(-9, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right), 0\right)\right) \]

   7. Applied egg-rr 86.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, \mathsf{fma}\left(-9, \left(y \cdot z\right) \cdot t, 0\right)\right)} \]
   8. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(-9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(-9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(y \cdot -9\right) \cdot \left(z \cdot t\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(t \cdot \left(y \cdot -9\right)\right) \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot -9\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot -9\right)\right), z\right)\right) \]

      10. *-lowering-*.f64 83.5%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, -9\right)\right), z\right)\right) \]

   9. Applied egg-rr 83.5%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -1 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(t \cdot -9\right), y, \mathsf{fma}\left(27, a \cdot b, 0\right)\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+89}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(z \cdot -9\right), t, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot t, y \cdot -9, 27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+89}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(z \cdot -9\right), t, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= t_1 -1e+41)
     (fma (* z t) (* y -9.0) (* 27.0 (* a b)))
     (if (<= t_1 2e+89)
       (fma (* y (* z -9.0)) t (* x 2.0))
       (fma (* 27.0 b) a (* z (* t (* y -9.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -1e+41) {
		tmp = fma((z * t), (y * -9.0), (27.0 * (a * b)));
	} else if (t_1 <= 2e+89) {
		tmp = fma((y * (z * -9.0)), t, (x * 2.0));
	} else {
		tmp = fma((27.0 * b), a, (z * (t * (y * -9.0))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -1e+41)
		tmp = fma(Float64(z * t), Float64(y * -9.0), Float64(27.0 * Float64(a * b)));
	elseif (t_1 <= 2e+89)
		tmp = fma(Float64(y * Float64(z * -9.0)), t, Float64(x * 2.0));
	else
		tmp = fma(Float64(27.0 * b), a, Float64(z * Float64(t * Float64(y * -9.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+41], N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+89], N[(N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * b), $MachinePrecision] * a + N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.00000000000000001e41

   1. Initial program 96.3%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(z \cdot t\right), \color{blue}{\left(\mathsf{neg}\left(y \cdot 9\right)\right)}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, t\right), \left(\mathsf{neg}\left(\color{blue}{y \cdot 9}\right)\right), \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, t\right), \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right), \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right), \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(y, -9\right), \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(y, -9\right), \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(y, -9\right), \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(y, -9\right), \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(y, -9\right), \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(y, -9\right), \color{blue}{\left(27 \cdot \left(a \cdot b\right)\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(y, -9\right), \mathsf{*.f64}\left(27, \left(a \cdot b\right)\right)\right) \]

      2. *-lowering-*.f64 87.8%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(y, -9\right), \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 87.8%

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

   if -1.00000000000000001e41 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.99999999999999999e89

   1. Initial program 97.7%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 97.7%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \color{blue}{\left(2 \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 90.7%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{*.f64}\left(2, x\right)\right) \]

   7. Simplified 90.7%

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

   if 1.99999999999999999e89 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   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. Add Preprocessing

   3. Taylor expanded in x around 0

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

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

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

      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. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)}, \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      8. +-lft-identity N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 + \color{blue}{-9 \cdot \left(y \cdot z\right)}\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(-9 \cdot \left(y \cdot z\right) + \color{blue}{0}\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(\left(y \cdot z\right) \cdot -9 + 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      11. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\left(y \cdot z\right), \color{blue}{-9}, 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      13. +-rgt-identity N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, \color{blue}{0}\right), \left(27 \cdot \left(a \cdot b\right) + 0\right)\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, \color{blue}{0}\right), \mathsf{fma.f64}\left(27, \left(a \cdot b\right), 0\right)\right) \]

      15. *-lowering-*.f64 80.6%

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), 0\right)\right) \]

   5. Simplified 80.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(y \cdot z, -9, 0\right), \mathsf{fma}\left(27, a \cdot b, 0\right)\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + \left(27 \cdot \color{blue}{\left(a \cdot b\right)} + 0\right) \]

      2. +-rgt-identity N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(27 \cdot b\right), \color{blue}{a}, \left(\left(y \cdot \left(z \cdot -9\right)\right) \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(y \cdot \left(z \cdot -9\right)\right) \cdot t\right)\right) \]

      10. +-rgt-identity N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(y \cdot \left(z \cdot -9\right)\right) \cdot t + 0\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(\left(y \cdot z\right) \cdot -9\right) \cdot t + 0\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(-9 \cdot \left(y \cdot z\right)\right) \cdot t + 0\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(-9 \cdot \left(\left(y \cdot z\right) \cdot t\right) + 0\right)\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{fma.f64}\left(-9, \left(\left(y \cdot z\right) \cdot t\right), 0\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{fma.f64}\left(-9, \mathsf{*.f64}\left(\left(y \cdot z\right), t\right), 0\right)\right) \]

      16. *-lowering-*.f64 86.0%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{fma.f64}\left(-9, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right), 0\right)\right) \]

   7. Applied egg-rr 86.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, \mathsf{fma}\left(-9, \left(y \cdot z\right) \cdot t, 0\right)\right)} \]
   8. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(-9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(-9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(y \cdot -9\right) \cdot \left(z \cdot t\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(t \cdot \left(y \cdot -9\right)\right) \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot -9\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot -9\right)\right), z\right)\right) \]

      10. *-lowering-*.f64 83.5%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, -9\right)\right), z\right)\right) \]

   9. Applied egg-rr 83.5%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -1 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot t, y \cdot -9, 27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+89}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(z \cdot -9\right), t, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+89}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(z \cdot -9\right), t, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= t_1 -4e+100)
     (fma 27.0 (* a b) (* x 2.0))
     (if (<= t_1 2e+89)
       (fma (* y (* z -9.0)) t (* x 2.0))
       (fma (* 27.0 b) a (* z (* t (* y -9.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -4e+100) {
		tmp = fma(27.0, (a * b), (x * 2.0));
	} else if (t_1 <= 2e+89) {
		tmp = fma((y * (z * -9.0)), t, (x * 2.0));
	} else {
		tmp = fma((27.0 * b), a, (z * (t * (y * -9.0))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -4e+100)
		tmp = fma(27.0, Float64(a * b), Float64(x * 2.0));
	elseif (t_1 <= 2e+89)
		tmp = fma(Float64(y * Float64(z * -9.0)), t, Float64(x * 2.0));
	else
		tmp = fma(Float64(27.0 * b), a, Float64(z * Float64(t * Float64(y * -9.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+100], N[(27.0 * N[(a * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+89], N[(N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * b), $MachinePrecision] * a + N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.00000000000000006e100

   1. Initial program 97.4%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 97.4%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 97.4%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(27, \color{blue}{\left(a \cdot b\right)}, \left(2 \cdot x\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right), \left(2 \cdot x\right)\right) \]

      4. *-lowering-*.f64 92.7%

         \[\leadsto \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(2, x\right)\right) \]

   7. Simplified 92.7%

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

   if -4.00000000000000006e100 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.99999999999999999e89

   1. Initial program 97.4%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 97.3%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 97.3%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \color{blue}{\left(2 \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 88.1%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{*.f64}\left(2, x\right)\right) \]

   7. Simplified 88.1%

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

   if 1.99999999999999999e89 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   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. Add Preprocessing

   3. Taylor expanded in x around 0

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

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

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

      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. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)}, \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      8. +-lft-identity N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 + \color{blue}{-9 \cdot \left(y \cdot z\right)}\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(-9 \cdot \left(y \cdot z\right) + \color{blue}{0}\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(\left(y \cdot z\right) \cdot -9 + 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      11. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\left(y \cdot z\right), \color{blue}{-9}, 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      13. +-rgt-identity N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, \color{blue}{0}\right), \left(27 \cdot \left(a \cdot b\right) + 0\right)\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, \color{blue}{0}\right), \mathsf{fma.f64}\left(27, \left(a \cdot b\right), 0\right)\right) \]

      15. *-lowering-*.f64 80.6%

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), 0\right)\right) \]

   5. Simplified 80.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(y \cdot z, -9, 0\right), \mathsf{fma}\left(27, a \cdot b, 0\right)\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + \left(27 \cdot \color{blue}{\left(a \cdot b\right)} + 0\right) \]

      2. +-rgt-identity N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(27 \cdot b\right), \color{blue}{a}, \left(\left(y \cdot \left(z \cdot -9\right)\right) \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(y \cdot \left(z \cdot -9\right)\right) \cdot t\right)\right) \]

      10. +-rgt-identity N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(y \cdot \left(z \cdot -9\right)\right) \cdot t + 0\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(\left(y \cdot z\right) \cdot -9\right) \cdot t + 0\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(-9 \cdot \left(y \cdot z\right)\right) \cdot t + 0\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(-9 \cdot \left(\left(y \cdot z\right) \cdot t\right) + 0\right)\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{fma.f64}\left(-9, \left(\left(y \cdot z\right) \cdot t\right), 0\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{fma.f64}\left(-9, \mathsf{*.f64}\left(\left(y \cdot z\right), t\right), 0\right)\right) \]

      16. *-lowering-*.f64 86.0%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{fma.f64}\left(-9, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right), 0\right)\right) \]

   7. Applied egg-rr 86.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, \mathsf{fma}\left(-9, \left(y \cdot z\right) \cdot t, 0\right)\right)} \]
   8. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(-9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(-9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(y \cdot -9\right) \cdot \left(z \cdot t\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(t \cdot \left(y \cdot -9\right)\right) \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot -9\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot -9\right)\right), z\right)\right) \]

      10. *-lowering-*.f64 83.5%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, -9\right)\right), z\right)\right) \]

   9. Applied egg-rr 83.5%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -4 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+89}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(z \cdot -9\right), t, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+89}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(z \cdot -9\right), t, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, \left(t \cdot -9\right) \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= t_1 -4e+100)
     (fma 27.0 (* a b) (* x 2.0))
     (if (<= t_1 2e+89)
       (fma (* y (* z -9.0)) t (* x 2.0))
       (fma 27.0 (* a b) (* (* t -9.0) (* y z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -4e+100) {
		tmp = fma(27.0, (a * b), (x * 2.0));
	} else if (t_1 <= 2e+89) {
		tmp = fma((y * (z * -9.0)), t, (x * 2.0));
	} else {
		tmp = fma(27.0, (a * b), ((t * -9.0) * (y * z)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -4e+100)
		tmp = fma(27.0, Float64(a * b), Float64(x * 2.0));
	elseif (t_1 <= 2e+89)
		tmp = fma(Float64(y * Float64(z * -9.0)), t, Float64(x * 2.0));
	else
		tmp = fma(27.0, Float64(a * b), Float64(Float64(t * -9.0) * Float64(y * z)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+100], N[(27.0 * N[(a * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+89], N[(N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision] + N[(N[(t * -9.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.00000000000000006e100

   1. Initial program 97.4%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 97.4%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 97.4%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(27, \color{blue}{\left(a \cdot b\right)}, \left(2 \cdot x\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right), \left(2 \cdot x\right)\right) \]

      4. *-lowering-*.f64 92.7%

         \[\leadsto \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(2, x\right)\right) \]

   7. Simplified 92.7%

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

   if -4.00000000000000006e100 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.99999999999999999e89

   1. Initial program 97.4%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 97.3%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 97.3%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \color{blue}{\left(2 \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 88.1%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{*.f64}\left(2, x\right)\right) \]

   7. Simplified 88.1%

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

   if 1.99999999999999999e89 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   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. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 89.2%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 89.2%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(27, \color{blue}{\left(a \cdot b\right)}, \left(-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right), \left(-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), \left(\left(-9 \cdot t\right) \cdot \left(y \cdot z\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), \left(\left(y \cdot z\right) \cdot \left(-9 \cdot t\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\left(y \cdot z\right), \left(-9 \cdot t\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(-9 \cdot t\right)\right)\right) \]

      8. *-lowering-*.f64 80.6%

         \[\leadsto \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(-9, t\right)\right)\right) \]

   7. Simplified 80.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -4 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+89}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(z \cdot -9\right), t, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, \left(t \cdot -9\right) \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(z \cdot -9\right), t, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, 0\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= t_1 -4e+100)
     (fma 27.0 (* a b) (* x 2.0))
     (if (<= t_1 2e+111)
       (fma (* y (* z -9.0)) t (* x 2.0))
       (fma (* a 27.0) b (fma x 2.0 0.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -4e+100) {
		tmp = fma(27.0, (a * b), (x * 2.0));
	} else if (t_1 <= 2e+111) {
		tmp = fma((y * (z * -9.0)), t, (x * 2.0));
	} else {
		tmp = fma((a * 27.0), b, fma(x, 2.0, 0.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -4e+100)
		tmp = fma(27.0, Float64(a * b), Float64(x * 2.0));
	elseif (t_1 <= 2e+111)
		tmp = fma(Float64(y * Float64(z * -9.0)), t, Float64(x * 2.0));
	else
		tmp = fma(Float64(a * 27.0), b, fma(x, 2.0, 0.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+100], N[(27.0 * N[(a * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+111], N[(N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x * 2.0 + 0.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.00000000000000006e100

   1. Initial program 97.4%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 97.4%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 97.4%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(27, \color{blue}{\left(a \cdot b\right)}, \left(2 \cdot x\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right), \left(2 \cdot x\right)\right) \]

      4. *-lowering-*.f64 92.7%

         \[\leadsto \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(2, x\right)\right) \]

   7. Simplified 92.7%

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

   if -4.00000000000000006e100 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.99999999999999991e111

   1. Initial program 97.4%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 97.4%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 97.4%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \color{blue}{\left(2 \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 87.9%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{*.f64}\left(2, x\right)\right) \]

   7. Simplified 87.9%

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

   if 1.99999999999999991e111 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 88.1%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(2 \cdot x\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]
   4. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot x + 0\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

      2. accelerator-lowering-fma.f64 76.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{fma.f64}\left(2, x, 0\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(a, 27\right)}, b\right)\right) \]

   5. Simplified 76.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 0\right)} + \left(a \cdot 27\right) \cdot b \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(2 \cdot x + 0\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(a \cdot 27\right), \color{blue}{b}, \left(2 \cdot x + 0\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(a, 27\right), b, \left(2 \cdot x + 0\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(a, 27\right), b, \left(x \cdot 2 + 0\right)\right) \]

      5. accelerator-lowering-fma.f64 76.8%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(a, 27\right), b, \mathsf{fma.f64}\left(x, 2, 0\right)\right) \]

   7. Applied egg-rr 76.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, 0\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -4 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(z \cdot -9\right), t, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, 0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+41}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+111}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= t_1 -1e+41) (* 27.0 (* a b)) (if (<= t_1 2e+111) (* x 2.0) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -1e+41) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= 2e+111) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    if (t_1 <= (-1d+41)) then
        tmp = 27.0d0 * (a * b)
    else if (t_1 <= 2d+111) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -1e+41) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= 2e+111) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -1e+41:
		tmp = 27.0 * (a * b)
	elif t_1 <= 2e+111:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -1e+41)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t_1 <= 2e+111)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -1e+41)
		tmp = 27.0 * (a * b);
	elseif (t_1 <= 2e+111)
		tmp = x * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+41], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+111], N[(x * 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.00000000000000001e41

   1. Initial program 96.3%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 96.4%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 67.5%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 67.5%

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

   if -1.00000000000000001e41 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.99999999999999991e111

   1. Initial program 97.8%

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

   3. Taylor expanded in x around inf

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

      1. +-rgt-identity N/A

         \[\leadsto 2 \cdot x + \color{blue}{0} \]

      2. accelerator-lowering-fma.f64 46.4%

         \[\leadsto \mathsf{fma.f64}\left(2, \color{blue}{x}, 0\right) \]

   5. Simplified 46.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 46.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{2}\right) \]

   7. Applied egg-rr 46.4%

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

   if 1.99999999999999991e111 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 88.1%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 88.0%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 88.0%

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

   5. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 64.8%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 64.8%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot 27\right), \color{blue}{b}\right) \]

      4. *-lowering-*.f64 64.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right) \]

   9. Applied egg-rr 64.7%

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

Alternative 10: 97.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(z \cdot -9\right), t, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.6e+122)
   (fma (* 27.0 b) a (* z (* t (* y -9.0))))
   (fma (* y (* z -9.0)) t (fma a (* 27.0 b) (* x 2.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.6e+122) {
		tmp = fma((27.0 * b), a, (z * (t * (y * -9.0))));
	} else {
		tmp = fma((y * (z * -9.0)), t, fma(a, (27.0 * b), (x * 2.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.6e+122)
		tmp = fma(Float64(27.0 * b), a, Float64(z * Float64(t * Float64(y * -9.0))));
	else
		tmp = fma(Float64(y * Float64(z * -9.0)), t, fma(a, Float64(27.0 * b), Float64(x * 2.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.6e+122], N[(N[(27.0 * b), $MachinePrecision] * a + N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision] * t + N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5999999999999999e122

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0

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

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

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

      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. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)}, \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      8. +-lft-identity N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 + \color{blue}{-9 \cdot \left(y \cdot z\right)}\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(-9 \cdot \left(y \cdot z\right) + \color{blue}{0}\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \left(\left(y \cdot z\right) \cdot -9 + 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      11. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\left(y \cdot z\right), \color{blue}{-9}, 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), \left(27 \cdot \left(a \cdot b\right)\right)\right) \]

      13. +-rgt-identity N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, \color{blue}{0}\right), \left(27 \cdot \left(a \cdot b\right) + 0\right)\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, \color{blue}{0}\right), \mathsf{fma.f64}\left(27, \left(a \cdot b\right), 0\right)\right) \]

      15. *-lowering-*.f64 74.5%

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), 0\right)\right) \]

   5. Simplified 74.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(y \cdot z, -9, 0\right), \mathsf{fma}\left(27, a \cdot b, 0\right)\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + \left(27 \cdot \color{blue}{\left(a \cdot b\right)} + 0\right) \]

      2. +-rgt-identity N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(27 \cdot b\right), \color{blue}{a}, \left(\left(y \cdot \left(z \cdot -9\right)\right) \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(y \cdot \left(z \cdot -9\right)\right) \cdot t\right)\right) \]

      10. +-rgt-identity N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(y \cdot \left(z \cdot -9\right)\right) \cdot t + 0\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(\left(y \cdot z\right) \cdot -9\right) \cdot t + 0\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(-9 \cdot \left(y \cdot z\right)\right) \cdot t + 0\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(-9 \cdot \left(\left(y \cdot z\right) \cdot t\right) + 0\right)\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{fma.f64}\left(-9, \left(\left(y \cdot z\right) \cdot t\right), 0\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{fma.f64}\left(-9, \mathsf{*.f64}\left(\left(y \cdot z\right), t\right), 0\right)\right) \]

      16. *-lowering-*.f64 80.8%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{fma.f64}\left(-9, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), t\right), 0\right)\right) \]

   7. Applied egg-rr 80.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27 \cdot b, a, \mathsf{fma}\left(-9, \left(y \cdot z\right) \cdot t, 0\right)\right)} \]
   8. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(-9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(-9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(y \cdot -9\right) \cdot \left(z \cdot t\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\right)\right) \]

      6. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \left(\left(t \cdot \left(y \cdot -9\right)\right) \cdot z\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot -9\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot -9\right)\right), z\right)\right) \]

      10. *-lowering-*.f64 83.8%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(27, b\right), a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, -9\right)\right), z\right)\right) \]

   9. Applied egg-rr 83.8%

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

   if -5.5999999999999999e122 < z

   1. Initial program 97.4%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 97.4%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 97.4%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(z \cdot -9\right), t, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -1 \cdot 10^{-16}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \cdot 2 \leq 1000000000:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x 2.0) -1e-16)
   (* x 2.0)
   (if (<= (* x 2.0) 1000000000.0) (* 27.0 (* a b)) (* x 2.0))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * 2.0) <= -1e-16) {
		tmp = x * 2.0;
	} else if ((x * 2.0) <= 1000000000.0) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x * 2.0d0) <= (-1d-16)) then
        tmp = x * 2.0d0
    else if ((x * 2.0d0) <= 1000000000.0d0) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * 2.0) <= -1e-16) {
		tmp = x * 2.0;
	} else if ((x * 2.0) <= 1000000000.0) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x * 2.0) <= -1e-16:
		tmp = x * 2.0
	elif (x * 2.0) <= 1000000000.0:
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * 2.0) <= -1e-16)
		tmp = Float64(x * 2.0);
	elseif (Float64(x * 2.0) <= 1000000000.0)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * 2.0) <= -1e-16)
		tmp = x * 2.0;
	elseif ((x * 2.0) <= 1000000000.0)
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * 2.0), $MachinePrecision], -1e-16], N[(x * 2.0), $MachinePrecision], If[LessEqual[N[(x * 2.0), $MachinePrecision], 1000000000.0], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 2 binary64)) < -9.9999999999999998e-17 or 1e9 < (*.f64 x #s(literal 2 binary64))

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf

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

      1. +-rgt-identity N/A

         \[\leadsto 2 \cdot x + \color{blue}{0} \]

      2. accelerator-lowering-fma.f64 56.9%

         \[\leadsto \mathsf{fma.f64}\left(2, \color{blue}{x}, 0\right) \]

   5. Simplified 56.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 56.9%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{2}\right) \]

   7. Applied egg-rr 56.9%

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

   if -9.9999999999999998e-17 < (*.f64 x #s(literal 2 binary64)) < 1e9

   1. Initial program 94.7%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 94.7%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 94.7%

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

   5. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 44.2%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 44.2%

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

Alternative 12: 93.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return fma(Float64(y * t), Float64(z * -9.0), fma(a, Float64(27.0 * b), Float64(x * 2.0)))
end

Wolfram

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

Derivation

1. Initial program 96.2%

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

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

   4. *-commutative N/A

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

   5. associate-*l* N/A

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

   6. associate-*r* N/A

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

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

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

   8. +-commutative N/A

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

   9. accelerator-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\left(t \cdot y\right), \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot t\right), \left(\mathsf{neg}\left(\color{blue}{9 \cdot z}\right)\right), \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

   11. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, t\right), \left(\mathsf{neg}\left(\color{blue}{9 \cdot z}\right)\right), \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

   12. *-commutative N/A

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, t\right), \left(\mathsf{neg}\left(z \cdot 9\right)\right), \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, t\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right), \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

   14. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, t\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right), \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

   15. metadata-eval N/A

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, t\right), \mathsf{*.f64}\left(z, -9\right), \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

   16. associate-*l* N/A

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, t\right), \mathsf{*.f64}\left(z, -9\right), \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

   17. accelerator-lowering-fma.f64 N/A

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, t\right), \mathsf{*.f64}\left(z, -9\right), \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

   18. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, t\right), \mathsf{*.f64}\left(z, -9\right), \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

   19. *-lowering-*.f64 93.5%

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, t\right), \mathsf{*.f64}\left(z, -9\right), \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

4. Applied egg-rr 93.5%

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

Alternative 13: 75.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+41}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-35}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.65e+41)
   (* (* z -9.0) (* y t))
   (if (<= z 3.9e-35) (fma 27.0 (* a b) (* x 2.0)) (* t (* z (* y -9.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.65e+41) {
		tmp = (z * -9.0) * (y * t);
	} else if (z <= 3.9e-35) {
		tmp = fma(27.0, (a * b), (x * 2.0));
	} else {
		tmp = t * (z * (y * -9.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.65e+41)
		tmp = Float64(Float64(z * -9.0) * Float64(y * t));
	elseif (z <= 3.9e-35)
		tmp = fma(27.0, Float64(a * b), Float64(x * 2.0));
	else
		tmp = Float64(t * Float64(z * Float64(y * -9.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.65e+41], N[(N[(z * -9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e-35], N[(27.0 * N[(a * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e41

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf

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

      1. +-lft-identity N/A

         \[\leadsto 0 + \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{0} \]

      3. *-commutative N/A

         \[\leadsto \left(t \cdot \left(y \cdot z\right)\right) \cdot -9 + 0 \]

      4. associate-*l* N/A

         \[\leadsto t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + 0 \]

      5. *-commutative N/A

         \[\leadsto t \cdot \left(-9 \cdot \left(y \cdot z\right)\right) + 0 \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)}, 0\right) \]

      7. +-lft-identity N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 + \color{blue}{-9 \cdot \left(y \cdot z\right)}\right), 0\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(-9 \cdot \left(y \cdot z\right) + \color{blue}{0}\right), 0\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(\left(y \cdot z\right) \cdot -9 + 0\right), 0\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\left(y \cdot z\right), \color{blue}{-9}, 0\right), 0\right) \]

      11. *-lowering-*.f64 50.5%

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), 0\right) \]

   5. Simplified 50.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(y \cdot z, -9, 0\right), 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + 0 \]

      2. *-commutative N/A

         \[\leadsto \left(\left(y \cdot z\right) \cdot -9\right) \cdot t + 0 \]

      3. associate-*r* N/A

         \[\leadsto \left(y \cdot \left(z \cdot -9\right)\right) \cdot t + 0 \]

      4. +-rgt-identity N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-lowering-*.f64 51.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -9\right), \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right) \]

   7. Applied egg-rr 51.8%

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

   if -1.65e41 < z < 3.8999999999999998e-35

   1. Initial program 98.6%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot z\right)\right), \color{blue}{t}, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

         \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(9 \cdot z\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

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

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(9\right)\right)\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right)\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \left(27 \cdot b\right), \left(x \cdot 2\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \left(x \cdot 2\right)\right)\right) \]

      17. *-lowering-*.f64 98.5%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, -9\right)\right), t, \mathsf{fma.f64}\left(a, \mathsf{*.f64}\left(27, b\right), \mathsf{*.f64}\left(x, 2\right)\right)\right) \]

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(27, \color{blue}{\left(a \cdot b\right)}, \left(2 \cdot x\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right), \left(2 \cdot x\right)\right) \]

      4. *-lowering-*.f64 74.8%

         \[\leadsto \mathsf{fma.f64}\left(27, \mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(2, x\right)\right) \]

   7. Simplified 74.8%

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

   if 3.8999999999999998e-35 < z

   1. Initial program 94.6%

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

   3. Taylor expanded in y around inf

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

      1. +-lft-identity N/A

         \[\leadsto 0 + \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{0} \]

      3. *-commutative N/A

         \[\leadsto \left(t \cdot \left(y \cdot z\right)\right) \cdot -9 + 0 \]

      4. associate-*l* N/A

         \[\leadsto t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + 0 \]

      5. *-commutative N/A

         \[\leadsto t \cdot \left(-9 \cdot \left(y \cdot z\right)\right) + 0 \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \color{blue}{\left(-9 \cdot \left(y \cdot z\right)\right)}, 0\right) \]

      7. +-lft-identity N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(0 + \color{blue}{-9 \cdot \left(y \cdot z\right)}\right), 0\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(-9 \cdot \left(y \cdot z\right) + \color{blue}{0}\right), 0\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma.f64}\left(t, \left(\left(y \cdot z\right) \cdot -9 + 0\right), 0\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\left(y \cdot z\right), \color{blue}{-9}, 0\right), 0\right) \]

      11. *-lowering-*.f64 50.6%

          \[\leadsto \mathsf{fma.f64}\left(t, \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, z\right), -9, 0\right), 0\right) \]

   5. Simplified 50.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(y \cdot z, -9, 0\right), 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + 0 \]

      2. *-commutative N/A

         \[\leadsto \left(\left(y \cdot z\right) \cdot -9\right) \cdot t + 0 \]

      3. associate-*r* N/A

         \[\leadsto \left(y \cdot \left(z \cdot -9\right)\right) \cdot t + 0 \]

      4. +-rgt-identity N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-lowering-*.f64 50.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, -9\right), \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right) \]

   7. Applied egg-rr 50.5%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(-9 \cdot \left(z \cdot y\right)\right), t\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(-9 \cdot z\right) \cdot y\right), t\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(z \cdot -9\right) \cdot y\right), t\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot \left(-9 \cdot y\right)\right), t\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(z \cdot \left(y \cdot -9\right)\right), t\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot -9\right)\right), t\right) \]

      12. *-lowering-*.f64 50.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, -9\right)\right), t\right) \]

   9. Applied egg-rr 50.6%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+41}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-35}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.0% accurate, 6.2× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* x 2.0))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * 2.0d0
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return x * 2.0

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(x * 2.0)
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = x * 2.0;
end

Wolfram

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

Derivation

1. Initial program 96.2%

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

3. Taylor expanded in x around inf

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

   1. +-rgt-identity N/A

      \[\leadsto 2 \cdot x + \color{blue}{0} \]

   2. accelerator-lowering-fma.f64 35.0%

      \[\leadsto \mathsf{fma.f64}\left(2, \color{blue}{x}, 0\right) \]

5. Simplified 35.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 0\right)} \]
6. Step-by-step derivation

   1. +-rgt-identity N/A

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

   2. *-commutative N/A

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

   3. *-lowering-*.f64 35.0%

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{2}\right) \]

7. Applied egg-rr 35.0%

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

Developer Target 1: 95.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (< y 7.590524218811189e-161)
   (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y < 7.590524218811189d-161) then
        tmp = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + (a * (27.0d0 * b))
    else
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (t * z)))) + ((a * 27.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y < 7.590524218811189e-161:
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b))
	else:
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y < 7.590524218811189e-161)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(t * z)))) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y < 7.590524218811189e-161)
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	else
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Less[y, 7.590524218811189e-161], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024193 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y 7590524218811189/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x 2) (* (* (* y 9) z) t)) (* a (* 27 b))) (+ (- (* x 2) (* 9 (* y (* t z)))) (* (* a 27) b))))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))