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

Percentage Accurate: 95.5% → 98.3%

Time: 28.7s

Alternatives: 17

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: 98.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-289}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot t, y \cdot -9, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 2e-289)
   (fma (* z t) (* y -9.0) (fma a (* 27.0 b) (* x 2.0)))
   (+ (- (* x 2.0) (* t (* z (* y 9.0)))) (* b (* a 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2e-289) {
		tmp = fma((z * t), (y * -9.0), fma(a, (27.0 * b), (x * 2.0)));
	} else {
		tmp = ((x * 2.0) - (t * (z * (y * 9.0)))) + (b * (a * 27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 2e-289)
		tmp = fma(Float64(z * t), Float64(y * -9.0), fma(a, Float64(27.0 * b), Float64(x * 2.0)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(y * 9.0)))) + Float64(b * Float64(a * 27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 2e-289], N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2e-289

   1. Initial program 96.8%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

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

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

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

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 95.4

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

   4. Applied egg-rr 95.4%

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

   if 2e-289 < z

   1. Initial program 92.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-289}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot t, y \cdot -9, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, t \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* z (* y 9.0)))))
   (if (<= t_1 -1e+48)
     (fma t (* -9.0 (* z y)) (* x 2.0))
     (if (<= t_1 5e+18)
       (fma (* 27.0 b) a (* x 2.0))
       (fma -9.0 (* t (* z y)) (* x 2.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * (y * 9.0));
	double tmp;
	if (t_1 <= -1e+48) {
		tmp = fma(t, (-9.0 * (z * y)), (x * 2.0));
	} else if (t_1 <= 5e+18) {
		tmp = fma((27.0 * b), a, (x * 2.0));
	} else {
		tmp = fma(-9.0, (t * (z * y)), (x * 2.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_1 <= -1e+48)
		tmp = fma(t, Float64(-9.0 * Float64(z * y)), Float64(x * 2.0));
	elseif (t_1 <= 5e+18)
		tmp = fma(Float64(27.0 * b), a, Float64(x * 2.0));
	else
		tmp = fma(-9.0, Float64(t * Float64(z * y)), Float64(x * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+48], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+18], N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.00000000000000004e48

   1. Initial program 90.0%

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

   3. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

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

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

      8. *-commutative N/A

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

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

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

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

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

      11. *-lowering-*.f64 82.3

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

   5. Simplified 82.3%

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

   if -1.00000000000000004e48 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5e18

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. *-lowering-*.f64 95.1

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

   5. Simplified 95.1%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

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

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

      6. *-lowering-*.f64 95.1

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

   7. Applied egg-rr 95.1%

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

   if 5e18 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 86.0%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

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

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

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

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 92.1

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

   4. Applied egg-rr 92.1%

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

   5. Taylor expanded in a around 0

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

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

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

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

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

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

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

      4. *-lowering-*.f64 70.1

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

   7. Simplified 70.1%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -1 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 5 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, t \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-9, t \cdot \left(z \cdot y\right), x \cdot 2\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma -9.0 (* t (* z y)) (* x 2.0))) (t_2 (* t (* z (* y 9.0)))))
   (if (<= t_2 -1e+48)
     t_1
     (if (<= t_2 5e+18) (fma (* 27.0 b) a (* 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 = fma(-9.0, (t * (z * y)), (x * 2.0));
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -1e+48) {
		tmp = t_1;
	} else if (t_2 <= 5e+18) {
		tmp = fma((27.0 * b), a, (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 = fma(-9.0, Float64(t * Float64(z * y)), Float64(x * 2.0))
	t_2 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_2 <= -1e+48)
		tmp = t_1;
	elseif (t_2 <= 5e+18)
		tmp = fma(Float64(27.0 * b), a, Float64(x * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+48], t$95$1, If[LessEqual[t$95$2, 5e+18], N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.00000000000000004e48 or 5e18 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 88.2%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

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

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

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

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 88.3

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

   4. Applied egg-rr 88.3%

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

   5. Taylor expanded in a around 0

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

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

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

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

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

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

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

      4. *-lowering-*.f64 76.8

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

   7. Simplified 76.8%

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

   if -1.00000000000000004e48 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5e18

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. *-lowering-*.f64 95.1

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

   5. Simplified 95.1%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

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

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

      6. *-lowering-*.f64 95.1

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

   7. Applied egg-rr 95.1%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -1 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(-9, t \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 5 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, t \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(y \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(-9, t \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot t\right) \cdot y, -9, a \cdot \left(27 \cdot b\right)\right)\\ \end{array} \end{array} \]

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 (* z (* y 9.0))))
   (if (<= t_1 -5e-31)
     (fma -9.0 (* t (* z y)) (* x 2.0))
     (if (<= t_1 2e+90)
       (fma (* 27.0 b) a (* x 2.0))
       (fma (* (* z t) y) -9.0 (* a (* 27.0 b)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y * 9.0);
	double tmp;
	if (t_1 <= -5e-31) {
		tmp = fma(-9.0, (t * (z * y)), (x * 2.0));
	} else if (t_1 <= 2e+90) {
		tmp = fma((27.0 * b), a, (x * 2.0));
	} else {
		tmp = fma(((z * t) * y), -9.0, (a * (27.0 * b)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y * 9.0))
	tmp = 0.0
	if (t_1 <= -5e-31)
		tmp = fma(-9.0, Float64(t * Float64(z * y)), Float64(x * 2.0));
	elseif (t_1 <= 2e+90)
		tmp = fma(Float64(27.0 * b), a, Float64(x * 2.0));
	else
		tmp = fma(Float64(Float64(z * t) * y), -9.0, Float64(a * Float64(27.0 * b)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-31], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+90], N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] * y), $MachinePrecision] * -9.0 + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < -5e-31

   1. Initial program 90.2%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

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

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

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

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 93.0

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

   4. Applied egg-rr 93.0%

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

   5. Taylor expanded in a around 0

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

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

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

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

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

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

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

      4. *-lowering-*.f64 72.3

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

   7. Simplified 72.3%

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

   if -5e-31 < (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 1.99999999999999993e90

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. *-lowering-*.f64 88.7

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

   5. Simplified 88.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

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

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

      6. *-lowering-*.f64 88.6

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

   7. Applied egg-rr 88.6%

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

   if 1.99999999999999993e90 < (*.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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

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

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

      8. *-commutative N/A

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

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

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

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

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

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

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

      12. *-lowering-*.f64 73.3

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

   5. Simplified 73.3%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

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

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

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

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

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

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

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

      12. *-lowering-*.f64 78.4

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

   7. Applied egg-rr 78.4%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot 9\right) \leq -5 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(-9, t \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \mathbf{elif}\;z \cdot \left(y \cdot 9\right) \leq 2 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot t\right) \cdot y, -9, a \cdot \left(27 \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+243}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \end{array} \end{array} \]

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 (* t (* z (* y 9.0)))))
   (if (<= t_1 -1e+100)
     (* t (* y (* z -9.0)))
     (if (<= t_1 1e+243)
       (fma (* 27.0 b) a (* x 2.0))
       (* (* 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 = t * (z * (y * 9.0));
	double tmp;
	if (t_1 <= -1e+100) {
		tmp = t * (y * (z * -9.0));
	} else if (t_1 <= 1e+243) {
		tmp = fma((27.0 * b), a, (x * 2.0));
	} else {
		tmp = (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(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_1 <= -1e+100)
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	elseif (t_1 <= 1e+243)
		tmp = fma(Float64(27.0 * b), a, Float64(x * 2.0));
	else
		tmp = Float64(Float64(z * 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[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+100], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+243], N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.00000000000000002e100

   1. Initial program 88.9%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

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

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

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

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 85.4

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

   4. Applied egg-rr 85.4%

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

   5. Taylor expanded in a around 0

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

      1. *-lowering-*.f64 82.5

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

   7. Simplified 82.5%

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

   8. Taylor expanded in z around inf

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

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

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

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

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

      3. *-lowering-*.f64 76.8

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

   10. Simplified 76.8%

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

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

       4. associate-*l* N/A

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

       5. *-commutative N/A

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

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

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

       7. *-commutative N/A

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

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

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

       9. *-commutative N/A

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

       10. *-lowering-*.f64 76.9

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

   12. Applied egg-rr 76.9%

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

   if -1.00000000000000002e100 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1.0000000000000001e243

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. *-lowering-*.f64 89.0

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

   5. Simplified 89.0%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

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

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

      6. *-lowering-*.f64 89.0

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

   7. Applied egg-rr 89.0%

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

   if 1.0000000000000001e243 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 71.7%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

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

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

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

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 96.0

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in a around 0

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

      1. *-lowering-*.f64 96.0

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

   7. Simplified 96.0%

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

   8. Taylor expanded in z around inf

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

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

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

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

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

      3. *-lowering-*.f64 71.7

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

   10. Simplified 71.7%

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

       1. associate-*r* N/A

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

       2. *-commutative N/A

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

       5. associate-*r* N/A

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

       6. *-commutative N/A

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

       7. associate-*r* N/A

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

       8. associate-*l* N/A

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

       9. *-commutative N/A

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

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

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

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

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

       12. *-commutative N/A

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

       13. *-lowering-*.f64 83.6

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

   12. Applied egg-rr 83.6%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -1 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 10^{+243}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+243}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \end{array} \end{array} \]

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 (* t (* z (* y 9.0)))))
   (if (<= t_1 -1e+100)
     (* t (* y (* z -9.0)))
     (if (<= t_1 1e+243)
       (fma 27.0 (* a b) (* x 2.0))
       (* (* 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 = t * (z * (y * 9.0));
	double tmp;
	if (t_1 <= -1e+100) {
		tmp = t * (y * (z * -9.0));
	} else if (t_1 <= 1e+243) {
		tmp = fma(27.0, (a * b), (x * 2.0));
	} else {
		tmp = (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(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_1 <= -1e+100)
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	elseif (t_1 <= 1e+243)
		tmp = fma(27.0, Float64(a * b), Float64(x * 2.0));
	else
		tmp = Float64(Float64(z * 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[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+100], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+243], N[(27.0 * N[(a * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.00000000000000002e100

   1. Initial program 88.9%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

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

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

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

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 85.4

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

   4. Applied egg-rr 85.4%

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

   5. Taylor expanded in a around 0

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

      1. *-lowering-*.f64 82.5

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

   7. Simplified 82.5%

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

   8. Taylor expanded in z around inf

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

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

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

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

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

      3. *-lowering-*.f64 76.8

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

   10. Simplified 76.8%

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

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

       4. associate-*l* N/A

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

       5. *-commutative N/A

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

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

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

       7. *-commutative N/A

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

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

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

       9. *-commutative N/A

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

       10. *-lowering-*.f64 76.9

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

   12. Applied egg-rr 76.9%

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

   if -1.00000000000000002e100 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1.0000000000000001e243

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. *-lowering-*.f64 89.0

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

   5. Simplified 89.0%

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

   if 1.0000000000000001e243 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 71.7%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

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

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

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

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 96.0

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in a around 0

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

      1. *-lowering-*.f64 96.0

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

   7. Simplified 96.0%

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

   8. Taylor expanded in z around inf

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

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

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

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

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

      3. *-lowering-*.f64 71.7

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

   10. Simplified 71.7%

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

       1. associate-*r* N/A

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

       2. *-commutative N/A

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

       5. associate-*r* N/A

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

       6. *-commutative N/A

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

       7. associate-*r* N/A

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

       8. associate-*l* N/A

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

       9. *-commutative N/A

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

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

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

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

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

       12. *-commutative N/A

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

       13. *-lowering-*.f64 83.6

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

   12. Applied egg-rr 83.6%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -1 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 10^{+243}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+24}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* y (* z -9.0)))) (t_2 (* t (* z (* y 9.0)))))
   (if (<= t_2 -1e+48) t_1 (if (<= t_2 1e+24) (* a (* 27.0 b)) 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 = t * (y * (z * -9.0));
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -1e+48) {
		tmp = t_1;
	} else if (t_2 <= 1e+24) {
		tmp = a * (27.0 * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (y * (z * (-9.0d0)))
    t_2 = t * (z * (y * 9.0d0))
    if (t_2 <= (-1d+48)) then
        tmp = t_1
    else if (t_2 <= 1d+24) then
        tmp = a * (27.0d0 * b)
    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 = t * (y * (z * -9.0));
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -1e+48) {
		tmp = t_1;
	} else if (t_2 <= 1e+24) {
		tmp = a * (27.0 * b);
	} 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 = t * (y * (z * -9.0))
	t_2 = t * (z * (y * 9.0))
	tmp = 0
	if t_2 <= -1e+48:
		tmp = t_1
	elif t_2 <= 1e+24:
		tmp = a * (27.0 * b)
	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(t * Float64(y * Float64(z * -9.0)))
	t_2 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_2 <= -1e+48)
		tmp = t_1;
	elseif (t_2 <= 1e+24)
		tmp = Float64(a * Float64(27.0 * b));
	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 = t * (y * (z * -9.0));
	t_2 = t * (z * (y * 9.0));
	tmp = 0.0;
	if (t_2 <= -1e+48)
		tmp = t_1;
	elseif (t_2 <= 1e+24)
		tmp = a * (27.0 * b);
	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[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+48], t$95$1, If[LessEqual[t$95$2, 1e+24], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.00000000000000004e48 or 9.9999999999999998e23 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

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

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

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

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 88.2

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

   4. Applied egg-rr 88.2%

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

   5. Taylor expanded in a around 0

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

      1. *-lowering-*.f64 77.7

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

   7. Simplified 77.7%

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

   8. Taylor expanded in z around inf

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

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

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

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

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

      3. *-lowering-*.f64 65.7

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

   10. Simplified 65.7%

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

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

       4. associate-*l* N/A

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

       5. *-commutative N/A

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

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

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

       7. *-commutative N/A

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

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

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

       9. *-commutative N/A

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

       10. *-lowering-*.f64 65.7

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

   12. Applied egg-rr 65.7%

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

   if -1.00000000000000004e48 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 9.9999999999999998e23

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 57.5

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

   5. Simplified 57.5%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

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

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

      4. *-lowering-*.f64 57.5

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

   7. Applied egg-rr 57.5%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -1 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 10^{+24}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+24}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* -9.0 (* z y)))) (t_2 (* t (* z (* y 9.0)))))
   (if (<= t_2 -1e+48) t_1 (if (<= t_2 1e+24) (* a (* 27.0 b)) 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 = t * (-9.0 * (z * y));
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -1e+48) {
		tmp = t_1;
	} else if (t_2 <= 1e+24) {
		tmp = a * (27.0 * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((-9.0d0) * (z * y))
    t_2 = t * (z * (y * 9.0d0))
    if (t_2 <= (-1d+48)) then
        tmp = t_1
    else if (t_2 <= 1d+24) then
        tmp = a * (27.0d0 * b)
    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 = t * (-9.0 * (z * y));
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -1e+48) {
		tmp = t_1;
	} else if (t_2 <= 1e+24) {
		tmp = a * (27.0 * b);
	} 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 = t * (-9.0 * (z * y))
	t_2 = t * (z * (y * 9.0))
	tmp = 0
	if t_2 <= -1e+48:
		tmp = t_1
	elif t_2 <= 1e+24:
		tmp = a * (27.0 * b)
	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(t * Float64(-9.0 * Float64(z * y)))
	t_2 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_2 <= -1e+48)
		tmp = t_1;
	elseif (t_2 <= 1e+24)
		tmp = Float64(a * Float64(27.0 * b));
	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 = t * (-9.0 * (z * y));
	t_2 = t * (z * (y * 9.0));
	tmp = 0.0;
	if (t_2 <= -1e+48)
		tmp = t_1;
	elseif (t_2 <= 1e+24)
		tmp = a * (27.0 * b);
	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[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+48], t$95$1, If[LessEqual[t$95$2, 1e+24], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.00000000000000004e48 or 9.9999999999999998e23 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   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 y around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 65.6

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

   5. Simplified 65.6%

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

   if -1.00000000000000004e48 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 9.9999999999999998e23

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 57.5

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

   5. Simplified 57.5%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

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

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

      4. *-lowering-*.f64 57.5

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

   7. Applied egg-rr 57.5%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -1 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 10^{+24}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+24}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* z y)))) (t_2 (* t (* z (* y 9.0)))))
   (if (<= t_2 -1e+48) t_1 (if (<= t_2 1e+24) (* a (* 27.0 b)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (z * y));
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -1e+48) {
		tmp = t_1;
	} else if (t_2 <= 1e+24) {
		tmp = a * (27.0 * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-9.0d0) * (t * (z * y))
    t_2 = t * (z * (y * 9.0d0))
    if (t_2 <= (-1d+48)) then
        tmp = t_1
    else if (t_2 <= 1d+24) then
        tmp = a * (27.0d0 * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (z * y));
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -1e+48) {
		tmp = t_1;
	} else if (t_2 <= 1e+24) {
		tmp = a * (27.0 * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (t * (z * y))
	t_2 = t * (z * (y * 9.0))
	tmp = 0
	if t_2 <= -1e+48:
		tmp = t_1
	elif t_2 <= 1e+24:
		tmp = a * (27.0 * b)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(z * y)))
	t_2 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_2 <= -1e+48)
		tmp = t_1;
	elseif (t_2 <= 1e+24)
		tmp = Float64(a * Float64(27.0 * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (t * (z * y));
	t_2 = t * (z * (y * 9.0));
	tmp = 0.0;
	if (t_2 <= -1e+48)
		tmp = t_1;
	elseif (t_2 <= 1e+24)
		tmp = a * (27.0 * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+48], t$95$1, If[LessEqual[t$95$2, 1e+24], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.00000000000000004e48 or 9.9999999999999998e23 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   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

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

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

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

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

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 88.2

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

   4. Applied egg-rr 88.2%

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

   5. Taylor expanded in a around 0

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

      1. *-lowering-*.f64 77.7

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

   7. Simplified 77.7%

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

   8. Taylor expanded in z around inf

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

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

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

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

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

      3. *-lowering-*.f64 65.7

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

   10. Simplified 65.7%

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

   if -1.00000000000000004e48 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 9.9999999999999998e23

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 57.5

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

   5. Simplified 57.5%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

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

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

      4. *-lowering-*.f64 57.5

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

   7. Applied egg-rr 57.5%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -1 \cdot 10^{+48}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 10^{+24}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= t_1 -1e-44)
     (* a (* 27.0 b))
     (if (<= t_1 2e-14) (* x 2.0) (* 27.0 (* a b))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -1e-44) {
		tmp = a * (27.0 * b);
	} else if (t_1 <= 2e-14) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	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 = b * (a * 27.0d0)
    if (t_1 <= (-1d-44)) then
        tmp = a * (27.0d0 * b)
    else if (t_1 <= 2d-14) then
        tmp = x * 2.0d0
    else
        tmp = 27.0d0 * (a * b)
    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 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -1e-44) {
		tmp = a * (27.0 * b);
	} else if (t_1 <= 2e-14) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	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 = b * (a * 27.0)
	tmp = 0
	if t_1 <= -1e-44:
		tmp = a * (27.0 * b)
	elif t_1 <= 2e-14:
		tmp = x * 2.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (t_1 <= -1e-44)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (t_1 <= 2e-14)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	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 = b * (a * 27.0);
	tmp = 0.0;
	if (t_1 <= -1e-44)
		tmp = a * (27.0 * b);
	elseif (t_1 <= 2e-14)
		tmp = x * 2.0;
	else
		tmp = 27.0 * (a * b);
	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[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-44], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-14], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -9.99999999999999953e-45

   1. Initial program 97.0%

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

   3. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 63.7

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

   5. Simplified 63.7%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

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

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

      4. *-lowering-*.f64 63.8

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

   7. Applied egg-rr 63.8%

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

   if -9.99999999999999953e-45 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2e-14

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 52.8

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

   5. Simplified 52.8%

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

   if 2e-14 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   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 a around inf

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

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

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

      2. *-lowering-*.f64 68.5

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

   5. Simplified 68.5%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -1 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= t_1 -1e-44) t_1 (if (<= t_1 2e-14) (* x 2.0) (* 27.0 (* a b))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -1e-44) {
		tmp = t_1;
	} else if (t_1 <= 2e-14) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	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 = b * (a * 27.0d0)
    if (t_1 <= (-1d-44)) then
        tmp = t_1
    else if (t_1 <= 2d-14) then
        tmp = x * 2.0d0
    else
        tmp = 27.0d0 * (a * b)
    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 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -1e-44) {
		tmp = t_1;
	} else if (t_1 <= 2e-14) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	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 = b * (a * 27.0)
	tmp = 0
	if t_1 <= -1e-44:
		tmp = t_1
	elif t_1 <= 2e-14:
		tmp = x * 2.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (t_1 <= -1e-44)
		tmp = t_1;
	elseif (t_1 <= 2e-14)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	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 = b * (a * 27.0);
	tmp = 0.0;
	if (t_1 <= -1e-44)
		tmp = t_1;
	elseif (t_1 <= 2e-14)
		tmp = x * 2.0;
	else
		tmp = 27.0 * (a * b);
	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[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-44], t$95$1, If[LessEqual[t$95$1, 2e-14], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -9.99999999999999953e-45

   1. Initial program 97.0%

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

   3. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 63.7

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

   5. Simplified 63.7%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 63.8

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

   7. Applied egg-rr 63.8%

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

   if -9.99999999999999953e-45 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2e-14

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 52.8

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

   5. Simplified 52.8%

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

   if 2e-14 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   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 a around inf

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

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

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

      2. *-lowering-*.f64 68.5

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

   5. Simplified 68.5%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -1 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))) (t_2 (* 27.0 (* a b))))
   (if (<= t_1 -1e-44) t_2 (if (<= t_1 2e-14) (* x 2.0) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (t_1 <= -1e-44) {
		tmp = t_2;
	} else if (t_1 <= 2e-14) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    t_2 = 27.0d0 * (a * b)
    if (t_1 <= (-1d-44)) then
        tmp = t_2
    else if (t_1 <= 2d-14) then
        tmp = x * 2.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (t_1 <= -1e-44) {
		tmp = t_2;
	} else if (t_1 <= 2e-14) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	t_2 = 27.0 * (a * b)
	tmp = 0
	if t_1 <= -1e-44:
		tmp = t_2
	elif t_1 <= 2e-14:
		tmp = x * 2.0
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	t_2 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (t_1 <= -1e-44)
		tmp = t_2;
	elseif (t_1 <= 2e-14)
		tmp = Float64(x * 2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	t_2 = 27.0 * (a * b);
	tmp = 0.0;
	if (t_1 <= -1e-44)
		tmp = t_2;
	elseif (t_1 <= 2e-14)
		tmp = x * 2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-44], t$95$2, If[LessEqual[t$95$1, 2e-14], N[(x * 2.0), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -9.99999999999999953e-45 or 2e-14 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   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 a around inf

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

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

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

      2. *-lowering-*.f64 66.2

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

   5. Simplified 66.2%

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

   if -9.99999999999999953e-45 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2e-14

   1. Initial program 92.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 52.8

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

   5. Simplified 52.8%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -1 \cdot 10^{-44}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 98.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\\ \mathbf{if}\;z \leq 2 \cdot 10^{-76}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot t, y \cdot -9, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \left(y \cdot -9\right), z, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (* 27.0 b) (* x 2.0))))
   (if (<= z 2e-76)
     (fma (* z t) (* y -9.0) t_1)
     (fma (* t (* y -9.0)) z t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, (27.0 * b), (x * 2.0));
	double tmp;
	if (z <= 2e-76) {
		tmp = fma((z * t), (y * -9.0), t_1);
	} else {
		tmp = fma((t * (y * -9.0)), z, t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(a, Float64(27.0 * b), Float64(x * 2.0))
	tmp = 0.0
	if (z <= 2e-76)
		tmp = fma(Float64(z * t), Float64(y * -9.0), t_1);
	else
		tmp = fma(Float64(t * Float64(y * -9.0)), z, t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 2e-76], N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] * z + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 1.99999999999999985e-76

   1. Initial program 96.9%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

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

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

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

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 95.9

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

   4. Applied egg-rr 95.9%

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

   if 1.99999999999999985e-76 < z

   1. Initial program 90.5%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. +-commutative N/A

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

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

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

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

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

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

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

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

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

      13. metadata-eval N/A

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

      14. associate-*l* N/A

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

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

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

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

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

      17. *-lowering-*.f64 97.4

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

   4. Applied egg-rr 97.4%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-76}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot t, y \cdot -9, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \left(y \cdot -9\right), z, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 98.4% accurate, 0.9× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (* 27.0 b) (* x 2.0))))
   (if (<= z 5e-78)
     (fma (* z t) (* y -9.0) t_1)
     (fma (* t y) (* z -9.0) 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 = fma(a, (27.0 * b), (x * 2.0));
	double tmp;
	if (z <= 5e-78) {
		tmp = fma((z * t), (y * -9.0), t_1);
	} else {
		tmp = fma((t * y), (z * -9.0), t_1);
	}
	return tmp;
}

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < 4.9999999999999996e-78

   1. Initial program 96.9%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

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

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

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

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 95.9

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

   4. Applied egg-rr 95.9%

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

   if 4.9999999999999996e-78 < z

   1. Initial program 90.5%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-*r* N/A

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

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

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

      8. +-commutative N/A

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

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

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

      10. *-commutative N/A

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

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

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

      12. *-commutative N/A

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

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

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

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

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

      15. metadata-eval N/A

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

      16. associate-*l* N/A

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

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

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

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

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

      19. *-lowering-*.f64 97.4

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

   4. Applied egg-rr 97.4%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot t, y \cdot -9, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot y, z \cdot -9, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 98.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\\ \mathbf{if}\;z \leq 10^{-84}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot t\right) \cdot y, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot y, z \cdot -9, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (* 27.0 b) (* x 2.0))))
   (if (<= z 1e-84)
     (fma -9.0 (* (* z t) y) t_1)
     (fma (* t y) (* z -9.0) 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 = fma(a, (27.0 * b), (x * 2.0));
	double tmp;
	if (z <= 1e-84) {
		tmp = fma(-9.0, ((z * t) * y), t_1);
	} else {
		tmp = fma((t * y), (z * -9.0), t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(a, Float64(27.0 * b), Float64(x * 2.0))
	tmp = 0.0
	if (z <= 1e-84)
		tmp = fma(-9.0, Float64(Float64(z * t) * y), t_1);
	else
		tmp = fma(Float64(t * y), Float64(z * -9.0), t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 1e-84], N[(-9.0 * N[(N[(z * t), $MachinePrecision] * y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(t * y), $MachinePrecision] * N[(z * -9.0), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 1e-84

   1. Initial program 96.9%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

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

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

      8. +-commutative N/A

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

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

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

      10. metadata-eval N/A

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

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

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

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

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

      13. associate-*l* N/A

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

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

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

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

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

      16. *-lowering-*.f64 96.5

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

   4. Applied egg-rr 96.5%

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

   if 1e-84 < z

   1. Initial program 90.6%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-*r* N/A

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

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

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

      8. +-commutative N/A

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

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

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

      10. *-commutative N/A

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

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

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

      12. *-commutative N/A

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

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

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

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

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

      15. metadata-eval N/A

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

      16. associate-*l* N/A

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

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

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

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

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

      19. *-lowering-*.f64 97.4

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

   4. Applied egg-rr 97.4%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 10^{-84}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot t\right) \cdot y, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot y, z \cdot -9, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 97.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 2.2 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot t\right) \cdot y, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \left(y \cdot -9\right), z, x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 2.2e+106)
   (fma -9.0 (* (* z t) y) (fma a (* 27.0 b) (* x 2.0)))
   (fma (* t (* y -9.0)) z (* 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 <= 2.2e+106) {
		tmp = fma(-9.0, ((z * t) * y), fma(a, (27.0 * b), (x * 2.0)));
	} else {
		tmp = fma((t * (y * -9.0)), z, (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 <= 2.2e+106)
		tmp = fma(-9.0, Float64(Float64(z * t) * y), fma(a, Float64(27.0 * b), Float64(x * 2.0)));
	else
		tmp = fma(Float64(t * Float64(y * -9.0)), z, 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, 2.2e+106], N[(-9.0 * N[(N[(z * t), $MachinePrecision] * y), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] * z + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.19999999999999992e106

   1. Initial program 96.1%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      7. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      9. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(9\right), y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-9}, y \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-9, \color{blue}{y \cdot \left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \color{blue}{\left(z \cdot t\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      16. *-lowering-*.f64 97.1

          \[\leadsto \mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 97.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]

   if 2.19999999999999992e106 < z

   1. Initial program 87.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]

      4. associate-*l* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot \left(z \cdot t\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot \color{blue}{\left(t \cdot z\right)} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      7. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t\right) \cdot z} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t\right) \cdot z + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      9. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t, z, \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(y \cdot 9\right)\right) \cdot t}, z, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot \left(\mathsf{neg}\left(9\right)\right)\right)} \cdot t, z, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot \left(\mathsf{neg}\left(9\right)\right)\right)} \cdot t, z, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\left(y \cdot \color{blue}{-9}\right) \cdot t, z, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]

      14. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, \color{blue}{a \cdot \left(27 \cdot b\right)} + x \cdot 2\right) \]

      15. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)}\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right)\right) \]

      17. *-lowering-*.f64 97.3

          \[\leadsto \mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2}\right)\right) \]

   4. Applied egg-rr 97.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)} \]

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, \color{blue}{2 \cdot x}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 80.1

         \[\leadsto \mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, \color{blue}{2 \cdot x}\right) \]

   7. Simplified 80.1%

      \[\leadsto \mathsf{fma}\left(\left(y \cdot -9\right) \cdot t, z, \color{blue}{2 \cdot x}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.2 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot t\right) \cdot y, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \left(y \cdot -9\right), z, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.6% 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 94.8%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{2 \cdot x} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 30.2

      \[\leadsto \color{blue}{2 \cdot x} \]

5. Simplified 30.2%

   \[\leadsto \color{blue}{2 \cdot x} \]

6. Final simplification 30.2%

   \[\leadsto x \cdot 2 \]
7. 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 2024204 
(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)))