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

Percentage Accurate: 95.4% → 95.8%

Time: 21.5s

Alternatives: 15

Speedup: 1.1×

• 28.1% 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: 95.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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: 95.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return fma(y, Float64(Float64(z * -9.0) * t), fma(a, Float64(27.0 * b), Float64(x * 2.0)))
end

Wolfram

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

Derivation

1. Initial program 94.5%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. sub-neg N/A

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

   8. +-commutative N/A

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

   9. associate-+l+ N/A

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

   10. lift-*.f64 N/A

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

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

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

   12. lift-*.f64 N/A

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

   13. lift-*.f64 N/A

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

   14. associate-*l* N/A

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

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

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

   16. associate-*l* N/A

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

   17. +-commutative N/A

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

4. Applied egg-rr 95.0%

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

Alternative 2: 88.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ t_3 := \mathsf{fma}\left(t, -9 \cdot \left(y \cdot z\right), t\_1\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(z, y \cdot \left(-9 \cdot t\right), t\_1\right)\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-14}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 (* 27.0 (* a b)))
        (t_2 (* t (* z (* y 9.0))))
        (t_3 (fma t (* -9.0 (* y z)) t_1)))
   (if (<= t_2 (- INFINITY))
     (fma z (* y (* -9.0 t)) t_1)
     (if (<= t_2 -2e-14)
       t_3
       (if (<= t_2 5e+24) (fma (* 27.0 b) a (* x 2.0)) t_3)))))

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 = 27.0 * (a * b);
	double t_2 = t * (z * (y * 9.0));
	double t_3 = fma(t, (-9.0 * (y * z)), t_1);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(z, (y * (-9.0 * t)), t_1);
	} else if (t_2 <= -2e-14) {
		tmp = t_3;
	} else if (t_2 <= 5e+24) {
		tmp = fma((27.0 * b), a, (x * 2.0));
	} else {
		tmp = t_3;
	}
	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(27.0 * Float64(a * b))
	t_2 = Float64(t * Float64(z * Float64(y * 9.0)))
	t_3 = fma(t, Float64(-9.0 * Float64(y * z)), t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(z, Float64(y * Float64(-9.0 * t)), t_1);
	elseif (t_2 <= -2e-14)
		tmp = t_3;
	elseif (t_2 <= 5e+24)
		tmp = fma(Float64(27.0 * b), a, Float64(x * 2.0));
	else
		tmp = t_3;
	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[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(-9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[(y * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$2, -2e-14], t$95$3, If[LessEqual[t$95$2, 5e+24], N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 69.6%

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

   3. Taylor expanded in x around 0

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

      1. 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. lower-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. lower-*.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. lower-*.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. lower-*.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. lower-*.f64 74.1

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

   5. Simplified 74.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-*.f64 N/A

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

      19. lower-*.f64 90.8

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

   7. Applied egg-rr 90.8%

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

   if -inf.0 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -2e-14 or 5.00000000000000045e24 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 94.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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. lower-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. lower-*.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. lower-*.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. lower-*.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. lower-*.f64 89.5

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

   5. Simplified 89.5%

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

   if -2e-14 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5.00000000000000045e24

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 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. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 94.2

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

   5. Simplified 94.2%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 94.2

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

   7. Applied egg-rr 94.2%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(z, y \cdot \left(-9 \cdot t\right), 27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 5 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ t_2 := \mathsf{fma}\left(t, -9 \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* t (* z (* y 9.0))))
        (t_2 (fma t (* -9.0 (* y z)) (* 27.0 (* a b)))))
   (if (<= t_1 (- INFINITY))
     (* z (* -9.0 (* y t)))
     (if (<= t_1 -2e-14)
       t_2
       (if (<= t_1 5e+24) (fma (* 27.0 b) a (* 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 = t * (z * (y * 9.0));
	double t_2 = fma(t, (-9.0 * (y * z)), (27.0 * (a * b)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z * (-9.0 * (y * t));
	} else if (t_1 <= -2e-14) {
		tmp = t_2;
	} else if (t_1 <= 5e+24) {
		tmp = fma((27.0 * b), a, (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(t * Float64(z * Float64(y * 9.0)))
	t_2 = fma(t, Float64(-9.0 * Float64(y * z)), Float64(27.0 * Float64(a * b)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z * Float64(-9.0 * Float64(y * t)));
	elseif (t_1 <= -2e-14)
		tmp = t_2;
	elseif (t_1 <= 5e+24)
		tmp = fma(Float64(27.0 * b), a, Float64(x * 2.0));
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(t * N[(-9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-14], t$95$2, If[LessEqual[t$95$1, 5e+24], N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 69.6%

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

   3. Taylor expanded in y around inf

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

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

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

      7. lower-*.f64 74.1

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

   5. Simplified 74.1%

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

      1. lift-*.f64 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 95.2

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

   7. Applied egg-rr 95.2%

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

   if -inf.0 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -2e-14 or 5.00000000000000045e24 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 94.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   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. lower-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. lower-*.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. lower-*.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. lower-*.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. lower-*.f64 89.5

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

   5. Simplified 89.5%

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

   if -2e-14 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5.00000000000000045e24

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 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. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 94.2

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

   5. Simplified 94.2%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 94.2

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

   7. Applied egg-rr 94.2%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -\infty:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 5 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(y \cdot z\right), 27 \cdot \left(a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, z \cdot \left(y \cdot -9\right), 27 \cdot \left(a \cdot b\right)\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+293}:\\ \;\;\;\;y \cdot \left(\left(z \cdot -9\right) \cdot t\right)\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 t (* z (* y -9.0)) (* 27.0 (* a b))))
        (t_2 (* t (* z (* y 9.0)))))
   (if (<= t_2 -1e+293)
     (* y (* (* z -9.0) t))
     (if (<= t_2 -2e-14)
       t_1
       (if (<= t_2 5e+24) (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(t, (z * (y * -9.0)), (27.0 * (a * b)));
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -1e+293) {
		tmp = y * ((z * -9.0) * t);
	} else if (t_2 <= -2e-14) {
		tmp = t_1;
	} else if (t_2 <= 5e+24) {
		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(t, Float64(z * Float64(y * -9.0)), Float64(27.0 * Float64(a * b)))
	t_2 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_2 <= -1e+293)
		tmp = Float64(y * Float64(Float64(z * -9.0) * t));
	elseif (t_2 <= -2e-14)
		tmp = t_1;
	elseif (t_2 <= 5e+24)
		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[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+293], N[(y * N[(N[(z * -9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-14], t$95$1, If[LessEqual[t$95$2, 5e+24], N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -9.9999999999999992e292

   1. Initial program 72.1%

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

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

      7. lower-*.f64 76.3

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

   5. Simplified 76.3%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 92.1

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

   7. Applied egg-rr 92.1%

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

   if -9.9999999999999992e292 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -2e-14 or 5.00000000000000045e24 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 94.0%

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

   3. 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. lower-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. lower-*.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. lower-*.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. lower-*.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. lower-*.f64 89.3

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

   5. Simplified 89.3%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 89.3

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

   7. Applied egg-rr 89.3%

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

   if -2e-14 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5.00000000000000045e24

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 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. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 94.2

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

   5. Simplified 94.2%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 94.2

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

   7. Applied egg-rr 94.2%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -1 \cdot 10^{+293}:\\ \;\;\;\;y \cdot \left(\left(z \cdot -9\right) \cdot t\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(t, z \cdot \left(y \cdot -9\right), 27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 5 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, z \cdot \left(y \cdot -9\right), 27 \cdot \left(a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ t_2 := b \cdot \left(a \cdot 27\right)\\ t_3 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+28}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_2 \leq 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 (* y z))))
        (t_2 (* b (* a 27.0)))
        (t_3 (* a (* 27.0 b))))
   (if (<= t_2 -2e+28)
     t_3
     (if (<= t_2 -4e-50)
       t_1
       (if (<= t_2 0.0) (* x 2.0) (if (<= t_2 1e-16) t_1 t_3))))))

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 * (y * z));
	double t_2 = b * (a * 27.0);
	double t_3 = a * (27.0 * b);
	double tmp;
	if (t_2 <= -2e+28) {
		tmp = t_3;
	} else if (t_2 <= -4e-50) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = x * 2.0;
	} else if (t_2 <= 1e-16) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (-9.0d0) * (t * (y * z))
    t_2 = b * (a * 27.0d0)
    t_3 = a * (27.0d0 * b)
    if (t_2 <= (-2d+28)) then
        tmp = t_3
    else if (t_2 <= (-4d-50)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = x * 2.0d0
    else if (t_2 <= 1d-16) then
        tmp = t_1
    else
        tmp = t_3
    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 * (y * z));
	double t_2 = b * (a * 27.0);
	double t_3 = a * (27.0 * b);
	double tmp;
	if (t_2 <= -2e+28) {
		tmp = t_3;
	} else if (t_2 <= -4e-50) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = x * 2.0;
	} else if (t_2 <= 1e-16) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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 * (y * z))
	t_2 = b * (a * 27.0)
	t_3 = a * (27.0 * b)
	tmp = 0
	if t_2 <= -2e+28:
		tmp = t_3
	elif t_2 <= -4e-50:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = x * 2.0
	elif t_2 <= 1e-16:
		tmp = t_1
	else:
		tmp = t_3
	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(y * z)))
	t_2 = Float64(b * Float64(a * 27.0))
	t_3 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (t_2 <= -2e+28)
		tmp = t_3;
	elseif (t_2 <= -4e-50)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(x * 2.0);
	elseif (t_2 <= 1e-16)
		tmp = t_1;
	else
		tmp = t_3;
	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 * (y * z));
	t_2 = b * (a * 27.0);
	t_3 = a * (27.0 * b);
	tmp = 0.0;
	if (t_2 <= -2e+28)
		tmp = t_3;
	elseif (t_2 <= -4e-50)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = x * 2.0;
	elseif (t_2 <= 1e-16)
		tmp = t_1;
	else
		tmp = t_3;
	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[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+28], t$95$3, If[LessEqual[t$95$2, -4e-50], t$95$1, If[LessEqual[t$95$2, 0.0], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$2, 1e-16], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.99999999999999992e28 or 9.9999999999999998e-17 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 93.5%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 71.2

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

   5. Simplified 71.2%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 71.2

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

   7. Applied egg-rr 71.2%

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

   if -1.99999999999999992e28 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.00000000000000003e-50 or 0.0 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.9999999999999998e-17

   1. Initial program 94.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

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

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

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

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

      16. associate-*l* N/A

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

      17. +-commutative N/A

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

   4. Applied egg-rr 95.4%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.1

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

   7. Simplified 59.1%

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

   if -4.00000000000000003e-50 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 0.0

   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 x around inf

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

      1. lower-*.f64 52.8

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

   5. Simplified 52.8%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -2 \cdot 10^{+28}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq -4 \cdot 10^{-50}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 0:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 10^{-16}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := y \cdot \left(\left(z \cdot -9\right) \cdot t\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-261}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_2 \leq 10^{+146}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* y (* (* z -9.0) t))) (t_2 (* t (* z (* y 9.0)))))
   (if (<= t_2 -1e-25)
     t_1
     (if (<= t_2 -5e-261)
       (* x 2.0)
       (if (<= t_2 1e+146) (* 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 = y * ((z * -9.0) * t);
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -1e-25) {
		tmp = t_1;
	} else if (t_2 <= -5e-261) {
		tmp = x * 2.0;
	} else if (t_2 <= 1e+146) {
		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 = y * ((z * (-9.0d0)) * t)
    t_2 = t * (z * (y * 9.0d0))
    if (t_2 <= (-1d-25)) then
        tmp = t_1
    else if (t_2 <= (-5d-261)) then
        tmp = x * 2.0d0
    else if (t_2 <= 1d+146) 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 = y * ((z * -9.0) * t);
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -1e-25) {
		tmp = t_1;
	} else if (t_2 <= -5e-261) {
		tmp = x * 2.0;
	} else if (t_2 <= 1e+146) {
		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 = y * ((z * -9.0) * t)
	t_2 = t * (z * (y * 9.0))
	tmp = 0
	if t_2 <= -1e-25:
		tmp = t_1
	elif t_2 <= -5e-261:
		tmp = x * 2.0
	elif t_2 <= 1e+146:
		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(y * Float64(Float64(z * -9.0) * t))
	t_2 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_2 <= -1e-25)
		tmp = t_1;
	elseif (t_2 <= -5e-261)
		tmp = Float64(x * 2.0);
	elseif (t_2 <= 1e+146)
		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 = y * ((z * -9.0) * t);
	t_2 = t * (z * (y * 9.0));
	tmp = 0.0;
	if (t_2 <= -1e-25)
		tmp = t_1;
	elseif (t_2 <= -5e-261)
		tmp = x * 2.0;
	elseif (t_2 <= 1e+146)
		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[(y * N[(N[(z * -9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-25], t$95$1, If[LessEqual[t$95$2, -5e-261], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$2, 1e+146], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.00000000000000004e-25 or 9.99999999999999934e145 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 89.1%

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

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

      7. lower-*.f64 66.0

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

   5. Simplified 66.0%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 65.3

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

   7. Applied egg-rr 65.3%

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

   if -1.00000000000000004e-25 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999981e-261

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 66.7

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

   5. Simplified 66.7%

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

   if -4.99999999999999981e-261 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 9.99999999999999934e145

   1. Initial program 98.9%

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

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

      2. lower-*.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-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.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 3 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -1 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \left(\left(z \cdot -9\right) \cdot t\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -5 \cdot 10^{-261}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 10^{+146}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(z \cdot -9\right) \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z \cdot \left(-9 \cdot t\right), y, 27 \cdot \left(a \cdot b\right)\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* z (* -9.0 t)) y (* 27.0 (* a b))))
        (t_2 (* t (* z (* y 9.0)))))
   (if (<= t_2 -2e-14)
     t_1
     (if (<= t_2 5e+24) (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((z * (-9.0 * t)), y, (27.0 * (a * b)));
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -2e-14) {
		tmp = t_1;
	} else if (t_2 <= 5e+24) {
		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(Float64(z * Float64(-9.0 * t)), y, Float64(27.0 * Float64(a * b)))
	t_2 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_2 <= -2e-14)
		tmp = t_1;
	elseif (t_2 <= 5e+24)
		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[(N[(z * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision] * y + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-14], t$95$1, If[LessEqual[t$95$2, 5e+24], 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) < -2e-14 or 5.00000000000000045e24 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 89.8%

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

   3. Taylor expanded in x around 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. lower-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. lower-*.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. lower-*.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. lower-*.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. lower-*.f64 86.8

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

   5. Simplified 86.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 83.0

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. associate-*l* N/A

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

      17. lower-*.f64 N/A

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

      18. lower-*.f64 83.0

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

   7. Applied egg-rr 83.0%

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

   if -2e-14 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5.00000000000000045e24

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 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. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 94.2

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

   5. Simplified 94.2%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 94.2

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

   7. Applied egg-rr 94.2%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(-9 \cdot t\right), y, 27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 5 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(-9 \cdot t\right), y, 27 \cdot \left(a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := y \cdot \left(\left(z \cdot -9\right) \cdot t\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* y (* (* z -9.0) t))) (t_2 (* t (* z (* y 9.0)))))
   (if (<= t_2 -2e+120)
     t_1
     (if (<= t_2 1e+163) (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 = y * ((z * -9.0) * t);
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -2e+120) {
		tmp = t_1;
	} else if (t_2 <= 1e+163) {
		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 = Float64(y * Float64(Float64(z * -9.0) * t))
	t_2 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_2 <= -2e+120)
		tmp = t_1;
	elseif (t_2 <= 1e+163)
		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[(y * N[(N[(z * -9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+120], t$95$1, If[LessEqual[t$95$2, 1e+163], 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) < -2e120 or 9.9999999999999994e162 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 85.7%

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

   3. Taylor expanded in y around 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. lower-*.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. lower-*.f64 N/A

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

      7. lower-*.f64 75.1

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

   5. Simplified 75.1%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 73.1

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

   7. Applied egg-rr 73.1%

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

   if -2e120 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 9.9999999999999994e162

   1. Initial program 99.2%

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

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 85.8

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

   5. Simplified 85.8%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 85.8

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

   7. Applied egg-rr 85.8%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{+120}:\\ \;\;\;\;y \cdot \left(\left(z \cdot -9\right) \cdot t\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(z \cdot -9\right) \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := y \cdot \left(\left(z \cdot -9\right) \cdot t\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* y (* (* z -9.0) t))) (t_2 (* t (* z (* y 9.0)))))
   (if (<= t_2 -2e+120)
     t_1
     (if (<= t_2 1e+163) (fma 27.0 (* a b) (* 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 = y * ((z * -9.0) * t);
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -2e+120) {
		tmp = t_1;
	} else if (t_2 <= 1e+163) {
		tmp = fma(27.0, (a * b), (x * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(Float64(z * -9.0) * t))
	t_2 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_2 <= -2e+120)
		tmp = t_1;
	elseif (t_2 <= 1e+163)
		tmp = fma(27.0, Float64(a * b), 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[(y * N[(N[(z * -9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+120], t$95$1, If[LessEqual[t$95$2, 1e+163], N[(27.0 * N[(a * b), $MachinePrecision] + 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) < -2e120 or 9.9999999999999994e162 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 85.7%

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

   3. Taylor expanded in y around 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. lower-*.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. lower-*.f64 N/A

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

      7. lower-*.f64 75.1

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

   5. Simplified 75.1%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 73.1

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

   7. Applied egg-rr 73.1%

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

   if -2e120 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 9.9999999999999994e162

   1. Initial program 99.2%

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

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 85.8

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

   5. Simplified 85.8%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -2 \cdot 10^{+120}:\\ \;\;\;\;y \cdot \left(\left(z \cdot -9\right) \cdot t\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(z \cdot -9\right) \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(z \cdot -9\right) \cdot t, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (fma (* 27.0 b) a (* x 2.0))))
   (if (<= t_1 -2e+28)
     t_2
     (if (<= t_1 1e-16) (fma y (* (* z -9.0) t) (* 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 = fma((27.0 * b), a, (x * 2.0));
	double tmp;
	if (t_1 <= -2e+28) {
		tmp = t_2;
	} else if (t_1 <= 1e-16) {
		tmp = fma(y, ((z * -9.0) * t), (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 = fma(Float64(27.0 * b), a, Float64(x * 2.0))
	tmp = 0.0
	if (t_1 <= -2e+28)
		tmp = t_2;
	elseif (t_1 <= 1e-16)
		tmp = fma(y, Float64(Float64(z * -9.0) * t), Float64(x * 2.0));
	else
		tmp = t_2;
	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[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+28], t$95$2, If[LessEqual[t$95$1, 1e-16], N[(y * N[(N[(z * -9.0), $MachinePrecision] * t), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.99999999999999992e28 or 9.9999999999999998e-17 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 93.5%

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

   3. Taylor expanded in y around 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. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 82.7

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

   5. Simplified 82.7%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 82.7

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

   7. Applied egg-rr 82.7%

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

   if -1.99999999999999992e28 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.9999999999999998e-17

   1. Initial program 95.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. associate-+l+ N/A

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

      10. lift-*.f64 N/A

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

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

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. associate-*l* N/A

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

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

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

      16. associate-*l* N/A

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

      17. +-commutative N/A

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

   4. Applied egg-rr 96.9%

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

   5. Taylor expanded in a around 0

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

      1. lower-*.f64 89.1

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

   7. Simplified 89.1%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -2 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(z \cdot -9\right) \cdot t, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := \mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(y \cdot z\right), x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (fma (* 27.0 b) a (* x 2.0))))
   (if (<= t_1 -2e+28)
     t_2
     (if (<= t_1 1e-16) (fma t (* -9.0 (* y z)) (* 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 = fma((27.0 * b), a, (x * 2.0));
	double tmp;
	if (t_1 <= -2e+28) {
		tmp = t_2;
	} else if (t_1 <= 1e-16) {
		tmp = fma(t, (-9.0 * (y * z)), (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 = fma(Float64(27.0 * b), a, Float64(x * 2.0))
	tmp = 0.0
	if (t_1 <= -2e+28)
		tmp = t_2;
	elseif (t_1 <= 1e-16)
		tmp = fma(t, Float64(-9.0 * Float64(y * z)), Float64(x * 2.0));
	else
		tmp = t_2;
	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[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * b), $MachinePrecision] * a + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+28], t$95$2, If[LessEqual[t$95$1, 1e-16], N[(t * N[(-9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.99999999999999992e28 or 9.9999999999999998e-17 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 93.5%

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

   3. Taylor expanded in y around 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. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 82.7

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

   5. Simplified 82.7%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 82.7

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

   7. Applied egg-rr 82.7%

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

   if -1.99999999999999992e28 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.9999999999999998e-17

   1. Initial program 95.5%

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

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 87.7

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

   5. Simplified 87.7%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -2 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(y \cdot z\right), x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot b, a, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-16}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* a (* 27.0 b))))
   (if (<= t_1 -2e+28) t_2 (if (<= t_1 1e-16) (* t (* -9.0 (* y z))) 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 = a * (27.0 * b);
	double tmp;
	if (t_1 <= -2e+28) {
		tmp = t_2;
	} else if (t_1 <= 1e-16) {
		tmp = t * (-9.0 * (y * z));
	} 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 = a * (27.0d0 * b)
    if (t_1 <= (-2d+28)) then
        tmp = t_2
    else if (t_1 <= 1d-16) then
        tmp = t * ((-9.0d0) * (y * z))
    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 = a * (27.0 * b);
	double tmp;
	if (t_1 <= -2e+28) {
		tmp = t_2;
	} else if (t_1 <= 1e-16) {
		tmp = t * (-9.0 * (y * z));
	} 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 = a * (27.0 * b)
	tmp = 0
	if t_1 <= -2e+28:
		tmp = t_2
	elif t_1 <= 1e-16:
		tmp = t * (-9.0 * (y * z))
	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(a * Float64(27.0 * b))
	tmp = 0.0
	if (t_1 <= -2e+28)
		tmp = t_2;
	elseif (t_1 <= 1e-16)
		tmp = Float64(t * Float64(-9.0 * Float64(y * z)));
	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 = a * (27.0 * b);
	tmp = 0.0;
	if (t_1 <= -2e+28)
		tmp = t_2;
	elseif (t_1 <= 1e-16)
		tmp = t * (-9.0 * (y * z));
	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[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+28], t$95$2, If[LessEqual[t$95$1, 1e-16], N[(t * N[(-9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.99999999999999992e28 or 9.9999999999999998e-17 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 93.5%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 71.2

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

   5. Simplified 71.2%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 71.2

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

   7. Applied egg-rr 71.2%

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

   if -1.99999999999999992e28 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.9999999999999998e-17

   1. Initial program 95.5%

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

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

      7. lower-*.f64 49.9

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

   5. Simplified 49.9%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -2 \cdot 10^{+28}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 10^{-16}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-44}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* a (* 27.0 b))))
   (if (<= t_1 -1e-30) t_2 (if (<= t_1 1e-44) (* 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 = a * (27.0 * b);
	double tmp;
	if (t_1 <= -1e-30) {
		tmp = t_2;
	} else if (t_1 <= 1e-44) {
		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 = a * (27.0d0 * b)
    if (t_1 <= (-1d-30)) then
        tmp = t_2
    else if (t_1 <= 1d-44) 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 = a * (27.0 * b);
	double tmp;
	if (t_1 <= -1e-30) {
		tmp = t_2;
	} else if (t_1 <= 1e-44) {
		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 = a * (27.0 * b)
	tmp = 0
	if t_1 <= -1e-30:
		tmp = t_2
	elif t_1 <= 1e-44:
		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(a * Float64(27.0 * b))
	tmp = 0.0
	if (t_1 <= -1e-30)
		tmp = t_2;
	elseif (t_1 <= 1e-44)
		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 = a * (27.0 * b);
	tmp = 0.0;
	if (t_1 <= -1e-30)
		tmp = t_2;
	elseif (t_1 <= 1e-44)
		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[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-30], t$95$2, If[LessEqual[t$95$1, 1e-44], 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) < -1e-30 or 9.99999999999999953e-45 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   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. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 65.2

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

   5. Simplified 65.2%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 65.2

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

   7. Applied egg-rr 65.2%

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

   if -1e-30 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.99999999999999953e-45

   1. Initial program 96.6%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 42.6

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

   5. Simplified 42.6%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -1 \cdot 10^{-30}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 10^{-44}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+67}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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-30) t_2 (if (<= t_1 5e+67) (* 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-30) {
		tmp = t_2;
	} else if (t_1 <= 5e+67) {
		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-30)) then
        tmp = t_2
    else if (t_1 <= 5d+67) 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-30) {
		tmp = t_2;
	} else if (t_1 <= 5e+67) {
		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-30:
		tmp = t_2
	elif t_1 <= 5e+67:
		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-30)
		tmp = t_2;
	elseif (t_1 <= 5e+67)
		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-30)
		tmp = t_2;
	elseif (t_1 <= 5e+67)
		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-30], t$95$2, If[LessEqual[t$95$1, 5e+67], 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) < -1e-30 or 4.99999999999999976e67 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 91.4%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 72.7

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

   5. Simplified 72.7%

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

   if -1e-30 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 4.99999999999999976e67

   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 x around inf

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

      1. lower-*.f64 40.4

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

   5. Simplified 40.4%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -1 \cdot 10^{-30}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 5 \cdot 10^{+67}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.7% 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 94.5%

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

3. Taylor expanded in x around inf

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

   1. lower-*.f64 26.6

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

5. Simplified 26.6%

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

6. Final simplification 26.6%

   \[\leadsto x \cdot 2 \]
7. Add Preprocessing

Developer Target 1: 95.1% 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 2024207 
(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)))