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

Percentage Accurate: 95.5% → 97.5%

Time: 17.2s

Alternatives: 15

Speedup: 0.9×

• 27.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+228}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot t, -9, \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, \left(-9 \cdot \left(z \cdot t\right)\right) \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (* y 9.0) z) 5e+228)
   (fma (* (* y z) t) -9.0 (fma a (* 27.0 b) (* x 2.0)))
   (fma (* a 27.0) b (* (* -9.0 (* z t)) y))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * 9.0) * z) <= 5e+228) {
		tmp = fma(((y * z) * t), -9.0, fma(a, (27.0 * b), (x * 2.0)));
	} else {
		tmp = fma((a * 27.0), b, ((-9.0 * (z * t)) * y));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 5e+228)
		tmp = fma(Float64(Float64(y * z) * t), -9.0, fma(a, Float64(27.0 * b), Float64(x * 2.0)));
	else
		tmp = fma(Float64(a * 27.0), b, Float64(Float64(-9.0 * Float64(z * t)) * y));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 5e+228], N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * -9.0 + N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 27.0), $MachinePrecision] * b + N[(N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 5e228

   1. Initial program 97.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 94.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 97.8

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 97.8

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

      14. lift-fma.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 97.8

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

      17. lift-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 97.8

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 97.8

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

   6. Applied rewrites 97.8%

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

   if 5e228 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 99.7

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

   5. Applied rewrites 99.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.7

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

   7. Applied rewrites 99.9%

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

Alternative 2: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+50}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot y\right) \cdot -9\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot y\right) \cdot z, t, 2 \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -2e+50)
     (* (* (* t z) y) -9.0)
     (if (<= t_1 2e+26)
       (fma 2.0 x (* (* b a) 27.0))
       (fma (* (* -9.0 y) z) t (* 2.0 x))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -2e+50) {
		tmp = ((t * z) * y) * -9.0;
	} else if (t_1 <= 2e+26) {
		tmp = fma(2.0, x, ((b * a) * 27.0));
	} else {
		tmp = fma(((-9.0 * y) * z), t, (2.0 * x));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -2e+50)
		tmp = Float64(Float64(Float64(t * z) * y) * -9.0);
	elseif (t_1 <= 2e+26)
		tmp = fma(2.0, x, Float64(Float64(b * a) * 27.0));
	else
		tmp = fma(Float64(Float64(-9.0 * y) * z), t, Float64(2.0 * x));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+50], N[(N[(N[(t * z), $MachinePrecision] * y), $MachinePrecision] * -9.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+26], N[(2.0 * x + N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -2.0000000000000002e50

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 20.6

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

   5. Applied rewrites 20.6%

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

   7. Applied rewrites 19.0%

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

   8. Taylor expanded in a around 0

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

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 81.7

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

   10. Applied rewrites 81.7%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 66.2%

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

   if -2.0000000000000002e50 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.0000000000000001e26

   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. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 91.0

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

   5. Applied rewrites 91.0%

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

   if 2.0000000000000001e26 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   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 y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 30.2

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

   5. Applied rewrites 30.2%

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

   7. Applied rewrites 30.2%

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

   8. Taylor expanded in a around 0

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

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 82.0

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

   10. Applied rewrites 82.0%

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

Alternative 3: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+111} \lor \neg \left(t\_1 \leq 10^{-19}\right):\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, \left(-9 \cdot \left(z \cdot t\right)\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot y\right) \cdot z, t, 2 \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (or (<= t_1 -2e+111) (not (<= t_1 1e-19)))
     (fma (* a 27.0) b (* (* -9.0 (* z t)) y))
     (fma (* (* -9.0 y) z) t (* 2.0 x)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if ((t_1 <= -2e+111) || !(t_1 <= 1e-19)) {
		tmp = fma((a * 27.0), b, ((-9.0 * (z * t)) * y));
	} else {
		tmp = fma(((-9.0 * y) * z), t, (2.0 * x));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if ((t_1 <= -2e+111) || !(t_1 <= 1e-19))
		tmp = fma(Float64(a * 27.0), b, Float64(Float64(-9.0 * Float64(z * t)) * y));
	else
		tmp = fma(Float64(Float64(-9.0 * y) * z), t, Float64(2.0 * x));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+111], N[Not[LessEqual[t$95$1, 1e-19]], $MachinePrecision]], N[(N[(a * 27.0), $MachinePrecision] * b + N[(N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.99999999999999991e111 or 9.9999999999999998e-20 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 97.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 92.8

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

   5. Applied rewrites 92.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 93.7

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

   7. Applied rewrites 91.2%

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

   if -1.99999999999999991e111 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.9999999999999998e-20

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.4

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

   5. Applied rewrites 54.4%

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

   7. Applied rewrites 54.4%

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

   8. Taylor expanded in a around 0

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

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 92.3

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

   10. Applied rewrites 92.3%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{+111} \lor \neg \left(\left(a \cdot 27\right) \cdot b \leq 10^{-19}\right):\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, \left(-9 \cdot \left(z \cdot t\right)\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot y\right) \cdot z, t, 2 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+111} \lor \neg \left(t\_1 \leq 10^{-19}\right):\\ \;\;\;\;\mathsf{fma}\left(z, y \cdot \left(-9 \cdot t\right), \left(27 \cdot a\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot y\right) \cdot z, t, 2 \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (or (<= t_1 -2e+111) (not (<= t_1 1e-19)))
     (fma z (* y (* -9.0 t)) (* (* 27.0 a) b))
     (fma (* (* -9.0 y) z) t (* 2.0 x)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if ((t_1 <= -2e+111) || !(t_1 <= 1e-19)) {
		tmp = fma(z, (y * (-9.0 * t)), ((27.0 * a) * b));
	} else {
		tmp = fma(((-9.0 * y) * z), t, (2.0 * x));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if ((t_1 <= -2e+111) || !(t_1 <= 1e-19))
		tmp = fma(z, Float64(y * Float64(-9.0 * t)), Float64(Float64(27.0 * a) * b));
	else
		tmp = fma(Float64(Float64(-9.0 * y) * z), t, Float64(2.0 * x));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+111], N[Not[LessEqual[t$95$1, 1e-19]], $MachinePrecision]], N[(z * N[(y * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision] + N[(N[(27.0 * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.99999999999999991e111 or 9.9999999999999998e-20 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 97.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 91.0

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

   7. Applied rewrites 91.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 88.4

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

   9. Applied rewrites 88.5%

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

   if -1.99999999999999991e111 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.9999999999999998e-20

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.4

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

   5. Applied rewrites 54.4%

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

   7. Applied rewrites 54.4%

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

   8. Taylor expanded in a around 0

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

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 92.3

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

   10. Applied rewrites 92.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{+111} \lor \neg \left(\left(a \cdot 27\right) \cdot b \leq 10^{-19}\right):\\ \;\;\;\;\mathsf{fma}\left(z, y \cdot \left(-9 \cdot t\right), \left(27 \cdot a\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot y\right) \cdot z, t, 2 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+111} \lor \neg \left(t\_1 \leq 10^{-19}\right):\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot y\right) \cdot t, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot y\right) \cdot z, t, 2 \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (or (<= t_1 -2e+111) (not (<= t_1 1e-19)))
     (fma -9.0 (* (* z y) t) (* (* b a) 27.0))
     (fma (* (* -9.0 y) z) t (* 2.0 x)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if ((t_1 <= -2e+111) || !(t_1 <= 1e-19)) {
		tmp = fma(-9.0, ((z * y) * t), ((b * a) * 27.0));
	} else {
		tmp = fma(((-9.0 * y) * z), t, (2.0 * x));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if ((t_1 <= -2e+111) || !(t_1 <= 1e-19))
		tmp = fma(-9.0, Float64(Float64(z * y) * t), Float64(Float64(b * a) * 27.0));
	else
		tmp = fma(Float64(Float64(-9.0 * y) * z), t, Float64(2.0 * x));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+111], N[Not[LessEqual[t$95$1, 1e-19]], $MachinePrecision]], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] + N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.99999999999999991e111 or 9.9999999999999998e-20 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 97.9%

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

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

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 93.6

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

   5. Applied rewrites 93.6%

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

   if -1.99999999999999991e111 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.9999999999999998e-20

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.4

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

   5. Applied rewrites 54.4%

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

   7. Applied rewrites 54.4%

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

   8. Taylor expanded in a around 0

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

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 92.3

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

   10. Applied rewrites 92.3%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -2 \cdot 10^{+111} \lor \neg \left(\left(a \cdot 27\right) \cdot b \leq 10^{-19}\right):\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot y\right) \cdot t, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot y\right) \cdot z, t, 2 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(z \cdot y\right) \cdot t, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(\left(-9 \cdot y\right) \cdot z, t, 2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, \left(\left(y \cdot z\right) \cdot t\right) \cdot -9\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= t_1 -2e+111)
     (fma -9.0 (* (* z y) t) (* (* b a) 27.0))
     (if (<= t_1 1e-19)
       (fma (* (* -9.0 y) z) t (* 2.0 x))
       (fma (* a b) 27.0 (* (* (* y z) t) -9.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -2e+111) {
		tmp = fma(-9.0, ((z * y) * t), ((b * a) * 27.0));
	} else if (t_1 <= 1e-19) {
		tmp = fma(((-9.0 * y) * z), t, (2.0 * x));
	} else {
		tmp = fma((a * b), 27.0, (((y * z) * t) * -9.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -2e+111)
		tmp = fma(-9.0, Float64(Float64(z * y) * t), Float64(Float64(b * a) * 27.0));
	elseif (t_1 <= 1e-19)
		tmp = fma(Float64(Float64(-9.0 * y) * z), t, Float64(2.0 * x));
	else
		tmp = fma(Float64(a * b), 27.0, Float64(Float64(Float64(y * z) * t) * -9.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+111], N[(-9.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] + N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-19], N[(N[(N[(-9.0 * y), $MachinePrecision] * z), $MachinePrecision] * t + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * 27.0 + N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 97.6%

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

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 96.2

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

   5. Applied rewrites 96.2%

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

   if -1.99999999999999991e111 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.9999999999999998e-20

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.4

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

   5. Applied rewrites 54.4%

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

   7. Applied rewrites 54.4%

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

   8. Taylor expanded in a around 0

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

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 92.3

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

   10. Applied rewrites 92.3%

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

   if 9.9999999999999998e-20 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 98.2%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 74.6

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

   5. Applied rewrites 74.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   7. 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

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 91.9

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

   8. Applied rewrites 91.9%

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

Alternative 7: 82.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+50}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot y\right) \cdot -9\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+187}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(b \cdot a\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -2e+50)
     (* (* (* t z) y) -9.0)
     (if (<= t_1 5e+187)
       (fma 2.0 x (* (* b a) 27.0))
       (* (* (* t z) -9.0) y)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -2e+50) {
		tmp = ((t * z) * y) * -9.0;
	} else if (t_1 <= 5e+187) {
		tmp = fma(2.0, x, ((b * a) * 27.0));
	} else {
		tmp = ((t * z) * -9.0) * y;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -2e+50)
		tmp = Float64(Float64(Float64(t * z) * y) * -9.0);
	elseif (t_1 <= 5e+187)
		tmp = fma(2.0, x, Float64(Float64(b * a) * 27.0));
	else
		tmp = Float64(Float64(Float64(t * z) * -9.0) * y);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+50], N[(N[(N[(t * z), $MachinePrecision] * y), $MachinePrecision] * -9.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+187], N[(2.0 * x + N[(N[(b * a), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -2.0000000000000002e50

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 20.6

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

   5. Applied rewrites 20.6%

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

   7. Applied rewrites 19.0%

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

   8. Taylor expanded in a around 0

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

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 81.7

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

   10. Applied rewrites 81.7%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 66.2%

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

   if -2.0000000000000002e50 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5.0000000000000001e187

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 86.6

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

   5. Applied rewrites 86.6%

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

   if 5.0000000000000001e187 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 91.5%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 17.1

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

   5. Applied rewrites 17.1%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(t \cdot z\right)\right)} \]
   7. Step-by-step derivation

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 94.2%

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

   9. Taylor expanded in y around inf

      \[\leadsto \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 88.9%

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

Alternative 8: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+50}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot y\right) \cdot -9\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+187}:\\ \;\;\;\;\mathsf{fma}\left(2, x, \left(a \cdot 27\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot z\right) \cdot -9\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -2e+50)
     (* (* (* t z) y) -9.0)
     (if (<= t_1 5e+187)
       (fma 2.0 x (* (* a 27.0) b))
       (* (* (* t z) -9.0) y)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -2e+50) {
		tmp = ((t * z) * y) * -9.0;
	} else if (t_1 <= 5e+187) {
		tmp = fma(2.0, x, ((a * 27.0) * b));
	} else {
		tmp = ((t * z) * -9.0) * y;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -2e+50)
		tmp = Float64(Float64(Float64(t * z) * y) * -9.0);
	elseif (t_1 <= 5e+187)
		tmp = fma(2.0, x, Float64(Float64(a * 27.0) * b));
	else
		tmp = Float64(Float64(Float64(t * z) * -9.0) * y);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+50], N[(N[(N[(t * z), $MachinePrecision] * y), $MachinePrecision] * -9.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+187], N[(2.0 * x + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -2.0000000000000002e50

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 20.6

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

   5. Applied rewrites 20.6%

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

   7. Applied rewrites 19.0%

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

   8. Taylor expanded in a around 0

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

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 81.7

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

   10. Applied rewrites 81.7%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 66.2%

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

   if -2.0000000000000002e50 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 5.0000000000000001e187

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 86.6

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

   5. Applied rewrites 86.6%

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

   7. Applied rewrites 86.6%

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

   if 5.0000000000000001e187 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 91.5%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 17.1

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

   5. Applied rewrites 17.1%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(t \cdot z\right)\right)} \]
   7. Step-by-step derivation

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 94.2%

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

   9. Taylor expanded in y around inf

      \[\leadsto \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 88.9%

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

Alternative 9: 55.9% accurate, 0.6× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (or (<= t_1 -5e+27) (not (<= t_1 1e-27)))
     (* (* (* t z) y) -9.0)
     (* 2.0 x))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if ((t_1 <= -5e+27) || !(t_1 <= 1e-27)) {
		tmp = ((t * z) * y) * -9.0;
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y * 9.0d0) * z) * t
    if ((t_1 <= (-5d+27)) .or. (.not. (t_1 <= 1d-27))) then
        tmp = ((t * z) * y) * (-9.0d0)
    else
        tmp = 2.0d0 * x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if ((t_1 <= -5e+27) || !(t_1 <= 1e-27)) {
		tmp = ((t * z) * y) * -9.0;
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = ((y * 9.0) * z) * t
	tmp = 0
	if (t_1 <= -5e+27) or not (t_1 <= 1e-27):
		tmp = ((t * z) * y) * -9.0
	else:
		tmp = 2.0 * x
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if ((t_1 <= -5e+27) || !(t_1 <= 1e-27))
		tmp = Float64(Float64(Float64(t * z) * y) * -9.0);
	else
		tmp = Float64(2.0 * x);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * 9.0) * z) * t;
	tmp = 0.0;
	if ((t_1 <= -5e+27) || ~((t_1 <= 1e-27)))
		tmp = ((t * z) * y) * -9.0;
	else
		tmp = 2.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+27], N[Not[LessEqual[t$95$1, 1e-27]], $MachinePrecision]], N[(N[(N[(t * z), $MachinePrecision] * y), $MachinePrecision] * -9.0), $MachinePrecision], N[(2.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999979e27 or 1e-27 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 95.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 30.1

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

   5. Applied rewrites 30.1%

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

   7. Applied rewrites 29.3%

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

   8. Taylor expanded in a around 0

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

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 77.4

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

   10. Applied rewrites 77.4%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 65.8%

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

   if -4.99999999999999979e27 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1e-27

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 99.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 99.1

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 99.1

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

      14. lift-fma.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 99.1

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

      17. lift-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 99.1

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 99.1

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

   6. Applied rewrites 99.1%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 55.0

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

   9. Applied rewrites 55.0%

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

4. Final simplification 60.3%

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

Alternative 10: 55.9% accurate, 0.6× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -5e+27)
     (* (* (* t z) y) -9.0)
     (if (<= t_1 1e-27) (* 2.0 x) (* (* (* t z) -9.0) y)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -5e+27) {
		tmp = ((t * z) * y) * -9.0;
	} else if (t_1 <= 1e-27) {
		tmp = 2.0 * x;
	} else {
		tmp = ((t * z) * -9.0) * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y * 9.0d0) * z) * t
    if (t_1 <= (-5d+27)) then
        tmp = ((t * z) * y) * (-9.0d0)
    else if (t_1 <= 1d-27) then
        tmp = 2.0d0 * x
    else
        tmp = ((t * z) * (-9.0d0)) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -5e+27) {
		tmp = ((t * z) * y) * -9.0;
	} else if (t_1 <= 1e-27) {
		tmp = 2.0 * x;
	} else {
		tmp = ((t * z) * -9.0) * y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = ((y * 9.0) * z) * t
	tmp = 0
	if t_1 <= -5e+27:
		tmp = ((t * z) * y) * -9.0
	elif t_1 <= 1e-27:
		tmp = 2.0 * x
	else:
		tmp = ((t * z) * -9.0) * y
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -5e+27)
		tmp = Float64(Float64(Float64(t * z) * y) * -9.0);
	elseif (t_1 <= 1e-27)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(Float64(Float64(t * z) * -9.0) * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * 9.0) * z) * t;
	tmp = 0.0;
	if (t_1 <= -5e+27)
		tmp = ((t * z) * y) * -9.0;
	elseif (t_1 <= 1e-27)
		tmp = 2.0 * x;
	else
		tmp = ((t * z) * -9.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+27], N[(N[(N[(t * z), $MachinePrecision] * y), $MachinePrecision] * -9.0), $MachinePrecision], If[LessEqual[t$95$1, 1e-27], N[(2.0 * x), $MachinePrecision], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999979e27

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 27.6

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

   5. Applied rewrites 27.6%

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

   7. Applied rewrites 26.2%

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

   8. Taylor expanded in a around 0

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

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 76.2

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

   10. Applied rewrites 76.2%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 60.9%

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

   if -4.99999999999999979e27 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1e-27

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 99.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 99.1

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 99.1

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

      14. lift-fma.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 99.1

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

      17. lift-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 99.1

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 99.1

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

   6. Applied rewrites 99.1%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 55.0

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

   9. Applied rewrites 55.0%

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

   if 1e-27 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 32.9

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

   5. Applied rewrites 32.9%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(t \cdot z\right)\right)} \]
   7. Step-by-step derivation

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   8. Applied rewrites 96.4%

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

   9. Taylor expanded in y around inf

      \[\leadsto \left(-9 \cdot \left(t \cdot z\right)\right) \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 71.4%

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

Alternative 11: 55.0% accurate, 0.6× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* (* y 9.0) z) t)))
   (if (<= t_1 -5e+27)
     (* (* (* t z) y) -9.0)
     (if (<= t_1 1e-27) (* 2.0 x) (* (* (* y t) -9.0) z)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -5e+27) {
		tmp = ((t * z) * y) * -9.0;
	} else if (t_1 <= 1e-27) {
		tmp = 2.0 * x;
	} else {
		tmp = ((y * t) * -9.0) * z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y * 9.0d0) * z) * t
    if (t_1 <= (-5d+27)) then
        tmp = ((t * z) * y) * (-9.0d0)
    else if (t_1 <= 1d-27) then
        tmp = 2.0d0 * x
    else
        tmp = ((y * t) * (-9.0d0)) * z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_1 <= -5e+27) {
		tmp = ((t * z) * y) * -9.0;
	} else if (t_1 <= 1e-27) {
		tmp = 2.0 * x;
	} else {
		tmp = ((y * t) * -9.0) * z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = ((y * 9.0) * z) * t
	tmp = 0
	if t_1 <= -5e+27:
		tmp = ((t * z) * y) * -9.0
	elif t_1 <= 1e-27:
		tmp = 2.0 * x
	else:
		tmp = ((y * t) * -9.0) * z
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_1 <= -5e+27)
		tmp = Float64(Float64(Float64(t * z) * y) * -9.0);
	elseif (t_1 <= 1e-27)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(Float64(Float64(y * t) * -9.0) * z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * 9.0) * z) * t;
	tmp = 0.0;
	if (t_1 <= -5e+27)
		tmp = ((t * z) * y) * -9.0;
	elseif (t_1 <= 1e-27)
		tmp = 2.0 * x;
	else
		tmp = ((y * t) * -9.0) * z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+27], N[(N[(N[(t * z), $MachinePrecision] * y), $MachinePrecision] * -9.0), $MachinePrecision], If[LessEqual[t$95$1, 1e-27], N[(2.0 * x), $MachinePrecision], N[(N[(N[(y * t), $MachinePrecision] * -9.0), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999979e27

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 27.6

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

   5. Applied rewrites 27.6%

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

   7. Applied rewrites 26.2%

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

   8. Taylor expanded in a around 0

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

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 76.2

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

   10. Applied rewrites 76.2%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 60.9%

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

   if -4.99999999999999979e27 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 1e-27

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 99.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 99.1

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 99.1

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

      14. lift-fma.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 99.1

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

      17. lift-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 99.1

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 99.1

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

   6. Applied rewrites 99.1%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 55.0

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

   9. Applied rewrites 55.0%

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

   if 1e-27 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 94.9%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot \frac{2 \cdot x + 27 \cdot \left(a \cdot b\right)}{z} - -9 \cdot \left(t \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \left(-1 \cdot \frac{2 \cdot x + 27 \cdot \left(a \cdot b\right)}{z} - -9 \cdot \left(t \cdot y\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(-1 \cdot \frac{2 \cdot x + 27 \cdot \left(a \cdot b\right)}{z} - -9 \cdot \left(t \cdot y\right)\right) \cdot z}\right) \]

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

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \frac{2 \cdot x + 27 \cdot \left(a \cdot b\right)}{z} - -9 \cdot \left(t \cdot y\right)\right)\right)\right) \cdot z} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot \frac{2 \cdot x + 27 \cdot \left(a \cdot b\right)}{z} - -9 \cdot \left(t \cdot y\right)\right)\right)\right) \cdot z} \]

   5. Applied rewrites 83.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 66.8%

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

Alternative 12: 92.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -2 \cdot 10^{+50}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, \left(-9 \cdot \left(z \cdot t\right)\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(t \cdot y\right) \cdot z, \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (* (* y 9.0) z) t) -2e+50)
   (fma (* a 27.0) b (* (* -9.0 (* z t)) y))
   (fma -9.0 (* (* t y) z) (fma (* b 27.0) a (* 2.0 x)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((((y * 9.0) * z) * t) <= -2e+50) {
		tmp = fma((a * 27.0), b, ((-9.0 * (z * t)) * y));
	} else {
		tmp = fma(-9.0, ((t * y) * z), fma((b * 27.0), a, (2.0 * x)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(Float64(y * 9.0) * z) * t) <= -2e+50)
		tmp = fma(Float64(a * 27.0), b, Float64(Float64(-9.0 * Float64(z * t)) * y));
	else
		tmp = fma(-9.0, Float64(Float64(t * y) * z), fma(Float64(b * 27.0), a, Float64(2.0 * x)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision], -2e+50], N[(N[(a * 27.0), $MachinePrecision] * b + N[(N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -2.0000000000000002e50

   1. Initial program 96.4%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 94.1

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

   5. Applied rewrites 94.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 94.1

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

   7. Applied rewrites 79.4%

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

   if -2.0000000000000002e50 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 97.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

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

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. metadata-eval N/A

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

      16. *-commutative N/A

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

      17. associate-*r* N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. lower-*.f64 N/A

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

   4. Applied rewrites 95.4%

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

Alternative 13: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\\ \mathbf{if}\;y \cdot 9 \leq -1 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, -9 \cdot y, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(t \cdot y\right) \cdot z, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (* b 27.0) a (* 2.0 x))))
   (if (<= (* y 9.0) -1e+28)
     (fma (* t z) (* -9.0 y) t_1)
     (fma -9.0 (* (* t y) z) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b * 27.0), a, (2.0 * x));
	double tmp;
	if ((y * 9.0) <= -1e+28) {
		tmp = fma((t * z), (-9.0 * y), t_1);
	} else {
		tmp = fma(-9.0, ((t * y) * z), t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(Float64(b * 27.0), a, Float64(2.0 * x))
	tmp = 0.0
	if (Float64(y * 9.0) <= -1e+28)
		tmp = fma(Float64(t * z), Float64(-9.0 * y), t_1);
	else
		tmp = fma(-9.0, Float64(Float64(t * y) * z), t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * 9.0), $MachinePrecision], -1e+28], N[(N[(t * z), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(-9.0 * N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y #s(literal 9 binary64)) < -9.99999999999999958e27

   1. Initial program 95.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

   4. Applied rewrites 99.8%

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

   if -9.99999999999999958e27 < (*.f64 y #s(literal 9 binary64))

   1. Initial program 98.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

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

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. metadata-eval N/A

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

      16. *-commutative N/A

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

      17. associate-*r* N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. lower-*.f64 N/A

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

   4. Applied rewrites 96.3%

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

Alternative 14: 98.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b \cdot 27, a, 2 \cdot x\right)\\ \mathbf{if}\;z \leq 3.5 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-9 \cdot z\right) \cdot t, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(t \cdot y\right) \cdot z, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (* b 27.0) a (* 2.0 x))))
   (if (<= z 3.5e-9)
     (fma y (* (* -9.0 z) t) t_1)
     (fma -9.0 (* (* t y) z) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b * 27.0), a, (2.0 * x));
	double tmp;
	if (z <= 3.5e-9) {
		tmp = fma(y, ((-9.0 * z) * t), t_1);
	} else {
		tmp = fma(-9.0, ((t * y) * z), t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(Float64(b * 27.0), a, Float64(2.0 * x))
	tmp = 0.0
	if (z <= 3.5e-9)
		tmp = fma(y, Float64(Float64(-9.0 * z) * t), t_1);
	else
		tmp = fma(-9.0, Float64(Float64(t * y) * z), t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * 27.0), $MachinePrecision] * a + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 3.5e-9], N[(y * N[(N[(-9.0 * z), $MachinePrecision] * t), $MachinePrecision] + t$95$1), $MachinePrecision], N[(-9.0 * N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 3.4999999999999999e-9

   1. Initial program 97.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

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

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

      12. associate-*l* N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

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

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

      17. lower-*.f64 N/A

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

      18. metadata-eval N/A

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

   4. Applied rewrites 96.9%

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

   if 3.4999999999999999e-9 < z

   1. Initial program 96.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

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

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. metadata-eval N/A

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

      16. *-commutative N/A

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

      17. associate-*r* N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. lower-*.f64 N/A

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

   4. Applied rewrites 99.7%

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

Alternative 15: 31.0% accurate, 6.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ 2 \cdot x \end{array} \]

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 = 2.0d0 * x
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return 2.0 * x;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return 2.0 * x

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = 2.0 * x;
end

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. sub-neg N/A

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

   4. +-commutative N/A

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

   5. associate-+l+ N/A

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

   6. lift-*.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. associate-*l* N/A

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

   9. *-commutative N/A

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

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

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

   11. +-commutative N/A

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

   12. lower-fma.f64 N/A

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

   13. *-commutative N/A

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

   14. lower-*.f64 N/A

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

   15. lift-*.f64 N/A

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

   16. *-commutative N/A

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

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

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

   18. lower-*.f64 N/A

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

   19. metadata-eval N/A

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

4. Applied rewrites 95.0%

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

   1. lift-fma.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. associate-*r* N/A

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

   5. lift-*.f64 N/A

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

   6. associate-*r* N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lift-*.f64 N/A

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

   10. lower-fma.f64 97.9

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

   11. lift-*.f64 N/A

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

   12. *-commutative N/A

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

   13. lower-*.f64 97.9

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

   14. lift-fma.f64 N/A

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

   15. *-commutative N/A

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

   16. lower-fma.f64 97.9

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

   17. lift-*.f64 N/A

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

   18. *-commutative N/A

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

   19. lower-*.f64 97.9

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

   20. lift-*.f64 N/A

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

   21. *-commutative N/A

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

   22. lower-*.f64 97.9

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

6. Applied rewrites 97.9%

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

7. Taylor expanded in x around inf

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

   1. lower-*.f64 31.6

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

9. Applied rewrites 31.6%

   \[\leadsto \color{blue}{2 \cdot x} \]
10. Add Preprocessing

Developer Target 1: 95.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (< y 7.590524218811189e-161)
   (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y < 7.590524218811189d-161) then
        tmp = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + (a * (27.0d0 * b))
    else
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (t * z)))) + ((a * 27.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y < 7.590524218811189e-161:
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b))
	else:
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y < 7.590524218811189e-161)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(t * z)))) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y < 7.590524218811189e-161)
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	else
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Less[y, 7.590524218811189e-161], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024318 
(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)))