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

Percentage Accurate: 95.5% → 98.2%

Time: 23.4s

Alternatives: 10

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -2 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - \left(y \cdot 9\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + \left(z \cdot -9\right) \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

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) -2e+74)
   (fma (* a 27.0) b (- (* x 2.0) (* (* y 9.0) (* t z))))
   (+ (* x 2.0) (+ (* a (* 27.0 b)) (* (* z -9.0) (* y t))))))

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) <= -2e+74) {
		tmp = fma((a * 27.0), b, ((x * 2.0) - ((y * 9.0) * (t * z))));
	} else {
		tmp = (x * 2.0) + ((a * (27.0 * b)) + ((z * -9.0) * (y * t)));
	}
	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(y * 9.0) <= -2e+74)
		tmp = fma(Float64(a * 27.0), b, Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(t * z))));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(z * -9.0) * Float64(y * t))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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[(y * 9.0), $MachinePrecision], -2e+74], N[(N[(a * 27.0), $MachinePrecision] * b + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(z * -9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y #s(literal 9 binary64)) < -1.9999999999999999e74

   1. Initial program 85.0%

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

      1. associate-*r* N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. fma-define N/A

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

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

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

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

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

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

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

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

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

      9. associate-*l* N/A

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

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

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

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

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 97.9%

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

   4. Applied egg-rr 97.9%

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

   if -1.9999999999999999e74 < (*.f64 y #s(literal 9 binary64))

   1. Initial program 98.0%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 95.6%

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

   3. Simplified 95.6%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-lowering-*.f64 96.9%

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

   6. Applied egg-rr 96.9%

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

Alternative 2: 54.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+82}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-282}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+129}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= t_1 -4e+82)
     (* 27.0 (* a b))
     (if (<= t_1 -5e-282)
       (* (* t z) (* y -9.0))
       (if (<= t_1 4e-148)
         (* x 2.0)
         (if (<= t_1 2e+129) (* -9.0 (* y (* t z))) (* a (* 27.0 b))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -4e+82) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= -5e-282) {
		tmp = (t * z) * (y * -9.0);
	} else if (t_1 <= 4e-148) {
		tmp = x * 2.0;
	} else if (t_1 <= 2e+129) {
		tmp = -9.0 * (y * (t * z));
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    if (t_1 <= (-4d+82)) then
        tmp = 27.0d0 * (a * b)
    else if (t_1 <= (-5d-282)) then
        tmp = (t * z) * (y * (-9.0d0))
    else if (t_1 <= 4d-148) then
        tmp = x * 2.0d0
    else if (t_1 <= 2d+129) then
        tmp = (-9.0d0) * (y * (t * z))
    else
        tmp = a * (27.0d0 * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -4e+82) {
		tmp = 27.0 * (a * b);
	} else if (t_1 <= -5e-282) {
		tmp = (t * z) * (y * -9.0);
	} else if (t_1 <= 4e-148) {
		tmp = x * 2.0;
	} else if (t_1 <= 2e+129) {
		tmp = -9.0 * (y * (t * z));
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -4e+82:
		tmp = 27.0 * (a * b)
	elif t_1 <= -5e-282:
		tmp = (t * z) * (y * -9.0)
	elif t_1 <= 4e-148:
		tmp = x * 2.0
	elif t_1 <= 2e+129:
		tmp = -9.0 * (y * (t * z))
	else:
		tmp = a * (27.0 * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -4e+82)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t_1 <= -5e-282)
		tmp = Float64(Float64(t * z) * Float64(y * -9.0));
	elseif (t_1 <= 4e-148)
		tmp = Float64(x * 2.0);
	elseif (t_1 <= 2e+129)
		tmp = Float64(-9.0 * Float64(y * Float64(t * z)));
	else
		tmp = Float64(a * Float64(27.0 * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -4e+82)
		tmp = 27.0 * (a * b);
	elseif (t_1 <= -5e-282)
		tmp = (t * z) * (y * -9.0);
	elseif (t_1 <= 4e-148)
		tmp = x * 2.0;
	elseif (t_1 <= 2e+129)
		tmp = -9.0 * (y * (t * z));
	else
		tmp = a * (27.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+82], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-282], N[(N[(t * z), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-148], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+129], N[(-9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -3.9999999999999999e82

   1. Initial program 96.2%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 76.7%

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

   7. Simplified 76.7%

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

   if -3.9999999999999999e82 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -5.0000000000000001e-282

   1. Initial program 96.8%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in y around inf

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

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 53.2%

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

   7. Simplified 53.2%

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

      1. associate-*r* N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 53.4%

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

   9. Applied egg-rr 53.4%

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

   if -5.0000000000000001e-282 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 3.99999999999999974e-148

   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. Step-by-step derivation

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 65.7%

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

   7. Simplified 65.7%

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

   if 3.99999999999999974e-148 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2e129

   1. Initial program 95.5%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf

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

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 51.7%

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

   7. Simplified 51.7%

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

   if 2e129 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 88.0%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 90.8%

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

   7. Simplified 90.8%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-lowering-*.f64 90.8%

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

   9. Applied egg-rr 90.8%

      \[\leadsto \color{blue}{\left(27 \cdot b\right) \cdot a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -4 \cdot 10^{+82}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq -5 \cdot 10^{-282}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 4 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+129}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ t_2 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+82}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* y (* t z)))) (t_2 (* (* a 27.0) b)))
   (if (<= t_2 -4e+82)
     (* 27.0 (* a b))
     (if (<= t_2 -5e-282)
       t_1
       (if (<= t_2 4e-148)
         (* x 2.0)
         (if (<= t_2 2e+129) t_1 (* a (* 27.0 b))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (t * z));
	double t_2 = (a * 27.0) * b;
	double tmp;
	if (t_2 <= -4e+82) {
		tmp = 27.0 * (a * b);
	} else if (t_2 <= -5e-282) {
		tmp = t_1;
	} else if (t_2 <= 4e-148) {
		tmp = x * 2.0;
	} else if (t_2 <= 2e+129) {
		tmp = t_1;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-9.0d0) * (y * (t * z))
    t_2 = (a * 27.0d0) * b
    if (t_2 <= (-4d+82)) then
        tmp = 27.0d0 * (a * b)
    else if (t_2 <= (-5d-282)) then
        tmp = t_1
    else if (t_2 <= 4d-148) then
        tmp = x * 2.0d0
    else if (t_2 <= 2d+129) then
        tmp = t_1
    else
        tmp = a * (27.0d0 * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (t * z));
	double t_2 = (a * 27.0) * b;
	double tmp;
	if (t_2 <= -4e+82) {
		tmp = 27.0 * (a * b);
	} else if (t_2 <= -5e-282) {
		tmp = t_1;
	} else if (t_2 <= 4e-148) {
		tmp = x * 2.0;
	} else if (t_2 <= 2e+129) {
		tmp = t_1;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (y * (t * z))
	t_2 = (a * 27.0) * b
	tmp = 0
	if t_2 <= -4e+82:
		tmp = 27.0 * (a * b)
	elif t_2 <= -5e-282:
		tmp = t_1
	elif t_2 <= 4e-148:
		tmp = x * 2.0
	elif t_2 <= 2e+129:
		tmp = t_1
	else:
		tmp = a * (27.0 * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(y * Float64(t * z)))
	t_2 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_2 <= -4e+82)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (t_2 <= -5e-282)
		tmp = t_1;
	elseif (t_2 <= 4e-148)
		tmp = Float64(x * 2.0);
	elseif (t_2 <= 2e+129)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(27.0 * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (y * (t * z));
	t_2 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_2 <= -4e+82)
		tmp = 27.0 * (a * b);
	elseif (t_2 <= -5e-282)
		tmp = t_1;
	elseif (t_2 <= 4e-148)
		tmp = x * 2.0;
	elseif (t_2 <= 2e+129)
		tmp = t_1;
	else
		tmp = a * (27.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+82], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-282], t$95$1, If[LessEqual[t$95$2, 4e-148], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$2, 2e+129], t$95$1, N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -3.9999999999999999e82

   1. Initial program 96.2%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 76.7%

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

   7. Simplified 76.7%

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

   if -3.9999999999999999e82 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -5.0000000000000001e-282 or 3.99999999999999974e-148 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2e129

   1. Initial program 96.3%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in y around inf

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

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 52.6%

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

   7. Simplified 52.6%

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

   if -5.0000000000000001e-282 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 3.99999999999999974e-148

   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. Step-by-step derivation

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 65.7%

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

   7. Simplified 65.7%

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

   if 2e129 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 88.0%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 90.8%

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

   7. Simplified 90.8%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-lowering-*.f64 90.8%

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

   9. Applied egg-rr 90.8%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -4 \cdot 10^{+82}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq -5 \cdot 10^{-282}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 4 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 2 \cdot 10^{+129}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ t_2 := \left(a \cdot 27\right) \cdot b\\ t_3 := t\_2 + t\_1\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+81}:\\ \;\;\;\;x \cdot 2 + t\_2\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-76}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-18}:\\ \;\;\;\;x \cdot 2 + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* y (* t z)))) (t_2 (* (* a 27.0) b)) (t_3 (+ t_2 t_1)))
   (if (<= t_2 -1e+81)
     (+ (* x 2.0) t_2)
     (if (<= t_2 -1e-76) t_3 (if (<= t_2 5e-18) (+ (* x 2.0) t_1) t_3)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (t * z));
	double t_2 = (a * 27.0) * b;
	double t_3 = t_2 + t_1;
	double tmp;
	if (t_2 <= -1e+81) {
		tmp = (x * 2.0) + t_2;
	} else if (t_2 <= -1e-76) {
		tmp = t_3;
	} else if (t_2 <= 5e-18) {
		tmp = (x * 2.0) + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (-9.0d0) * (y * (t * z))
    t_2 = (a * 27.0d0) * b
    t_3 = t_2 + t_1
    if (t_2 <= (-1d+81)) then
        tmp = (x * 2.0d0) + t_2
    else if (t_2 <= (-1d-76)) then
        tmp = t_3
    else if (t_2 <= 5d-18) then
        tmp = (x * 2.0d0) + t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (t * z));
	double t_2 = (a * 27.0) * b;
	double t_3 = t_2 + t_1;
	double tmp;
	if (t_2 <= -1e+81) {
		tmp = (x * 2.0) + t_2;
	} else if (t_2 <= -1e-76) {
		tmp = t_3;
	} else if (t_2 <= 5e-18) {
		tmp = (x * 2.0) + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (y * (t * z))
	t_2 = (a * 27.0) * b
	t_3 = t_2 + t_1
	tmp = 0
	if t_2 <= -1e+81:
		tmp = (x * 2.0) + t_2
	elif t_2 <= -1e-76:
		tmp = t_3
	elif t_2 <= 5e-18:
		tmp = (x * 2.0) + t_1
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(y * Float64(t * z)))
	t_2 = Float64(Float64(a * 27.0) * b)
	t_3 = Float64(t_2 + t_1)
	tmp = 0.0
	if (t_2 <= -1e+81)
		tmp = Float64(Float64(x * 2.0) + t_2);
	elseif (t_2 <= -1e-76)
		tmp = t_3;
	elseif (t_2 <= 5e-18)
		tmp = Float64(Float64(x * 2.0) + t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (y * (t * z));
	t_2 = (a * 27.0) * b;
	t_3 = t_2 + t_1;
	tmp = 0.0;
	if (t_2 <= -1e+81)
		tmp = (x * 2.0) + t_2;
	elseif (t_2 <= -1e-76)
		tmp = t_3;
	elseif (t_2 <= 5e-18)
		tmp = (x * 2.0) + t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+81], N[(N[(x * 2.0), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[t$95$2, -1e-76], t$95$3, If[LessEqual[t$95$2, 5e-18], N[(N[(x * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -9.99999999999999921e80

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(2 \cdot x\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 90.6%

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

   5. Simplified 90.6%

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

   if -9.99999999999999921e80 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -9.99999999999999927e-77 or 5.00000000000000036e-18 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 93.9%

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

   3. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 85.4%

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

   5. Simplified 85.4%

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

   if -9.99999999999999927e-77 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 5.00000000000000036e-18

   1. Initial program 96.2%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in a around 0

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

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 93.5%

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

   7. Simplified 93.5%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -1 \cdot 10^{+81}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq -1 \cdot 10^{-76}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + -9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 5 \cdot 10^{-18}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + -9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := x \cdot 2 + t\_1\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+134}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)) (t_2 (+ (* x 2.0) t_1)))
   (if (<= t_1 -4e+82)
     t_2
     (if (<= t_1 1e+134) (+ (* x 2.0) (* -9.0 (* y (* t z)))) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = (x * 2.0) + t_1;
	double tmp;
	if (t_1 <= -4e+82) {
		tmp = t_2;
	} else if (t_1 <= 1e+134) {
		tmp = (x * 2.0) + (-9.0 * (y * (t * z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    t_2 = (x * 2.0d0) + t_1
    if (t_1 <= (-4d+82)) then
        tmp = t_2
    else if (t_1 <= 1d+134) then
        tmp = (x * 2.0d0) + ((-9.0d0) * (y * (t * z)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = (x * 2.0) + t_1;
	double tmp;
	if (t_1 <= -4e+82) {
		tmp = t_2;
	} else if (t_1 <= 1e+134) {
		tmp = (x * 2.0) + (-9.0 * (y * (t * z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	t_2 = (x * 2.0) + t_1
	tmp = 0
	if t_1 <= -4e+82:
		tmp = t_2
	elif t_1 <= 1e+134:
		tmp = (x * 2.0) + (-9.0 * (y * (t * z)))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	t_2 = Float64(Float64(x * 2.0) + t_1)
	tmp = 0.0
	if (t_1 <= -4e+82)
		tmp = t_2;
	elseif (t_1 <= 1e+134)
		tmp = Float64(Float64(x * 2.0) + Float64(-9.0 * Float64(y * Float64(t * z))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	t_2 = (x * 2.0) + t_1;
	tmp = 0.0;
	if (t_1 <= -4e+82)
		tmp = t_2;
	elseif (t_1 <= 1e+134)
		tmp = (x * 2.0) + (-9.0 * (y * (t * z)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+82], t$95$2, If[LessEqual[t$95$1, 1e+134], N[(N[(x * 2.0), $MachinePrecision] + N[(-9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -3.9999999999999999e82 or 9.99999999999999921e133 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 92.5%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(2 \cdot x\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 92.5%

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

   5. Simplified 92.5%

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

   if -3.9999999999999999e82 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.99999999999999921e133

   1. Initial program 97.0%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in a around 0

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

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 82.6%

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

   7. Simplified 82.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -4 \cdot 10^{+82}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 10^{+134}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot 27\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-18}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)) (t_2 (* a (* 27.0 b))))
   (if (<= t_1 -1e-85) t_2 (if (<= t_1 5e-18) (* x 2.0) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = a * (27.0 * b);
	double tmp;
	if (t_1 <= -1e-85) {
		tmp = t_2;
	} else if (t_1 <= 5e-18) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    t_2 = a * (27.0d0 * b)
    if (t_1 <= (-1d-85)) then
        tmp = t_2
    else if (t_1 <= 5d-18) then
        tmp = x * 2.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = a * (27.0 * b);
	double tmp;
	if (t_1 <= -1e-85) {
		tmp = t_2;
	} else if (t_1 <= 5e-18) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	t_2 = a * (27.0 * b)
	tmp = 0
	if t_1 <= -1e-85:
		tmp = t_2
	elif t_1 <= 5e-18:
		tmp = x * 2.0
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	t_2 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (t_1 <= -1e-85)
		tmp = t_2;
	elseif (t_1 <= 5e-18)
		tmp = Float64(x * 2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	t_2 = a * (27.0 * b);
	tmp = 0.0;
	if (t_1 <= -1e-85)
		tmp = t_2;
	elseif (t_1 <= 5e-18)
		tmp = x * 2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-85], t$95$2, If[LessEqual[t$95$1, 5e-18], N[(x * 2.0), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -9.9999999999999998e-86 or 5.00000000000000036e-18 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 94.8%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 63.1%

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

   7. Simplified 63.1%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-lowering-*.f64 63.1%

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

   9. Applied egg-rr 63.1%

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

   if -9.9999999999999998e-86 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 5.00000000000000036e-18

   1. Initial program 96.1%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 52.4%

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

   7. Simplified 52.4%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot 27\right) \cdot b \leq -1 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(a \cdot 27\right) \cdot b \leq 5 \cdot 10^{-18}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2800:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+34}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(y \cdot -9\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2800.0)
   (* (* z -9.0) (* y t))
   (if (<= z 6e+34) (+ (* x 2.0) (* (* a 27.0) b)) (* (* t z) (* y -9.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2800.0) {
		tmp = (z * -9.0) * (y * t);
	} else if (z <= 6e+34) {
		tmp = (x * 2.0) + ((a * 27.0) * b);
	} else {
		tmp = (t * z) * (y * -9.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2800.0d0)) then
        tmp = (z * (-9.0d0)) * (y * t)
    else if (z <= 6d+34) then
        tmp = (x * 2.0d0) + ((a * 27.0d0) * b)
    else
        tmp = (t * z) * (y * (-9.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2800.0) {
		tmp = (z * -9.0) * (y * t);
	} else if (z <= 6e+34) {
		tmp = (x * 2.0) + ((a * 27.0) * b);
	} else {
		tmp = (t * z) * (y * -9.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2800.0:
		tmp = (z * -9.0) * (y * t)
	elif z <= 6e+34:
		tmp = (x * 2.0) + ((a * 27.0) * b)
	else:
		tmp = (t * z) * (y * -9.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2800.0)
		tmp = Float64(Float64(z * -9.0) * Float64(y * t));
	elseif (z <= 6e+34)
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(a * 27.0) * b));
	else
		tmp = Float64(Float64(t * z) * Float64(y * -9.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2800.0)
		tmp = (z * -9.0) * (y * t);
	elseif (z <= 6e+34)
		tmp = (x * 2.0) + ((a * 27.0) * b);
	else
		tmp = (t * z) * (y * -9.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2800.0], N[(N[(z * -9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+34], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(t * z), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2800

   1. Initial program 88.6%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in y around inf

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

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 51.4%

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

   7. Simplified 51.4%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

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

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

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

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

      7. *-lowering-*.f64 54.3%

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

   9. Applied egg-rr 54.3%

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

   if -2800 < z < 6.00000000000000037e34

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(2 \cdot x\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, 27\right), b\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 82.1%

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

   5. Simplified 82.1%

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

   if 6.00000000000000037e34 < z

   1. Initial program 91.4%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

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

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

      7. associate-*l* N/A

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

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

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

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

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

      10. associate-*l* N/A

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

      11. associate-*l* N/A

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

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

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

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

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

      14. associate-*r* N/A

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

      15. *-commutative N/A

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

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

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

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

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

      18. *-commutative N/A

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

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

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

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

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

      21. metadata-eval 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in y around inf

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

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

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 48.6%

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

   7. Simplified 48.6%

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

      1. associate-*r* N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. *-lowering-*.f64 48.6%

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

   9. Applied egg-rr 48.6%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2800:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+34}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(y \cdot -9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * 2.0d0) + ((a * (27.0d0 * b)) + (y * (t * (z * (-9.0d0)))))
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (x * 2.0) + ((a * (27.0 * b)) + (y * (t * (z * -9.0))));
end

Wolfram

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

Derivation

1. Initial program 95.3%

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

   1. sub-neg N/A

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

   2. associate-+l+ N/A

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

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

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

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

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

   5. +-commutative N/A

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

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

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

   7. associate-*l* N/A

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

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

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

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

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

   10. associate-*l* N/A

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

   11. associate-*l* N/A

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

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

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

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

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

   14. associate-*r* N/A

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

   15. *-commutative N/A

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

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

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

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

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

   18. *-commutative N/A

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

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

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

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

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

   21. metadata-eval 95.6%

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

3. Simplified 95.6%

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

Alternative 9: 48.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-145}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= a -5.6e+38) t_1 (if (<= a 4.2e-145) (* x 2.0) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (a <= -5.6e+38) {
		tmp = t_1;
	} else if (a <= 4.2e-145) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (a <= (-5.6d+38)) then
        tmp = t_1
    else if (a <= 4.2d-145) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (a <= -5.6e+38) {
		tmp = t_1;
	} else if (a <= 4.2e-145) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if a <= -5.6e+38:
		tmp = t_1
	elif a <= 4.2e-145:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (a <= -5.6e+38)
		tmp = t_1;
	elseif (a <= 4.2e-145)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (a <= -5.6e+38)
		tmp = t_1;
	elseif (a <= 4.2e-145)
		tmp = x * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+38], t$95$1, If[LessEqual[a, 4.2e-145], N[(x * 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.6e38 or 4.19999999999999982e-145 < a

   1. Initial program 93.7%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

         \[\leadsto x \cdot 2 + \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(\left(a \cdot 27\right) \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(a \cdot \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot \color{blue}{t}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(9 \cdot z\right) \cdot t\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(t \cdot \left(9 \cdot z\right)\right)\right)\right)\right)\right) \]

      16. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval 95.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, -9\right)\right)\right)\right)\right) \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(27, \color{blue}{\left(a \cdot b\right)}\right) \]

      2. *-lowering-*.f64 56.2%

         \[\leadsto \mathsf{*.f64}\left(27, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   7. Simplified 56.2%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if -5.6e38 < a < 4.19999999999999982e-145

   1. Initial program 98.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto x \cdot 2 + \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(\left(a \cdot 27\right) \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(a \cdot \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot \color{blue}{t}\right)\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(9 \cdot z\right) \cdot t\right)\right)\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(t \cdot \left(9 \cdot z\right)\right)\right)\right)\right)\right) \]

      16. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right)\right)\right)\right) \]

      19. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      20. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

      21. metadata-eval 96.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, -9\right)\right)\right)\right)\right) \]

   3. Simplified 96.0%

      \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 43.7%

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{x}\right) \]

   7. Simplified 43.7%

      \[\leadsto \color{blue}{2 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+38}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-145}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.3% accurate, 5.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ x \cdot 2 \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* x 2.0))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * 2.0d0
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return x * 2.0

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(x * 2.0)
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = x * 2.0;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(x * 2.0), $MachinePrecision]

Derivation

1. Initial program 95.3%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto \left(x \cdot 2 + \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

   2. associate-+l+ N/A

      \[\leadsto x \cdot 2 + \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)} \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot 2\right), \color{blue}{\left(\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)}\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right)\right) \]

   5. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \left(\left(a \cdot 27\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

   6. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(\left(a \cdot 27\right) \cdot b\right), \color{blue}{\left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)}\right)\right) \]

   7. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\left(a \cdot \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(27 \cdot b\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right)\right)\right)\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot \color{blue}{t}\right)\right)\right)\right) \]

   10. associate-*l* N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)\right)\right) \]

   11. associate-*l* N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(\mathsf{neg}\left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\right)\right)\right) \]

   12. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \left(y \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

   13. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\mathsf{neg}\left(9 \cdot \left(z \cdot t\right)\right)\right)}\right)\right)\right) \]

   14. associate-*r* N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(\left(9 \cdot z\right) \cdot t\right)\right)\right)\right)\right) \]

   15. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(t \cdot \left(9 \cdot z\right)\right)\right)\right)\right)\right) \]

   16. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

   17. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(9 \cdot z\right)\right)}\right)\right)\right)\right) \]

   18. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(z \cdot 9\right)\right)\right)\right)\right)\right) \]

   19. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

   20. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\left(\mathsf{neg}\left(9\right)\right)}\right)\right)\right)\right)\right) \]

   21. metadata-eval 95.6%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, 2\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(27, b\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, -9\right)\right)\right)\right)\right) \]

3. Simplified 95.6%

   \[\leadsto \color{blue}{x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{2 \cdot x} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 28.7%

      \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{x}\right) \]

7. Simplified 28.7%

   \[\leadsto \color{blue}{2 \cdot x} \]

8. Final simplification 28.7%

   \[\leadsto x \cdot 2 \]
9. Add Preprocessing

Developer Target 1: 95.1% accurate, 0.8× 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 2024138 
(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)))