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

Percentage Accurate: 95.4% → 98.9%

Time: 18.2s

Alternatives: 20

Speedup: 0.8×

• 26.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1e-116)
   (fma a (* 27.0 b) (fma x 2.0 (* y (* z (* t -9.0)))))
   (fma a (* 27.0 b) (fma x 2.0 (* t (* y (* z -9.0)))))))

C

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 <= 1e-116) {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (y * (z * (t * -9.0)))));
	} else {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (t * (y * (z * -9.0)))));
	}
	return tmp;
}

Julia

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 <= 1e-116)
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(y * Float64(z * Float64(t * -9.0)))));
	else
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(t * Float64(y * Float64(z * -9.0)))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1e-116], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 9.9999999999999999e-117

   1. Initial program 95.6%

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

      1. +-commutative 95.6%

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

      2. associate-+r- 95.6%

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

      3. *-commutative 95.6%

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

      4. cancel-sign-sub-inv 95.6%

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

      5. associate-*r* 92.5%

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

      6. distribute-lft-neg-in 92.5%

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

      7. *-commutative 92.5%

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

      8. cancel-sign-sub-inv 92.5%

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

      9. associate-+r- 92.5%

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

      10. associate-*l* 92.5%

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

      11. fma-define 93.8%

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

      12. fma-neg 93.8%

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

      13. associate-*l* 95.0%

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

      14. distribute-rgt-neg-in 95.0%

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

      15. *-commutative 95.0%

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

      16. associate-*l* 95.0%

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

      17. *-commutative 95.0%

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

      18. distribute-lft-neg-in 95.0%

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

      19. associate-*r* 95.0%

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

   3. Simplified 95.0%

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

   if 9.9999999999999999e-117 < z

   1. Initial program 91.9%

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

      1. +-commutative 91.9%

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

      2. associate-+r- 91.9%

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

      3. *-commutative 91.9%

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

      4. cancel-sign-sub-inv 91.9%

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

      5. associate-*r* 95.8%

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

      6. distribute-lft-neg-in 95.8%

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

      7. *-commutative 95.8%

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

      8. cancel-sign-sub-inv 95.8%

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

      9. associate-+r- 95.8%

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

      10. associate-*l* 96.7%

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

      11. fma-define 98.8%

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

      12. cancel-sign-sub-inv 98.8%

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

      13. fma-define 98.8%

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

      14. distribute-lft-neg-in 98.8%

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

      15. distribute-rgt-neg-in 98.8%

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

      16. *-commutative 98.8%

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

      17. associate-*r* 94.9%

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

      18. associate-*l* 94.9%

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

      19. neg-mul-1 94.9%

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

      20. associate-*r* 94.9%

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

   3. Simplified 94.9%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 5 \cdot 10^{-192}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 5e-192)
   (+ (- (* x 2.0) (* 9.0 (* z (* y t)))) (* a (* 27.0 b)))
   (fma a (* 27.0 b) (fma x 2.0 (* t (* y (* z -9.0)))))))

C

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 (t <= 5e-192) {
		tmp = ((x * 2.0) - (9.0 * (z * (y * t)))) + (a * (27.0 * b));
	} else {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (t * (y * (z * -9.0)))));
	}
	return tmp;
}

Julia

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 (t <= 5e-192)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(z * Float64(y * t)))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(t * Float64(y * Float64(z * -9.0)))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 5e-192], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.0000000000000001e-192

   1. Initial program 91.3%

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

      1. sub-neg 91.3%

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

      2. sub-neg 91.3%

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

      3. associate-*l* 90.6%

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

      4. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in y around 0 92.0%

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

      1. associate-*r* 96.4%

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

   7. Simplified 96.4%

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

   if 5.0000000000000001e-192 < t

   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. +-commutative 98.0%

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

      2. associate-+r- 98.0%

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

      3. *-commutative 98.0%

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

      4. cancel-sign-sub-inv 98.0%

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

      5. associate-*r* 91.0%

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

      6. distribute-lft-neg-in 91.0%

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

      7. *-commutative 91.0%

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

      8. cancel-sign-sub-inv 91.0%

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

      9. associate-+r- 91.0%

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

      10. associate-*l* 91.0%

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

      11. fma-define 92.8%

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

      12. cancel-sign-sub-inv 92.8%

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

      13. fma-define 92.8%

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

      14. distribute-lft-neg-in 92.8%

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

      15. distribute-rgt-neg-in 92.8%

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

      16. *-commutative 92.8%

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

      17. associate-*r* 99.9%

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

      18. associate-*l* 99.8%

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

      19. neg-mul-1 99.8%

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

      20. associate-*r* 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5 \cdot 10^{-192}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+110}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-140}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-157}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-11} \lor \neg \left(x \leq 9.4 \cdot 10^{+36}\right) \land x \leq 3.4 \cdot 10^{+105}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2e+110)
   (* x 2.0)
   (if (<= x -6.6e-59)
     (* b (* a 27.0))
     (if (<= x -1.05e-140)
       (* -9.0 (* z (* y t)))
       (if (<= x -3.2e-157)
         (* 27.0 (* a b))
         (if (or (<= x 1.55e-11) (and (not (<= x 9.4e+36)) (<= x 3.4e+105)))
           (* -9.0 (* t (* z y)))
           (* x 2.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2e+110) {
		tmp = x * 2.0;
	} else if (x <= -6.6e-59) {
		tmp = b * (a * 27.0);
	} else if (x <= -1.05e-140) {
		tmp = -9.0 * (z * (y * t));
	} else if (x <= -3.2e-157) {
		tmp = 27.0 * (a * b);
	} else if ((x <= 1.55e-11) || (!(x <= 9.4e+36) && (x <= 3.4e+105))) {
		tmp = -9.0 * (t * (z * y));
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2d+110)) then
        tmp = x * 2.0d0
    else if (x <= (-6.6d-59)) then
        tmp = b * (a * 27.0d0)
    else if (x <= (-1.05d-140)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (x <= (-3.2d-157)) then
        tmp = 27.0d0 * (a * b)
    else if ((x <= 1.55d-11) .or. (.not. (x <= 9.4d+36)) .and. (x <= 3.4d+105)) then
        tmp = (-9.0d0) * (t * (z * y))
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2e+110) {
		tmp = x * 2.0;
	} else if (x <= -6.6e-59) {
		tmp = b * (a * 27.0);
	} else if (x <= -1.05e-140) {
		tmp = -9.0 * (z * (y * t));
	} else if (x <= -3.2e-157) {
		tmp = 27.0 * (a * b);
	} else if ((x <= 1.55e-11) || (!(x <= 9.4e+36) && (x <= 3.4e+105))) {
		tmp = -9.0 * (t * (z * y));
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2e+110:
		tmp = x * 2.0
	elif x <= -6.6e-59:
		tmp = b * (a * 27.0)
	elif x <= -1.05e-140:
		tmp = -9.0 * (z * (y * t))
	elif x <= -3.2e-157:
		tmp = 27.0 * (a * b)
	elif (x <= 1.55e-11) or (not (x <= 9.4e+36) and (x <= 3.4e+105)):
		tmp = -9.0 * (t * (z * y))
	else:
		tmp = x * 2.0
	return tmp

Julia

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 (x <= -2e+110)
		tmp = Float64(x * 2.0);
	elseif (x <= -6.6e-59)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (x <= -1.05e-140)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (x <= -3.2e-157)
		tmp = Float64(27.0 * Float64(a * b));
	elseif ((x <= 1.55e-11) || (!(x <= 9.4e+36) && (x <= 3.4e+105)))
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2e+110)
		tmp = x * 2.0;
	elseif (x <= -6.6e-59)
		tmp = b * (a * 27.0);
	elseif (x <= -1.05e-140)
		tmp = -9.0 * (z * (y * t));
	elseif (x <= -3.2e-157)
		tmp = 27.0 * (a * b);
	elseif ((x <= 1.55e-11) || (~((x <= 9.4e+36)) && (x <= 3.4e+105)))
		tmp = -9.0 * (t * (z * y));
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2e+110], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -6.6e-59], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.05e-140], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.2e-157], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.55e-11], And[N[Not[LessEqual[x, 9.4e+36]], $MachinePrecision], LessEqual[x, 3.4e+105]]], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2e110 or 1.55000000000000014e-11 < x < 9.39999999999999978e36 or 3.3999999999999999e105 < x

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. sub-neg 95.0%

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

      3. associate-*l* 91.0%

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

      4. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf 67.6%

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

   if -2e110 < x < -6.59999999999999964e-59

   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. Step-by-step derivation

      1. sub-neg 92.5%

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

      2. sub-neg 92.5%

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

      3. associate-*l* 97.3%

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

      4. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in a around inf 51.9%

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

      1. associate-*r* 51.9%

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

   7. Simplified 51.9%

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

   if -6.59999999999999964e-59 < x < -1.05000000000000009e-140

   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. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 95.3%

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

      4. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around inf 55.9%

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

      1. pow1 55.9%

         \[\leadsto -9 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} \]

      2. *-commutative 55.9%

         \[\leadsto -9 \cdot {\color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}}^{1} \]

      3. associate-*l* 59.5%

         \[\leadsto -9 \cdot {\color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}}^{1} \]

   7. Applied egg-rr 59.5%

      \[\leadsto -9 \cdot \color{blue}{{\left(y \cdot \left(z \cdot t\right)\right)}^{1}} \]
   8. Step-by-step derivation

      1. unpow1 59.5%

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

      2. associate-*r* 55.9%

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

      3. *-commutative 55.9%

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

      4. associate-*r* 45.9%

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

   9. Simplified 45.9%

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

   if -1.05000000000000009e-140 < x < -3.20000000000000021e-157

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around inf 99.6%

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

   if -3.20000000000000021e-157 < x < 1.55000000000000014e-11 or 9.39999999999999978e36 < x < 3.3999999999999999e105

   1. Initial program 92.8%

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

      1. sub-neg 92.8%

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

      2. sub-neg 92.8%

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

      3. associate-*l* 90.7%

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

      4. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in y around inf 60.0%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+110}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-140}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-157}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-11} \lor \neg \left(x \leq 9.4 \cdot 10^{+36}\right) \land x \leq 3.4 \cdot 10^{+105}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 46.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+109}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-141}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-158}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-16}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+38} \lor \neg \left(x \leq 3.2 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5.5e+109)
   (* x 2.0)
   (if (<= x -9e-59)
     (* b (* a 27.0))
     (if (<= x -1.35e-141)
       (* -9.0 (* z (* y t)))
       (if (<= x -1.4e-158)
         (* 27.0 (* a b))
         (if (<= x 6.8e-16)
           (* -9.0 (* t (* z y)))
           (if (or (<= x 4.3e+38) (not (<= x 3.2e+105)))
             (* x 2.0)
             (* t (* -9.0 (* z y))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.5e+109) {
		tmp = x * 2.0;
	} else if (x <= -9e-59) {
		tmp = b * (a * 27.0);
	} else if (x <= -1.35e-141) {
		tmp = -9.0 * (z * (y * t));
	} else if (x <= -1.4e-158) {
		tmp = 27.0 * (a * b);
	} else if (x <= 6.8e-16) {
		tmp = -9.0 * (t * (z * y));
	} else if ((x <= 4.3e+38) || !(x <= 3.2e+105)) {
		tmp = x * 2.0;
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-5.5d+109)) then
        tmp = x * 2.0d0
    else if (x <= (-9d-59)) then
        tmp = b * (a * 27.0d0)
    else if (x <= (-1.35d-141)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (x <= (-1.4d-158)) then
        tmp = 27.0d0 * (a * b)
    else if (x <= 6.8d-16) then
        tmp = (-9.0d0) * (t * (z * y))
    else if ((x <= 4.3d+38) .or. (.not. (x <= 3.2d+105))) then
        tmp = x * 2.0d0
    else
        tmp = t * ((-9.0d0) * (z * y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.5e+109) {
		tmp = x * 2.0;
	} else if (x <= -9e-59) {
		tmp = b * (a * 27.0);
	} else if (x <= -1.35e-141) {
		tmp = -9.0 * (z * (y * t));
	} else if (x <= -1.4e-158) {
		tmp = 27.0 * (a * b);
	} else if (x <= 6.8e-16) {
		tmp = -9.0 * (t * (z * y));
	} else if ((x <= 4.3e+38) || !(x <= 3.2e+105)) {
		tmp = x * 2.0;
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5.5e+109:
		tmp = x * 2.0
	elif x <= -9e-59:
		tmp = b * (a * 27.0)
	elif x <= -1.35e-141:
		tmp = -9.0 * (z * (y * t))
	elif x <= -1.4e-158:
		tmp = 27.0 * (a * b)
	elif x <= 6.8e-16:
		tmp = -9.0 * (t * (z * y))
	elif (x <= 4.3e+38) or not (x <= 3.2e+105):
		tmp = x * 2.0
	else:
		tmp = t * (-9.0 * (z * y))
	return tmp

Julia

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 (x <= -5.5e+109)
		tmp = Float64(x * 2.0);
	elseif (x <= -9e-59)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (x <= -1.35e-141)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (x <= -1.4e-158)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (x <= 6.8e-16)
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	elseif ((x <= 4.3e+38) || !(x <= 3.2e+105))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -5.5e+109)
		tmp = x * 2.0;
	elseif (x <= -9e-59)
		tmp = b * (a * 27.0);
	elseif (x <= -1.35e-141)
		tmp = -9.0 * (z * (y * t));
	elseif (x <= -1.4e-158)
		tmp = 27.0 * (a * b);
	elseif (x <= 6.8e-16)
		tmp = -9.0 * (t * (z * y));
	elseif ((x <= 4.3e+38) || ~((x <= 3.2e+105)))
		tmp = x * 2.0;
	else
		tmp = t * (-9.0 * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5.5e+109], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -9e-59], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.35e-141], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.4e-158], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e-16], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 4.3e+38], N[Not[LessEqual[x, 3.2e+105]], $MachinePrecision]], N[(x * 2.0), $MachinePrecision], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -5.4999999999999998e109 or 6.8e-16 < x < 4.2999999999999997e38 or 3.2e105 < x

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. sub-neg 95.0%

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

      3. associate-*l* 91.0%

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

      4. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf 67.6%

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

   if -5.4999999999999998e109 < x < -9.00000000000000023e-59

   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. Step-by-step derivation

      1. sub-neg 92.5%

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

      2. sub-neg 92.5%

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

      3. associate-*l* 97.3%

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

      4. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in a around inf 51.9%

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

      1. associate-*r* 51.9%

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

   7. Simplified 51.9%

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

   if -9.00000000000000023e-59 < x < -1.3500000000000001e-141

   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. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 95.3%

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

      4. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around inf 55.9%

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

      1. pow1 55.9%

         \[\leadsto -9 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} \]

      2. *-commutative 55.9%

         \[\leadsto -9 \cdot {\color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}}^{1} \]

      3. associate-*l* 59.5%

         \[\leadsto -9 \cdot {\color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}}^{1} \]

   7. Applied egg-rr 59.5%

      \[\leadsto -9 \cdot \color{blue}{{\left(y \cdot \left(z \cdot t\right)\right)}^{1}} \]
   8. Step-by-step derivation

      1. unpow1 59.5%

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

      2. associate-*r* 55.9%

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

      3. *-commutative 55.9%

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

      4. associate-*r* 45.9%

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

   9. Simplified 45.9%

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

   if -1.3500000000000001e-141 < x < -1.40000000000000001e-158

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around inf 99.6%

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

   if -1.40000000000000001e-158 < x < 6.8e-16

   1. Initial program 91.0%

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

      1. sub-neg 91.0%

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

      2. sub-neg 91.0%

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

      3. associate-*l* 89.7%

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

      4. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around inf 60.3%

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

   if 4.2999999999999997e38 < x < 3.2e105

   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. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 94.8%

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

      4. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

      1. +-commutative 94.8%

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

      2. associate-+r- 94.8%

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

      3. associate-*r* 94.8%

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

      4. *-commutative 94.8%

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

      5. associate-*l* 94.8%

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

      6. associate-*l* 94.7%

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

      7. associate-*r* 94.8%

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

   6. Applied egg-rr 94.8%

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

   7. Taylor expanded in y around 0 99.8%

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

      1. associate-*r* 90.0%

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

      2. associate-*r* 89.9%

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

      3. metadata-eval 89.9%

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

      4. distribute-lft-neg-in 89.9%

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

      5. *-commutative 89.9%

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

      6. distribute-lft-neg-in 89.9%

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

      7. metadata-eval 89.9%

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

      8. associate-*r* 89.8%

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

      9. *-commutative 89.8%

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

      10. associate-*l* 89.9%

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

   9. Simplified 89.9%

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

   10. Taylor expanded in z around inf 58.7%

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

       1. *-commutative 58.7%

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

       2. *-commutative 58.7%

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

       3. associate-*r* 58.8%

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

       4. *-commutative 58.8%

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

       5. *-commutative 58.8%

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

   12. Simplified 58.8%

       \[\leadsto \color{blue}{t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+109}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-141}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-158}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-16}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+38} \lor \neg \left(x \leq 3.2 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+111}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-142}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-159}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-14}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 4.05 \cdot 10^{+37} \lor \neg \left(x \leq 6.2 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.35e+111)
   (* x 2.0)
   (if (<= x -5.5e-59)
     (* b (* a 27.0))
     (if (<= x -9.5e-142)
       (* -9.0 (* z (* y t)))
       (if (<= x -1.6e-159)
         (* 27.0 (* a b))
         (if (<= x 3.7e-14)
           (* -9.0 (* t (* z y)))
           (if (or (<= x 4.05e+37) (not (<= x 6.2e+105)))
             (* x 2.0)
             (* t (* y (* z -9.0))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.35e+111) {
		tmp = x * 2.0;
	} else if (x <= -5.5e-59) {
		tmp = b * (a * 27.0);
	} else if (x <= -9.5e-142) {
		tmp = -9.0 * (z * (y * t));
	} else if (x <= -1.6e-159) {
		tmp = 27.0 * (a * b);
	} else if (x <= 3.7e-14) {
		tmp = -9.0 * (t * (z * y));
	} else if ((x <= 4.05e+37) || !(x <= 6.2e+105)) {
		tmp = x * 2.0;
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.35d+111)) then
        tmp = x * 2.0d0
    else if (x <= (-5.5d-59)) then
        tmp = b * (a * 27.0d0)
    else if (x <= (-9.5d-142)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (x <= (-1.6d-159)) then
        tmp = 27.0d0 * (a * b)
    else if (x <= 3.7d-14) then
        tmp = (-9.0d0) * (t * (z * y))
    else if ((x <= 4.05d+37) .or. (.not. (x <= 6.2d+105))) then
        tmp = x * 2.0d0
    else
        tmp = t * (y * (z * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.35e+111) {
		tmp = x * 2.0;
	} else if (x <= -5.5e-59) {
		tmp = b * (a * 27.0);
	} else if (x <= -9.5e-142) {
		tmp = -9.0 * (z * (y * t));
	} else if (x <= -1.6e-159) {
		tmp = 27.0 * (a * b);
	} else if (x <= 3.7e-14) {
		tmp = -9.0 * (t * (z * y));
	} else if ((x <= 4.05e+37) || !(x <= 6.2e+105)) {
		tmp = x * 2.0;
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.35e+111:
		tmp = x * 2.0
	elif x <= -5.5e-59:
		tmp = b * (a * 27.0)
	elif x <= -9.5e-142:
		tmp = -9.0 * (z * (y * t))
	elif x <= -1.6e-159:
		tmp = 27.0 * (a * b)
	elif x <= 3.7e-14:
		tmp = -9.0 * (t * (z * y))
	elif (x <= 4.05e+37) or not (x <= 6.2e+105):
		tmp = x * 2.0
	else:
		tmp = t * (y * (z * -9.0))
	return tmp

Julia

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 (x <= -2.35e+111)
		tmp = Float64(x * 2.0);
	elseif (x <= -5.5e-59)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (x <= -9.5e-142)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (x <= -1.6e-159)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (x <= 3.7e-14)
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	elseif ((x <= 4.05e+37) || !(x <= 6.2e+105))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.35e+111)
		tmp = x * 2.0;
	elseif (x <= -5.5e-59)
		tmp = b * (a * 27.0);
	elseif (x <= -9.5e-142)
		tmp = -9.0 * (z * (y * t));
	elseif (x <= -1.6e-159)
		tmp = 27.0 * (a * b);
	elseif (x <= 3.7e-14)
		tmp = -9.0 * (t * (z * y));
	elseif ((x <= 4.05e+37) || ~((x <= 6.2e+105)))
		tmp = x * 2.0;
	else
		tmp = t * (y * (z * -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.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.35e+111], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -5.5e-59], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.5e-142], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.6e-159], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e-14], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 4.05e+37], N[Not[LessEqual[x, 6.2e+105]], $MachinePrecision]], N[(x * 2.0), $MachinePrecision], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.35000000000000004e111 or 3.70000000000000001e-14 < x < 4.05000000000000003e37 or 6.20000000000000008e105 < x

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. sub-neg 95.0%

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

      3. associate-*l* 91.0%

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

      4. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf 67.6%

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

   if -2.35000000000000004e111 < x < -5.50000000000000014e-59

   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. Step-by-step derivation

      1. sub-neg 92.5%

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

      2. sub-neg 92.5%

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

      3. associate-*l* 97.3%

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

      4. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in a around inf 51.9%

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

      1. associate-*r* 51.9%

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

   7. Simplified 51.9%

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

   if -5.50000000000000014e-59 < x < -9.49999999999999967e-142

   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. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 95.3%

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

      4. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around inf 55.9%

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

      1. pow1 55.9%

         \[\leadsto -9 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} \]

      2. *-commutative 55.9%

         \[\leadsto -9 \cdot {\color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}}^{1} \]

      3. associate-*l* 59.5%

         \[\leadsto -9 \cdot {\color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}}^{1} \]

   7. Applied egg-rr 59.5%

      \[\leadsto -9 \cdot \color{blue}{{\left(y \cdot \left(z \cdot t\right)\right)}^{1}} \]
   8. Step-by-step derivation

      1. unpow1 59.5%

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

      2. associate-*r* 55.9%

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

      3. *-commutative 55.9%

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

      4. associate-*r* 45.9%

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

   9. Simplified 45.9%

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

   if -9.49999999999999967e-142 < x < -1.6e-159

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around inf 99.6%

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

   if -1.6e-159 < x < 3.70000000000000001e-14

   1. Initial program 91.0%

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

      1. sub-neg 91.0%

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

      2. sub-neg 91.0%

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

      3. associate-*l* 89.7%

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

      4. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around inf 60.3%

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

   if 4.05000000000000003e37 < x < 6.20000000000000008e105

   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. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 94.8%

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

      4. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in a around 0 79.1%

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

   6. Taylor expanded in t around inf 74.1%

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

   7. Taylor expanded in x around 0 58.8%

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

      1. *-commutative 58.8%

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

      2. associate-*l* 58.8%

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

   9. Simplified 58.8%

      \[\leadsto t \cdot \color{blue}{\left(y \cdot \left(z \cdot -9\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+111}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-142}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-159}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-14}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 4.05 \cdot 10^{+37} \lor \neg \left(x \leq 6.2 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 46.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+110}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-141}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-158}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+38} \lor \neg \left(x \leq 2.5 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.2e+110)
   (* x 2.0)
   (if (<= x -8.5e-59)
     (* b (* a 27.0))
     (if (<= x -6.4e-141)
       (* -9.0 (* z (* y t)))
       (if (<= x -1.65e-158)
         (* 27.0 (* a b))
         (if (<= x 3.2e-14)
           (* y (* -9.0 (* z t)))
           (if (or (<= x 1.2e+38) (not (<= x 2.5e+105)))
             (* x 2.0)
             (* t (* y (* z -9.0))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.2e+110) {
		tmp = x * 2.0;
	} else if (x <= -8.5e-59) {
		tmp = b * (a * 27.0);
	} else if (x <= -6.4e-141) {
		tmp = -9.0 * (z * (y * t));
	} else if (x <= -1.65e-158) {
		tmp = 27.0 * (a * b);
	} else if (x <= 3.2e-14) {
		tmp = y * (-9.0 * (z * t));
	} else if ((x <= 1.2e+38) || !(x <= 2.5e+105)) {
		tmp = x * 2.0;
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.2d+110)) then
        tmp = x * 2.0d0
    else if (x <= (-8.5d-59)) then
        tmp = b * (a * 27.0d0)
    else if (x <= (-6.4d-141)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (x <= (-1.65d-158)) then
        tmp = 27.0d0 * (a * b)
    else if (x <= 3.2d-14) then
        tmp = y * ((-9.0d0) * (z * t))
    else if ((x <= 1.2d+38) .or. (.not. (x <= 2.5d+105))) then
        tmp = x * 2.0d0
    else
        tmp = t * (y * (z * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.2e+110) {
		tmp = x * 2.0;
	} else if (x <= -8.5e-59) {
		tmp = b * (a * 27.0);
	} else if (x <= -6.4e-141) {
		tmp = -9.0 * (z * (y * t));
	} else if (x <= -1.65e-158) {
		tmp = 27.0 * (a * b);
	} else if (x <= 3.2e-14) {
		tmp = y * (-9.0 * (z * t));
	} else if ((x <= 1.2e+38) || !(x <= 2.5e+105)) {
		tmp = x * 2.0;
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.2e+110:
		tmp = x * 2.0
	elif x <= -8.5e-59:
		tmp = b * (a * 27.0)
	elif x <= -6.4e-141:
		tmp = -9.0 * (z * (y * t))
	elif x <= -1.65e-158:
		tmp = 27.0 * (a * b)
	elif x <= 3.2e-14:
		tmp = y * (-9.0 * (z * t))
	elif (x <= 1.2e+38) or not (x <= 2.5e+105):
		tmp = x * 2.0
	else:
		tmp = t * (y * (z * -9.0))
	return tmp

Julia

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 (x <= -3.2e+110)
		tmp = Float64(x * 2.0);
	elseif (x <= -8.5e-59)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (x <= -6.4e-141)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (x <= -1.65e-158)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (x <= 3.2e-14)
		tmp = Float64(y * Float64(-9.0 * Float64(z * t)));
	elseif ((x <= 1.2e+38) || !(x <= 2.5e+105))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.2e+110)
		tmp = x * 2.0;
	elseif (x <= -8.5e-59)
		tmp = b * (a * 27.0);
	elseif (x <= -6.4e-141)
		tmp = -9.0 * (z * (y * t));
	elseif (x <= -1.65e-158)
		tmp = 27.0 * (a * b);
	elseif (x <= 3.2e-14)
		tmp = y * (-9.0 * (z * t));
	elseif ((x <= 1.2e+38) || ~((x <= 2.5e+105)))
		tmp = x * 2.0;
	else
		tmp = t * (y * (z * -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.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.2e+110], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -8.5e-59], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.4e-141], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.65e-158], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-14], N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.2e+38], N[Not[LessEqual[x, 2.5e+105]], $MachinePrecision]], N[(x * 2.0), $MachinePrecision], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.19999999999999994e110 or 3.2000000000000002e-14 < x < 1.20000000000000009e38 or 2.50000000000000023e105 < x

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. sub-neg 95.0%

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

      3. associate-*l* 91.0%

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

      4. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf 67.6%

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

   if -3.19999999999999994e110 < x < -8.49999999999999933e-59

   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. Step-by-step derivation

      1. sub-neg 92.5%

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

      2. sub-neg 92.5%

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

      3. associate-*l* 97.3%

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

      4. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in a around inf 51.9%

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

      1. associate-*r* 51.9%

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

   7. Simplified 51.9%

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

   if -8.49999999999999933e-59 < x < -6.4000000000000003e-141

   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. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 95.3%

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

      4. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around inf 55.9%

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

      1. pow1 55.9%

         \[\leadsto -9 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} \]

      2. *-commutative 55.9%

         \[\leadsto -9 \cdot {\color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}}^{1} \]

      3. associate-*l* 59.5%

         \[\leadsto -9 \cdot {\color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}}^{1} \]

   7. Applied egg-rr 59.5%

      \[\leadsto -9 \cdot \color{blue}{{\left(y \cdot \left(z \cdot t\right)\right)}^{1}} \]
   8. Step-by-step derivation

      1. unpow1 59.5%

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

      2. associate-*r* 55.9%

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

      3. *-commutative 55.9%

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

      4. associate-*r* 45.9%

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

   9. Simplified 45.9%

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

   if -6.4000000000000003e-141 < x < -1.6500000000000001e-158

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around inf 99.6%

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

   if -1.6500000000000001e-158 < x < 3.2000000000000002e-14

   1. Initial program 91.0%

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

      1. sub-neg 91.0%

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

      2. sub-neg 91.0%

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

      3. associate-*l* 89.7%

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

      4. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in a around 0 65.2%

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

   6. Taylor expanded in y around inf 62.7%

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

   7. Taylor expanded in x around 0 57.8%

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

   if 1.20000000000000009e38 < x < 2.50000000000000023e105

   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. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 94.8%

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

      4. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in a around 0 79.1%

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

   6. Taylor expanded in t around inf 74.1%

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

   7. Taylor expanded in x around 0 58.8%

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

      1. *-commutative 58.8%

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

      2. associate-*l* 58.8%

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

   9. Simplified 58.8%

      \[\leadsto t \cdot \color{blue}{\left(y \cdot \left(z \cdot -9\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+110}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-141}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-158}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+38} \lor \neg \left(x \leq 2.5 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 46.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+111}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-141}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-158}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+38} \lor \neg \left(x \leq 3.4 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.6e+111)
   (* x 2.0)
   (if (<= x -7e-59)
     (* b (* a 27.0))
     (if (<= x -4.1e-141)
       (* z (* y (* t -9.0)))
       (if (<= x -3.1e-158)
         (* 27.0 (* a b))
         (if (<= x 1.05e-12)
           (* y (* -9.0 (* z t)))
           (if (or (<= x 8e+38) (not (<= x 3.4e+105)))
             (* x 2.0)
             (* t (* y (* z -9.0))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.6e+111) {
		tmp = x * 2.0;
	} else if (x <= -7e-59) {
		tmp = b * (a * 27.0);
	} else if (x <= -4.1e-141) {
		tmp = z * (y * (t * -9.0));
	} else if (x <= -3.1e-158) {
		tmp = 27.0 * (a * b);
	} else if (x <= 1.05e-12) {
		tmp = y * (-9.0 * (z * t));
	} else if ((x <= 8e+38) || !(x <= 3.4e+105)) {
		tmp = x * 2.0;
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.6d+111)) then
        tmp = x * 2.0d0
    else if (x <= (-7d-59)) then
        tmp = b * (a * 27.0d0)
    else if (x <= (-4.1d-141)) then
        tmp = z * (y * (t * (-9.0d0)))
    else if (x <= (-3.1d-158)) then
        tmp = 27.0d0 * (a * b)
    else if (x <= 1.05d-12) then
        tmp = y * ((-9.0d0) * (z * t))
    else if ((x <= 8d+38) .or. (.not. (x <= 3.4d+105))) then
        tmp = x * 2.0d0
    else
        tmp = t * (y * (z * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.6e+111) {
		tmp = x * 2.0;
	} else if (x <= -7e-59) {
		tmp = b * (a * 27.0);
	} else if (x <= -4.1e-141) {
		tmp = z * (y * (t * -9.0));
	} else if (x <= -3.1e-158) {
		tmp = 27.0 * (a * b);
	} else if (x <= 1.05e-12) {
		tmp = y * (-9.0 * (z * t));
	} else if ((x <= 8e+38) || !(x <= 3.4e+105)) {
		tmp = x * 2.0;
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.6e+111:
		tmp = x * 2.0
	elif x <= -7e-59:
		tmp = b * (a * 27.0)
	elif x <= -4.1e-141:
		tmp = z * (y * (t * -9.0))
	elif x <= -3.1e-158:
		tmp = 27.0 * (a * b)
	elif x <= 1.05e-12:
		tmp = y * (-9.0 * (z * t))
	elif (x <= 8e+38) or not (x <= 3.4e+105):
		tmp = x * 2.0
	else:
		tmp = t * (y * (z * -9.0))
	return tmp

Julia

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 (x <= -1.6e+111)
		tmp = Float64(x * 2.0);
	elseif (x <= -7e-59)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (x <= -4.1e-141)
		tmp = Float64(z * Float64(y * Float64(t * -9.0)));
	elseif (x <= -3.1e-158)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (x <= 1.05e-12)
		tmp = Float64(y * Float64(-9.0 * Float64(z * t)));
	elseif ((x <= 8e+38) || !(x <= 3.4e+105))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.6e+111)
		tmp = x * 2.0;
	elseif (x <= -7e-59)
		tmp = b * (a * 27.0);
	elseif (x <= -4.1e-141)
		tmp = z * (y * (t * -9.0));
	elseif (x <= -3.1e-158)
		tmp = 27.0 * (a * b);
	elseif (x <= 1.05e-12)
		tmp = y * (-9.0 * (z * t));
	elseif ((x <= 8e+38) || ~((x <= 3.4e+105)))
		tmp = x * 2.0;
	else
		tmp = t * (y * (z * -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.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.6e+111], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -7e-59], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.1e-141], N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.1e-158], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-12], N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 8e+38], N[Not[LessEqual[x, 3.4e+105]], $MachinePrecision]], N[(x * 2.0), $MachinePrecision], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.6e111 or 1.04999999999999997e-12 < x < 7.99999999999999982e38 or 3.3999999999999999e105 < x

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. sub-neg 95.0%

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

      3. associate-*l* 91.0%

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

      4. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf 67.6%

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

   if -1.6e111 < x < -7.0000000000000002e-59

   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. Step-by-step derivation

      1. sub-neg 92.5%

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

      2. sub-neg 92.5%

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

      3. associate-*l* 97.3%

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

      4. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in a around inf 51.9%

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

      1. associate-*r* 51.9%

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

   7. Simplified 51.9%

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

   if -7.0000000000000002e-59 < x < -4.10000000000000002e-141

   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. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 95.3%

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

      4. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

      1. +-commutative 95.3%

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

      2. associate-+r- 95.3%

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

      3. associate-*r* 95.3%

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

      4. *-commutative 95.3%

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

      5. associate-*l* 95.4%

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

      6. associate-*l* 95.5%

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

      7. associate-*r* 95.5%

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

   6. Applied egg-rr 95.5%

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

   7. Taylor expanded in y around 0 99.8%

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

      1. associate-*r* 89.9%

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

      2. associate-*r* 90.1%

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

      3. metadata-eval 90.1%

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

      4. distribute-lft-neg-in 90.1%

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

      5. *-commutative 90.1%

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

      6. distribute-lft-neg-in 90.1%

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

      7. metadata-eval 90.1%

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

      8. associate-*r* 90.1%

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

      9. *-commutative 90.1%

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

      10. associate-*l* 90.1%

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

   9. Simplified 90.1%

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

   10. Taylor expanded in z around inf 55.9%

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

       1. associate-*r* 56.0%

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

       2. *-commutative 56.0%

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

       3. *-commutative 56.0%

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

       4. *-commutative 56.0%

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

       5. associate-*r* 46.0%

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

   12. Simplified 46.0%

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

   if -4.10000000000000002e-141 < x < -3.10000000000000018e-158

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around inf 99.6%

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

   if -3.10000000000000018e-158 < x < 1.04999999999999997e-12

   1. Initial program 91.0%

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

      1. sub-neg 91.0%

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

      2. sub-neg 91.0%

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

      3. associate-*l* 89.7%

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

      4. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in a around 0 65.2%

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

   6. Taylor expanded in y around inf 62.7%

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

   7. Taylor expanded in x around 0 57.8%

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

   if 7.99999999999999982e38 < x < 3.3999999999999999e105

   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. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 94.8%

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

      4. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in a around 0 79.1%

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

   6. Taylor expanded in t around inf 74.1%

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

   7. Taylor expanded in x around 0 58.8%

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

      1. *-commutative 58.8%

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

      2. associate-*l* 58.8%

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

   9. Simplified 58.8%

      \[\leadsto t \cdot \color{blue}{\left(y \cdot \left(z \cdot -9\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+111}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-141}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-158}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+38} \lor \neg \left(x \leq 3.4 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right) + x \cdot 2\\ t_2 := z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{-168}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-269}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-270}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-168}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* 27.0 (* a b)) (* x 2.0)))
        (t_2 (+ (* z (* -9.0 (* y t))) (* x 2.0))))
   (if (<= z -6.6e-168)
     t_2
     (if (<= z -2.9e-230)
       t_1
       (if (<= z -2.35e-269)
         t_2
         (if (<= z -3.6e-270)
           (* y (* -9.0 (* z t)))
           (if (<= z 1.2e-168) t_1 t_2)))))))

C

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)) + (x * 2.0);
	double t_2 = (z * (-9.0 * (y * t))) + (x * 2.0);
	double tmp;
	if (z <= -6.6e-168) {
		tmp = t_2;
	} else if (z <= -2.9e-230) {
		tmp = t_1;
	} else if (z <= -2.35e-269) {
		tmp = t_2;
	} else if (z <= -3.6e-270) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= 1.2e-168) {
		tmp = t_1;
	} 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.
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 = (27.0d0 * (a * b)) + (x * 2.0d0)
    t_2 = (z * ((-9.0d0) * (y * t))) + (x * 2.0d0)
    if (z <= (-6.6d-168)) then
        tmp = t_2
    else if (z <= (-2.9d-230)) then
        tmp = t_1
    else if (z <= (-2.35d-269)) then
        tmp = t_2
    else if (z <= (-3.6d-270)) then
        tmp = y * ((-9.0d0) * (z * t))
    else if (z <= 1.2d-168) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

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)) + (x * 2.0);
	double t_2 = (z * (-9.0 * (y * t))) + (x * 2.0);
	double tmp;
	if (z <= -6.6e-168) {
		tmp = t_2;
	} else if (z <= -2.9e-230) {
		tmp = t_1;
	} else if (z <= -2.35e-269) {
		tmp = t_2;
	} else if (z <= -3.6e-270) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= 1.2e-168) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[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)) + (x * 2.0)
	t_2 = (z * (-9.0 * (y * t))) + (x * 2.0)
	tmp = 0
	if z <= -6.6e-168:
		tmp = t_2
	elif z <= -2.9e-230:
		tmp = t_1
	elif z <= -2.35e-269:
		tmp = t_2
	elif z <= -3.6e-270:
		tmp = y * (-9.0 * (z * t))
	elif z <= 1.2e-168:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

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(27.0 * Float64(a * b)) + Float64(x * 2.0))
	t_2 = Float64(Float64(z * Float64(-9.0 * Float64(y * t))) + Float64(x * 2.0))
	tmp = 0.0
	if (z <= -6.6e-168)
		tmp = t_2;
	elseif (z <= -2.9e-230)
		tmp = t_1;
	elseif (z <= -2.35e-269)
		tmp = t_2;
	elseif (z <= -3.6e-270)
		tmp = Float64(y * Float64(-9.0 * Float64(z * t)));
	elseif (z <= 1.2e-168)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

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)) + (x * 2.0);
	t_2 = (z * (-9.0 * (y * t))) + (x * 2.0);
	tmp = 0.0;
	if (z <= -6.6e-168)
		tmp = t_2;
	elseif (z <= -2.9e-230)
		tmp = t_1;
	elseif (z <= -2.35e-269)
		tmp = t_2;
	elseif (z <= -3.6e-270)
		tmp = y * (-9.0 * (z * t));
	elseif (z <= 1.2e-168)
		tmp = t_1;
	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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e-168], t$95$2, If[LessEqual[z, -2.9e-230], t$95$1, If[LessEqual[z, -2.35e-269], t$95$2, If[LessEqual[z, -3.6e-270], N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-168], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.6000000000000003e-168 or -2.90000000000000005e-230 < z < -2.3499999999999999e-269 or 1.2e-168 < z

   1. Initial program 92.7%

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

      1. sub-neg 92.7%

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

      2. sub-neg 92.7%

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

      3. associate-*l* 90.8%

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

      4. associate-*l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in a around 0 72.6%

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

      1. cancel-sign-sub-inv 72.6%

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

      2. *-commutative 72.6%

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

      3. metadata-eval 72.6%

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

      4. +-commutative 72.6%

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

      5. associate-*r* 72.5%

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

      6. associate-*r* 73.9%

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

      7. *-commutative 73.9%

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

   7. Applied egg-rr 73.9%

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

   8. Taylor expanded in t around 0 73.9%

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

   if -6.6000000000000003e-168 < z < -2.90000000000000005e-230 or -3.5999999999999998e-270 < z < 1.2e-168

   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. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 98.2%

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

      4. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in y around 0 90.9%

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

   if -2.3499999999999999e-269 < z < -3.5999999999999998e-270

   1. Initial program 99.2%

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

      1. sub-neg 99.2%

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

      2. sub-neg 99.2%

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

      3. associate-*l* 99.2%

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

      4. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around 0 98.4%

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

   6. Taylor expanded in y around inf 100.0%

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

   7. Taylor expanded in x around 0 100.0%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-168}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-230}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-269}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-270}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-168}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ t_2 := 27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-168}:\\ \;\;\;\;x \cdot 2 + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-230}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-270}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-175}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (* -9.0 (* y t))) (* x 2.0)))
        (t_2 (+ (* 27.0 (* a b)) (* x 2.0))))
   (if (<= z -6.2e-168)
     (+ (* x 2.0) (* z (* y (* t -9.0))))
     (if (<= z -2.9e-230)
       t_2
       (if (<= z -2.35e-269)
         t_1
         (if (<= z -3.6e-270)
           (* y (* -9.0 (* z t)))
           (if (<= z 1.06e-175) t_2 t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (-9.0 * (y * t))) + (x * 2.0);
	double t_2 = (27.0 * (a * b)) + (x * 2.0);
	double tmp;
	if (z <= -6.2e-168) {
		tmp = (x * 2.0) + (z * (y * (t * -9.0)));
	} else if (z <= -2.9e-230) {
		tmp = t_2;
	} else if (z <= -2.35e-269) {
		tmp = t_1;
	} else if (z <= -3.6e-270) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= 1.06e-175) {
		tmp = t_2;
	} 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.
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 = (z * ((-9.0d0) * (y * t))) + (x * 2.0d0)
    t_2 = (27.0d0 * (a * b)) + (x * 2.0d0)
    if (z <= (-6.2d-168)) then
        tmp = (x * 2.0d0) + (z * (y * (t * (-9.0d0))))
    else if (z <= (-2.9d-230)) then
        tmp = t_2
    else if (z <= (-2.35d-269)) then
        tmp = t_1
    else if (z <= (-3.6d-270)) then
        tmp = y * ((-9.0d0) * (z * t))
    else if (z <= 1.06d-175) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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 = (z * (-9.0 * (y * t))) + (x * 2.0);
	double t_2 = (27.0 * (a * b)) + (x * 2.0);
	double tmp;
	if (z <= -6.2e-168) {
		tmp = (x * 2.0) + (z * (y * (t * -9.0)));
	} else if (z <= -2.9e-230) {
		tmp = t_2;
	} else if (z <= -2.35e-269) {
		tmp = t_1;
	} else if (z <= -3.6e-270) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= 1.06e-175) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (z * (-9.0 * (y * t))) + (x * 2.0)
	t_2 = (27.0 * (a * b)) + (x * 2.0)
	tmp = 0
	if z <= -6.2e-168:
		tmp = (x * 2.0) + (z * (y * (t * -9.0)))
	elif z <= -2.9e-230:
		tmp = t_2
	elif z <= -2.35e-269:
		tmp = t_1
	elif z <= -3.6e-270:
		tmp = y * (-9.0 * (z * t))
	elif z <= 1.06e-175:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

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(z * Float64(-9.0 * Float64(y * t))) + Float64(x * 2.0))
	t_2 = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0))
	tmp = 0.0
	if (z <= -6.2e-168)
		tmp = Float64(Float64(x * 2.0) + Float64(z * Float64(y * Float64(t * -9.0))));
	elseif (z <= -2.9e-230)
		tmp = t_2;
	elseif (z <= -2.35e-269)
		tmp = t_1;
	elseif (z <= -3.6e-270)
		tmp = Float64(y * Float64(-9.0 * Float64(z * t)));
	elseif (z <= 1.06e-175)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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 = (z * (-9.0 * (y * t))) + (x * 2.0);
	t_2 = (27.0 * (a * b)) + (x * 2.0);
	tmp = 0.0;
	if (z <= -6.2e-168)
		tmp = (x * 2.0) + (z * (y * (t * -9.0)));
	elseif (z <= -2.9e-230)
		tmp = t_2;
	elseif (z <= -2.35e-269)
		tmp = t_1;
	elseif (z <= -3.6e-270)
		tmp = y * (-9.0 * (z * t));
	elseif (z <= 1.06e-175)
		tmp = t_2;
	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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e-168], N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-230], t$95$2, If[LessEqual[z, -2.35e-269], t$95$1, If[LessEqual[z, -3.6e-270], N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e-175], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.2e-168

   1. Initial program 92.7%

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

      1. sub-neg 92.7%

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

      2. sub-neg 92.7%

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

      3. associate-*l* 90.5%

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

      4. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in a around 0 68.9%

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

      1. cancel-sign-sub-inv 68.9%

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

      2. *-commutative 68.9%

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

      3. metadata-eval 68.9%

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

      4. +-commutative 68.9%

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

      5. associate-*r* 68.9%

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

      6. associate-*r* 69.9%

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

      7. *-commutative 69.9%

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

   7. Applied egg-rr 69.9%

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

   if -6.2e-168 < z < -2.90000000000000005e-230 or -3.5999999999999998e-270 < z < 1.06000000000000002e-175

   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. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 98.1%

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

      4. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in y around 0 90.7%

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

   if -2.90000000000000005e-230 < z < -2.3499999999999999e-269 or 1.06000000000000002e-175 < z

   1. Initial program 92.8%

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

      1. sub-neg 92.8%

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

      2. sub-neg 92.8%

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

      3. associate-*l* 91.1%

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

      4. associate-*l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in a around 0 75.9%

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

      1. cancel-sign-sub-inv 75.9%

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

      2. *-commutative 75.9%

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

      3. metadata-eval 75.9%

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

      4. +-commutative 75.9%

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

      5. associate-*r* 75.9%

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

      6. associate-*r* 77.6%

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

      7. *-commutative 77.6%

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

   7. Applied egg-rr 77.6%

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

   8. Taylor expanded in t around 0 77.7%

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

   if -2.3499999999999999e-269 < z < -3.5999999999999998e-270

   1. Initial program 99.2%

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

      1. sub-neg 99.2%

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

      2. sub-neg 99.2%

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

      3. associate-*l* 99.2%

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

      4. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around 0 98.4%

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

   6. Taylor expanded in y around inf 100.0%

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

   7. Taylor expanded in x around 0 100.0%

      \[\leadsto y \cdot \color{blue}{\left(-9 \cdot \left(t \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-168}:\\ \;\;\;\;x \cdot 2 + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-230}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-269}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-270}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-175}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+110}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-71}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-11} \lor \neg \left(x \leq 1.35 \cdot 10^{+37}\right) \land x \leq 2.5 \cdot 10^{+105}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.25e+110)
   (* x 2.0)
   (if (<= x -4.6e-71)
     (* b (* a 27.0))
     (if (or (<= x 4.2e-11) (and (not (<= x 1.35e+37)) (<= x 2.5e+105)))
       (* -9.0 (* t (* z y)))
       (* x 2.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.25e+110) {
		tmp = x * 2.0;
	} else if (x <= -4.6e-71) {
		tmp = b * (a * 27.0);
	} else if ((x <= 4.2e-11) || (!(x <= 1.35e+37) && (x <= 2.5e+105))) {
		tmp = -9.0 * (t * (z * y));
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.25d+110)) then
        tmp = x * 2.0d0
    else if (x <= (-4.6d-71)) then
        tmp = b * (a * 27.0d0)
    else if ((x <= 4.2d-11) .or. (.not. (x <= 1.35d+37)) .and. (x <= 2.5d+105)) then
        tmp = (-9.0d0) * (t * (z * y))
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.25e+110) {
		tmp = x * 2.0;
	} else if (x <= -4.6e-71) {
		tmp = b * (a * 27.0);
	} else if ((x <= 4.2e-11) || (!(x <= 1.35e+37) && (x <= 2.5e+105))) {
		tmp = -9.0 * (t * (z * y));
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.25e+110:
		tmp = x * 2.0
	elif x <= -4.6e-71:
		tmp = b * (a * 27.0)
	elif (x <= 4.2e-11) or (not (x <= 1.35e+37) and (x <= 2.5e+105)):
		tmp = -9.0 * (t * (z * y))
	else:
		tmp = x * 2.0
	return tmp

Julia

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 (x <= -1.25e+110)
		tmp = Float64(x * 2.0);
	elseif (x <= -4.6e-71)
		tmp = Float64(b * Float64(a * 27.0));
	elseif ((x <= 4.2e-11) || (!(x <= 1.35e+37) && (x <= 2.5e+105)))
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.25e+110)
		tmp = x * 2.0;
	elseif (x <= -4.6e-71)
		tmp = b * (a * 27.0);
	elseif ((x <= 4.2e-11) || (~((x <= 1.35e+37)) && (x <= 2.5e+105)))
		tmp = -9.0 * (t * (z * y));
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.25e+110], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -4.6e-71], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 4.2e-11], And[N[Not[LessEqual[x, 1.35e+37]], $MachinePrecision], LessEqual[x, 2.5e+105]]], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.24999999999999995e110 or 4.1999999999999997e-11 < x < 1.34999999999999993e37 or 2.50000000000000023e105 < x

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. sub-neg 95.0%

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

      3. associate-*l* 91.0%

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

      4. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf 67.6%

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

   if -1.24999999999999995e110 < x < -4.5999999999999997e-71

   1. Initial program 92.9%

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

      1. sub-neg 92.9%

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

      2. sub-neg 92.9%

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

      3. associate-*l* 97.5%

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

      4. associate-*l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in a around inf 50.7%

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

      1. associate-*r* 50.7%

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

   7. Simplified 50.7%

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

   if -4.5999999999999997e-71 < x < 4.1999999999999997e-11 or 1.34999999999999993e37 < x < 2.50000000000000023e105

   1. Initial program 94.0%

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

      1. sub-neg 94.0%

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

      2. sub-neg 94.0%

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

      3. associate-*l* 91.5%

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

      4. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in y around inf 58.0%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+110}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-71}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-11} \lor \neg \left(x \leq 1.35 \cdot 10^{+37}\right) \land x \leq 2.5 \cdot 10^{+105}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(2 \cdot \frac{x}{y} - 9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2000000:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-259}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* 27.0 (* a b)) (* x 2.0))))
   (if (<= y -9.6e+105)
     (* y (- (* 2.0 (/ x y)) (* 9.0 (* z t))))
     (if (<= y -5.2e+93)
       t_1
       (if (<= y -2000000.0)
         (- (* x 2.0) (* 9.0 (* t (* z y))))
         (if (<= y 9.4e-259) t_1 (+ (* z (* -9.0 (* y t))) (* x 2.0))))))))

C

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)) + (x * 2.0);
	double tmp;
	if (y <= -9.6e+105) {
		tmp = y * ((2.0 * (x / y)) - (9.0 * (z * t)));
	} else if (y <= -5.2e+93) {
		tmp = t_1;
	} else if (y <= -2000000.0) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else if (y <= 9.4e-259) {
		tmp = t_1;
	} else {
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0);
	}
	return tmp;
}

Fortran

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)) + (x * 2.0d0)
    if (y <= (-9.6d+105)) then
        tmp = y * ((2.0d0 * (x / y)) - (9.0d0 * (z * t)))
    else if (y <= (-5.2d+93)) then
        tmp = t_1
    else if (y <= (-2000000.0d0)) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    else if (y <= 9.4d-259) then
        tmp = t_1
    else
        tmp = (z * ((-9.0d0) * (y * t))) + (x * 2.0d0)
    end if
    code = tmp
end function

Java

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)) + (x * 2.0);
	double tmp;
	if (y <= -9.6e+105) {
		tmp = y * ((2.0 * (x / y)) - (9.0 * (z * t)));
	} else if (y <= -5.2e+93) {
		tmp = t_1;
	} else if (y <= -2000000.0) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else if (y <= 9.4e-259) {
		tmp = t_1;
	} else {
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0);
	}
	return tmp;
}

Python

[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)) + (x * 2.0)
	tmp = 0
	if y <= -9.6e+105:
		tmp = y * ((2.0 * (x / y)) - (9.0 * (z * t)))
	elif y <= -5.2e+93:
		tmp = t_1
	elif y <= -2000000.0:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	elif y <= 9.4e-259:
		tmp = t_1
	else:
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0)
	return tmp

Julia

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(27.0 * Float64(a * b)) + Float64(x * 2.0))
	tmp = 0.0
	if (y <= -9.6e+105)
		tmp = Float64(y * Float64(Float64(2.0 * Float64(x / y)) - Float64(9.0 * Float64(z * t))));
	elseif (y <= -5.2e+93)
		tmp = t_1;
	elseif (y <= -2000000.0)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	elseif (y <= 9.4e-259)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * Float64(-9.0 * Float64(y * t))) + Float64(x * 2.0));
	end
	return tmp
end

MATLAB

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)) + (x * 2.0);
	tmp = 0.0;
	if (y <= -9.6e+105)
		tmp = y * ((2.0 * (x / y)) - (9.0 * (z * t)));
	elseif (y <= -5.2e+93)
		tmp = t_1;
	elseif (y <= -2000000.0)
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	elseif (y <= 9.4e-259)
		tmp = t_1;
	else
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e+105], N[(y * N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.2e+93], t$95$1, If[LessEqual[y, -2000000.0], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.4e-259], t$95$1, N[(N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.599999999999999e105

   1. Initial program 89.9%

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

      1. sub-neg 89.9%

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

      2. sub-neg 89.9%

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

      3. associate-*l* 92.6%

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

      4. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in a around 0 85.6%

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

   6. Taylor expanded in y around inf 87.5%

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

   if -9.599999999999999e105 < y < -5.19999999999999999e93 or -2e6 < y < 9.39999999999999996e-259

   1. Initial program 98.8%

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

      1. sub-neg 98.8%

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

      2. sub-neg 98.8%

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

      3. associate-*l* 89.2%

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

      4. associate-*l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in y around 0 77.7%

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

   if -5.19999999999999999e93 < y < -2e6

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l* 99.9%

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

      4. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 92.9%

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

   if 9.39999999999999996e-259 < y

   1. Initial program 91.3%

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

      1. sub-neg 91.3%

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

      2. sub-neg 91.3%

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

      3. associate-*l* 93.8%

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

      4. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in a around 0 68.2%

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

      1. cancel-sign-sub-inv 68.2%

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

      2. *-commutative 68.2%

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

      3. metadata-eval 68.2%

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

      4. +-commutative 68.2%

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

      5. associate-*r* 68.1%

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

      6. associate-*r* 68.0%

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

      7. *-commutative 68.0%

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

   7. Applied egg-rr 68.0%

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

   8. Taylor expanded in t around 0 68.1%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(2 \cdot \frac{x}{y} - 9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+93}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;y \leq -2000000:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-259}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-168}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* 27.0 (* a b)) (* x 2.0))))
   (if (<= z -6.5e-5)
     (* z (* y (* t -9.0)))
     (if (<= z -1.25e-122)
       t_1
       (if (<= z -6.6e-168)
         (* -9.0 (* t (* z y)))
         (if (<= z 5.2e-24) t_1 (* t (* y (* z -9.0)))))))))

C

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)) + (x * 2.0);
	double tmp;
	if (z <= -6.5e-5) {
		tmp = z * (y * (t * -9.0));
	} else if (z <= -1.25e-122) {
		tmp = t_1;
	} else if (z <= -6.6e-168) {
		tmp = -9.0 * (t * (z * y));
	} else if (z <= 5.2e-24) {
		tmp = t_1;
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Fortran

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)) + (x * 2.0d0)
    if (z <= (-6.5d-5)) then
        tmp = z * (y * (t * (-9.0d0)))
    else if (z <= (-1.25d-122)) then
        tmp = t_1
    else if (z <= (-6.6d-168)) then
        tmp = (-9.0d0) * (t * (z * y))
    else if (z <= 5.2d-24) then
        tmp = t_1
    else
        tmp = t * (y * (z * (-9.0d0)))
    end if
    code = tmp
end function

Java

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)) + (x * 2.0);
	double tmp;
	if (z <= -6.5e-5) {
		tmp = z * (y * (t * -9.0));
	} else if (z <= -1.25e-122) {
		tmp = t_1;
	} else if (z <= -6.6e-168) {
		tmp = -9.0 * (t * (z * y));
	} else if (z <= 5.2e-24) {
		tmp = t_1;
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Python

[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)) + (x * 2.0)
	tmp = 0
	if z <= -6.5e-5:
		tmp = z * (y * (t * -9.0))
	elif z <= -1.25e-122:
		tmp = t_1
	elif z <= -6.6e-168:
		tmp = -9.0 * (t * (z * y))
	elif z <= 5.2e-24:
		tmp = t_1
	else:
		tmp = t * (y * (z * -9.0))
	return tmp

Julia

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(27.0 * Float64(a * b)) + Float64(x * 2.0))
	tmp = 0.0
	if (z <= -6.5e-5)
		tmp = Float64(z * Float64(y * Float64(t * -9.0)));
	elseif (z <= -1.25e-122)
		tmp = t_1;
	elseif (z <= -6.6e-168)
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	elseif (z <= 5.2e-24)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	end
	return tmp
end

MATLAB

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)) + (x * 2.0);
	tmp = 0.0;
	if (z <= -6.5e-5)
		tmp = z * (y * (t * -9.0));
	elseif (z <= -1.25e-122)
		tmp = t_1;
	elseif (z <= -6.6e-168)
		tmp = -9.0 * (t * (z * y));
	elseif (z <= 5.2e-24)
		tmp = t_1;
	else
		tmp = t * (y * (z * -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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e-5], N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e-122], t$95$1, If[LessEqual[z, -6.6e-168], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-24], t$95$1, N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.49999999999999943e-5

   1. Initial program 90.2%

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

      1. sub-neg 90.2%

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

      2. sub-neg 90.2%

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

      3. associate-*l* 86.6%

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

      4. associate-*l* 86.6%

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

   3. Simplified 86.6%

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

      1. +-commutative 86.6%

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

      2. associate-+r- 86.6%

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

      3. associate-*r* 86.6%

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

      4. *-commutative 86.6%

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

      5. associate-*l* 86.6%

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

      6. associate-*l* 86.5%

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

      7. associate-*r* 86.5%

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

   6. Applied egg-rr 86.5%

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

   7. Taylor expanded in y around 0 90.2%

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

      1. associate-*r* 98.1%

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

      2. associate-*r* 98.0%

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

      3. metadata-eval 98.0%

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

      4. distribute-lft-neg-in 98.0%

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

      5. *-commutative 98.0%

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

      6. distribute-lft-neg-in 98.0%

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

      7. metadata-eval 98.0%

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

      8. associate-*r* 98.0%

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

      9. *-commutative 98.0%

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

      10. associate-*l* 98.0%

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

   9. Simplified 98.0%

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

   10. Taylor expanded in z around inf 48.5%

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

       1. associate-*r* 48.5%

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

       2. *-commutative 48.5%

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

       3. *-commutative 48.5%

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

       4. *-commutative 48.5%

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

       5. associate-*r* 53.2%

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

   12. Simplified 53.2%

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

   if -6.49999999999999943e-5 < z < -1.25e-122 or -6.6000000000000003e-168 < z < 5.2e-24

   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. Step-by-step derivation

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 99.0%

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

      4. associate-*l* 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in y around 0 80.6%

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

   if -1.25e-122 < z < -6.6000000000000003e-168

   1. Initial program 90.9%

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

      1. sub-neg 90.9%

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

      2. sub-neg 90.9%

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

      3. associate-*l* 90.8%

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

      4. associate-*l* 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in y around inf 47.3%

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

   if 5.2e-24 < z

   1. Initial program 90.5%

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

      1. sub-neg 90.5%

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

      2. sub-neg 90.5%

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

      3. associate-*l* 88.2%

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

      4. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in a around 0 75.1%

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

   6. Taylor expanded in t around inf 64.7%

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

   7. Taylor expanded in x around 0 56.3%

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

      1. *-commutative 56.3%

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

      2. associate-*l* 56.4%

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

   9. Simplified 56.4%

      \[\leadsto t \cdot \color{blue}{\left(y \cdot \left(z \cdot -9\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-122}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-168}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-24}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 98.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 7.4 \cdot 10^{-91}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(2 \cdot \frac{x}{t} + 27 \cdot \frac{a \cdot b}{t}\right) - 9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 7.4e-91)
   (+ (* a (* 27.0 b)) (- (* x 2.0) (* (* y 9.0) (* z t))))
   (* t (- (+ (* 2.0 (/ x t)) (* 27.0 (/ (* a b) t))) (* 9.0 (* z y))))))

C

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 <= 7.4e-91) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (z * y)));
	}
	return tmp;
}

Fortran

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 <= 7.4d-91) then
        tmp = (a * (27.0d0 * b)) + ((x * 2.0d0) - ((y * 9.0d0) * (z * t)))
    else
        tmp = t * (((2.0d0 * (x / t)) + (27.0d0 * ((a * b) / t))) - (9.0d0 * (z * y)))
    end if
    code = tmp
end function

Java

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 <= 7.4e-91) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (z * y)));
	}
	return tmp;
}

Python

[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 <= 7.4e-91:
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)))
	else:
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (z * y)))
	return tmp

Julia

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 <= 7.4e-91)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(z * t))));
	else
		tmp = Float64(t * Float64(Float64(Float64(2.0 * Float64(x / t)) + Float64(27.0 * Float64(Float64(a * b) / t))) - Float64(9.0 * Float64(z * y))));
	end
	return tmp
end

MATLAB

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 <= 7.4e-91)
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	else
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 7.4e-91], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(N[(2.0 * N[(x / t), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(N[(a * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.4000000000000004e-91

   1. Initial program 95.7%

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

      1. sub-neg 95.7%

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

      2. sub-neg 95.7%

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

      3. associate-*l* 93.9%

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

      4. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   if 7.4000000000000004e-91 < z

   1. Initial program 91.5%

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

      1. sub-neg 91.5%

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

      2. sub-neg 91.5%

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

      3. associate-*l* 89.5%

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

      4. associate-*l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in t around inf 77.0%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7.4 \cdot 10^{-91}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(2 \cdot \frac{x}{t} + 27 \cdot \frac{a \cdot b}{t}\right) - 9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 98.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -400000:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - z \cdot \left(t \cdot \left(y \cdot 9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* y 9.0) -400000.0)
   (+ (* a (* 27.0 b)) (- (* x 2.0) (* (* y 9.0) (* z t))))
   (- (+ (* 27.0 (* a b)) (* x 2.0)) (* z (* t (* y 9.0))))))

C

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) <= -400000.0) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (z * (t * (y * 9.0)));
	}
	return tmp;
}

Fortran

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 ((y * 9.0d0) <= (-400000.0d0)) then
        tmp = (a * (27.0d0 * b)) + ((x * 2.0d0) - ((y * 9.0d0) * (z * t)))
    else
        tmp = ((27.0d0 * (a * b)) + (x * 2.0d0)) - (z * (t * (y * 9.0d0)))
    end if
    code = tmp
end function

Java

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 ((y * 9.0) <= -400000.0) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (z * (t * (y * 9.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (y * 9.0) <= -400000.0:
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)))
	else:
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (z * (t * (y * 9.0)))
	return tmp

Julia

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) <= -400000.0)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(z * t))));
	else
		tmp = Float64(Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0)) - Float64(z * Float64(t * Float64(y * 9.0))));
	end
	return tmp
end

MATLAB

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 ((y * 9.0) <= -400000.0)
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	else
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (z * (t * (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.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(y * 9.0), $MachinePrecision], -400000.0], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y #s(literal 9 binary64)) < -4e5

   1. Initial program 93.2%

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

      1. sub-neg 93.2%

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

      2. sub-neg 93.2%

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

      3. associate-*l* 95.0%

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

      4. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   if -4e5 < (*.f64 y #s(literal 9 binary64))

   1. Initial program 94.5%

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

      1. sub-neg 94.5%

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

      2. sub-neg 94.5%

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

      3. associate-*l* 91.5%

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

      4. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

      1. +-commutative 92.0%

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

      2. associate-+r- 92.0%

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

      3. associate-*r* 91.5%

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

      4. *-commutative 91.5%

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

      5. associate-*l* 92.0%

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

      6. associate-*l* 92.0%

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

      7. associate-*r* 92.1%

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

   6. Applied egg-rr 92.1%

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

   7. Taylor expanded in y around 0 95.0%

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

      1. associate-*r* 95.9%

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

      2. associate-*r* 95.9%

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

      3. metadata-eval 95.9%

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

      4. distribute-lft-neg-in 95.9%

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

      5. *-commutative 95.9%

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

      6. distribute-lft-neg-in 95.9%

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

      7. metadata-eval 95.9%

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

      8. associate-*r* 95.9%

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

      9. *-commutative 95.9%

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

      10. associate-*l* 95.9%

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

   9. Simplified 95.9%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -400000:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - z \cdot \left(t \cdot \left(y \cdot 9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 92.2% accurate, 0.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 9e+243)
   (+ (- (* x 2.0) (* 9.0 (* z (* y t)))) (* a (* 27.0 b)))
   (- (* x 2.0) (* 9.0 (* t (* z y))))))

C

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 (t <= 9e+243) {
		tmp = ((x * 2.0) - (9.0 * (z * (y * t)))) + (a * (27.0 * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Fortran

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 (t <= 9d+243) then
        tmp = ((x * 2.0d0) - (9.0d0 * (z * (y * t)))) + (a * (27.0d0 * b))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    end if
    code = tmp
end function

Java

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 (t <= 9e+243) {
		tmp = ((x * 2.0) - (9.0 * (z * (y * t)))) + (a * (27.0 * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 9e+243:
		tmp = ((x * 2.0) - (9.0 * (z * (y * t)))) + (a * (27.0 * b))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	return tmp

Julia

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 (t <= 9e+243)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(z * Float64(y * t)))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	end
	return tmp
end

MATLAB

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 (t <= 9e+243)
		tmp = ((x * 2.0) - (9.0 * (z * (y * t)))) + (a * (27.0 * b));
	else
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 9e+243], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 8.9999999999999999e243

   1. Initial program 93.8%

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

      1. sub-neg 93.8%

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

      2. sub-neg 93.8%

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

      3. associate-*l* 93.0%

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

      4. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in y around 0 94.1%

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

      1. associate-*r* 95.3%

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

   7. Simplified 95.3%

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

   if 8.9999999999999999e243 < t

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. sub-neg 100.0%

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

      3. associate-*l* 84.0%

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

      4. associate-*l* 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in a around 0 99.7%

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

4. Final simplification 95.6%

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

Alternative 16: 96.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 2.4 \cdot 10^{+30}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 2.4e+30)
   (+ (* a (* 27.0 b)) (- (* x 2.0) (* (* y 9.0) (* z t))))
   (+ (* z (* -9.0 (* y t))) (* x 2.0))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2.4e+30) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0);
	}
	return tmp;
}

Fortran

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 <= 2.4d+30) then
        tmp = (a * (27.0d0 * b)) + ((x * 2.0d0) - ((y * 9.0d0) * (z * t)))
    else
        tmp = (z * ((-9.0d0) * (y * t))) + (x * 2.0d0)
    end if
    code = tmp
end function

Java

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 <= 2.4e+30) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0);
	}
	return tmp;
}

Python

[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 <= 2.4e+30:
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)))
	else:
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 2.4e+30)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(z * t))));
	else
		tmp = Float64(Float64(z * Float64(-9.0 * Float64(y * t))) + Float64(x * 2.0));
	end
	return tmp
end

MATLAB

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 <= 2.4e+30)
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	else
		tmp = (z * (-9.0 * (y * t))) + (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 2.4e+30], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.3999999999999999e30

   1. Initial program 95.7%

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

      1. sub-neg 95.7%

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

      2. sub-neg 95.7%

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

      3. associate-*l* 94.1%

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

      4. associate-*l* 94.6%

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

   3. Simplified 94.6%

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

   if 2.3999999999999999e30 < z

   1. Initial program 90.4%

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

      1. sub-neg 90.4%

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

      2. sub-neg 90.4%

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

      3. associate-*l* 87.9%

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

      4. associate-*l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in a around 0 78.3%

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

      1. cancel-sign-sub-inv 78.3%

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

      2. *-commutative 78.3%

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

      3. metadata-eval 78.3%

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

      4. +-commutative 78.3%

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

      5. associate-*r* 78.3%

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

      6. associate-*r* 80.9%

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

      7. *-commutative 80.9%

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

   7. Applied egg-rr 80.9%

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

   8. Taylor expanded in t around 0 81.0%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.4 \cdot 10^{+30}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+144} \lor \neg \left(a \leq 2.5 \cdot 10^{-108}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -8.2e+144) (not (<= a 2.5e-108)))
   (+ (* 27.0 (* a b)) (* x 2.0))
   (- (* x 2.0) (* 9.0 (* t (* z y))))))

C

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 ((a <= -8.2e+144) || !(a <= 2.5e-108)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Fortran

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 ((a <= (-8.2d+144)) .or. (.not. (a <= 2.5d-108))) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    end if
    code = tmp
end function

Java

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 ((a <= -8.2e+144) || !(a <= 2.5e-108)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -8.2e+144) or not (a <= 2.5e-108):
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	return tmp

Julia

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 ((a <= -8.2e+144) || !(a <= 2.5e-108))
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	end
	return tmp
end

MATLAB

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 ((a <= -8.2e+144) || ~((a <= 2.5e-108)))
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -8.2e+144], N[Not[LessEqual[a, 2.5e-108]], $MachinePrecision]], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.20000000000000002e144 or 2.5e-108 < a

   1. Initial program 91.6%

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

      1. sub-neg 91.6%

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

      2. sub-neg 91.6%

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

      3. associate-*l* 88.8%

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

      4. associate-*l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in y around 0 67.8%

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

   if -8.20000000000000002e144 < a < 2.5e-108

   1. Initial program 96.0%

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

      1. sub-neg 96.0%

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

      2. sub-neg 96.0%

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

      3. associate-*l* 94.8%

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

      4. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in a around 0 82.8%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+144} \lor \neg \left(a \leq 2.5 \cdot 10^{-108}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+119}:\\ \;\;\;\;t\_1 - t\_2\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-105}:\\ \;\;\;\;x \cdot 2 - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))) (t_2 (* 9.0 (* t (* z y)))))
   (if (<= a -6.2e+119)
     (- t_1 t_2)
     (if (<= a 1.46e-105) (- (* x 2.0) t_2) (+ t_1 (* x 2.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = 9.0 * (t * (z * y));
	double tmp;
	if (a <= -6.2e+119) {
		tmp = t_1 - t_2;
	} else if (a <= 1.46e-105) {
		tmp = (x * 2.0) - t_2;
	} else {
		tmp = t_1 + (x * 2.0);
	}
	return tmp;
}

Fortran

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 = 27.0d0 * (a * b)
    t_2 = 9.0d0 * (t * (z * y))
    if (a <= (-6.2d+119)) then
        tmp = t_1 - t_2
    else if (a <= 1.46d-105) then
        tmp = (x * 2.0d0) - t_2
    else
        tmp = t_1 + (x * 2.0d0)
    end if
    code = tmp
end function

Java

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 t_2 = 9.0 * (t * (z * y));
	double tmp;
	if (a <= -6.2e+119) {
		tmp = t_1 - t_2;
	} else if (a <= 1.46e-105) {
		tmp = (x * 2.0) - t_2;
	} else {
		tmp = t_1 + (x * 2.0);
	}
	return tmp;
}

Python

[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)
	t_2 = 9.0 * (t * (z * y))
	tmp = 0
	if a <= -6.2e+119:
		tmp = t_1 - t_2
	elif a <= 1.46e-105:
		tmp = (x * 2.0) - t_2
	else:
		tmp = t_1 + (x * 2.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(9.0 * Float64(t * Float64(z * y)))
	tmp = 0.0
	if (a <= -6.2e+119)
		tmp = Float64(t_1 - t_2);
	elseif (a <= 1.46e-105)
		tmp = Float64(Float64(x * 2.0) - t_2);
	else
		tmp = Float64(t_1 + Float64(x * 2.0));
	end
	return tmp
end

MATLAB

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);
	t_2 = 9.0 * (t * (z * y));
	tmp = 0.0;
	if (a <= -6.2e+119)
		tmp = t_1 - t_2;
	elseif (a <= 1.46e-105)
		tmp = (x * 2.0) - t_2;
	else
		tmp = t_1 + (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e+119], N[(t$95$1 - t$95$2), $MachinePrecision], If[LessEqual[a, 1.46e-105], N[(N[(x * 2.0), $MachinePrecision] - t$95$2), $MachinePrecision], N[(t$95$1 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.1999999999999999e119

   1. Initial program 85.1%

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

      1. sub-neg 85.1%

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

      2. sub-neg 85.1%

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

      3. associate-*l* 88.2%

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

      4. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around 0 78.8%

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

   if -6.1999999999999999e119 < a < 1.45999999999999998e-105

   1. Initial program 96.5%

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

      1. sub-neg 96.5%

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

      2. sub-neg 96.5%

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

      3. associate-*l* 95.2%

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

      4. associate-*l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in a around 0 84.5%

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

   if 1.45999999999999998e-105 < a

   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. Step-by-step derivation

      1. sub-neg 93.9%

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

      2. sub-neg 93.9%

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

      3. associate-*l* 89.0%

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

      4. associate-*l* 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in y around 0 66.8%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+119}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-105}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 45.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+110} \lor \neg \left(a \leq 9 \cdot 10^{-60}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.9e+110) (not (<= a 9e-60))) (* 27.0 (* a b)) (* x 2.0)))

C

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 ((a <= -1.9e+110) || !(a <= 9e-60)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 ((a <= (-1.9d+110)) .or. (.not. (a <= 9d-60))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.9e+110) || !(a <= 9e-60)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.9e+110) or not (a <= 9e-60):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.9e+110) || !(a <= 9e-60))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.9e+110) || ~((a <= 9e-60)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.9e+110], N[Not[LessEqual[a, 9e-60]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.89999999999999994e110 or 9.00000000000000001e-60 < a

   1. Initial program 90.5%

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

      1. sub-neg 90.5%

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

      2. sub-neg 90.5%

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

      3. associate-*l* 88.6%

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

      4. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around inf 47.0%

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

   if -1.89999999999999994e110 < a < 9.00000000000000001e-60

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. sub-neg 96.7%

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

      3. associate-*l* 94.8%

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

      4. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in x around inf 43.7%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+110} \lor \neg \left(a \leq 9 \cdot 10^{-60}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.0% accurate, 5.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ x \cdot 2 \end{array} \]

FPCore

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

C

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.
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;
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])
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])
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])){:}
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.
code[x_, y_, z_, t_, a_, b_] := N[(x * 2.0), $MachinePrecision]

Derivation

1. Initial program 94.2%

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

   1. sub-neg 94.2%

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

   2. sub-neg 94.2%

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

   3. associate-*l* 92.3%

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

   4. associate-*l* 92.7%

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

3. Simplified 92.7%

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

5. Taylor expanded in x around inf 35.2%

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

6. Final simplification 35.2%

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

Developer target: 94.9% 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 2024079 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (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)))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))