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

Percentage Accurate: 95.3% → 98.3%

Time: 15.3s

Alternatives: 19

Speedup: 0.8×

• 27.9% 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: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -5 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= (* y 9.0) -5e+172)
   (* y (- (+ (* 2.0 (/ x y)) (* 27.0 (/ (* a b) y))) (* 9.0 (* t z))))
   (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 ((y * 9.0) <= -5e+172) {
		tmp = y * (((2.0 * (x / y)) + (27.0 * ((a * b) / y))) - (9.0 * (t * z)));
	} 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 (Float64(y * 9.0) <= -5e+172)
		tmp = Float64(y * Float64(Float64(Float64(2.0 * Float64(x / y)) + Float64(27.0 * Float64(Float64(a * b) / y))) - Float64(9.0 * Float64(t * z))));
	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[N[(y * 9.0), $MachinePrecision], -5e+172], N[(y * N[(N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(t * z), $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 (*.f64 y #s(literal 9 binary64)) < -5.0000000000000001e172

   1. Initial program 71.5%

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

      1. associate-+l- 71.5%

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

      2. *-commutative 71.5%

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

      3. *-commutative 71.5%

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

      4. associate-*l* 71.6%

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

      5. associate-+l- 71.6%

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

      6. associate-*l* 71.5%

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

      7. *-commutative 71.5%

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

      8. *-commutative 71.5%

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

      9. associate-*l* 97.1%

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

      10. associate-*l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in y around inf 97.1%

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

   if -5.0000000000000001e172 < (*.f64 y #s(literal 9 binary64))

   1. Initial program 93.7%

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

      1. +-commutative 93.7%

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

      2. associate-+r- 93.7%

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

      3. *-commutative 93.7%

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

      4. cancel-sign-sub-inv 93.7%

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

      5. associate-*r* 93.3%

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

      6. distribute-lft-neg-in 93.3%

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

      7. *-commutative 93.3%

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

      8. cancel-sign-sub-inv 93.3%

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

      9. associate-+r- 93.3%

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

      10. associate-*l* 93.7%

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

      11. fma-define 94.2%

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

      12. cancel-sign-sub-inv 94.2%

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

      13. fma-define 94.2%

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

      14. *-commutative 94.2%

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

      15. distribute-rgt-neg-in 94.2%

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

      16. distribute-lft-neg-out 94.2%

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

      17. associate-*r* 94.5%

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

      18. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -5 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + b \cdot \left(27 \cdot a\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 350000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

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 (+ (* y (* t (* z -9.0))) (* b (* 27.0 a)))))
   (if (<= z -2.5e-40)
     t_1
     (if (<= z 5.2e-58)
       (+ (* 2.0 x) (* 27.0 (* a b)))
       (if (<= z 350000000.0) t_1 (- (* 2.0 x) (* 9.0 (* t (* y z)))))))))

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 = (y * (t * (z * -9.0))) + (b * (27.0 * a));
	double tmp;
	if (z <= -2.5e-40) {
		tmp = t_1;
	} else if (z <= 5.2e-58) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} else if (z <= 350000000.0) {
		tmp = t_1;
	} else {
		tmp = (2.0 * x) - (9.0 * (t * (y * z)));
	}
	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 = (y * (t * (z * (-9.0d0)))) + (b * (27.0d0 * a))
    if (z <= (-2.5d-40)) then
        tmp = t_1
    else if (z <= 5.2d-58) then
        tmp = (2.0d0 * x) + (27.0d0 * (a * b))
    else if (z <= 350000000.0d0) then
        tmp = t_1
    else
        tmp = (2.0d0 * x) - (9.0d0 * (t * (y * z)))
    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 = (y * (t * (z * -9.0))) + (b * (27.0 * a));
	double tmp;
	if (z <= -2.5e-40) {
		tmp = t_1;
	} else if (z <= 5.2e-58) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} else if (z <= 350000000.0) {
		tmp = t_1;
	} else {
		tmp = (2.0 * x) - (9.0 * (t * (y * z)));
	}
	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 = (y * (t * (z * -9.0))) + (b * (27.0 * a))
	tmp = 0
	if z <= -2.5e-40:
		tmp = t_1
	elif z <= 5.2e-58:
		tmp = (2.0 * x) + (27.0 * (a * b))
	elif z <= 350000000.0:
		tmp = t_1
	else:
		tmp = (2.0 * x) - (9.0 * (t * (y * z)))
	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(y * Float64(t * Float64(z * -9.0))) + Float64(b * Float64(27.0 * a)))
	tmp = 0.0
	if (z <= -2.5e-40)
		tmp = t_1;
	elseif (z <= 5.2e-58)
		tmp = Float64(Float64(2.0 * x) + Float64(27.0 * Float64(a * b)));
	elseif (z <= 350000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(2.0 * x) - Float64(9.0 * Float64(t * Float64(y * z))));
	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 = (y * (t * (z * -9.0))) + (b * (27.0 * a));
	tmp = 0.0;
	if (z <= -2.5e-40)
		tmp = t_1;
	elseif (z <= 5.2e-58)
		tmp = (2.0 * x) + (27.0 * (a * b));
	elseif (z <= 350000000.0)
		tmp = t_1;
	else
		tmp = (2.0 * x) - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e-40], t$95$1, If[LessEqual[z, 5.2e-58], N[(N[(2.0 * x), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 350000000.0], t$95$1, N[(N[(2.0 * x), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999982e-40 or 5.20000000000000013e-58 < z < 3.5e8

   1. Initial program 88.1%

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

      1. associate-+l- 88.1%

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

      2. *-commutative 88.1%

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

      3. *-commutative 88.1%

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

      4. associate-*l* 88.1%

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

      5. associate-+l- 88.1%

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

      6. associate-*l* 88.1%

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

      7. *-commutative 88.1%

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

      8. *-commutative 88.1%

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

      9. associate-*l* 93.8%

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

      10. 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 x around 0 71.2%

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

      1. sub-neg 71.2%

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

      2. +-commutative 71.2%

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

      3. distribute-lft-neg-in 71.2%

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

      4. metadata-eval 71.2%

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

      5. *-commutative 71.2%

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

      6. associate-*r* 76.0%

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

      7. associate-*l* 76.0%

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

      8. *-commutative 76.0%

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

      9. *-commutative 76.0%

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

      10. associate-*l* 75.9%

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

      11. associate-*r* 75.9%

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

      12. *-commutative 75.9%

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

   7. Applied egg-rr 75.9%

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

   if -2.49999999999999982e-40 < z < 5.20000000000000013e-58

   1. Initial program 97.7%

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

      1. associate-+l- 97.7%

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

      2. *-commutative 97.7%

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

      3. *-commutative 97.7%

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

      4. associate-*l* 97.7%

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

      5. associate-+l- 97.7%

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

      6. associate-*l* 97.7%

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

      7. *-commutative 97.7%

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

      8. *-commutative 97.7%

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

      9. associate-*l* 97.8%

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

      10. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in y around 0 82.5%

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

   if 3.5e8 < z

   1. Initial program 84.5%

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

      1. associate-+l- 84.5%

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

      2. *-commutative 84.5%

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

      3. *-commutative 84.5%

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

      4. associate-*l* 84.5%

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

      5. associate-+l- 84.5%

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

      6. associate-*l* 84.5%

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

      7. *-commutative 84.5%

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

      8. *-commutative 84.5%

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

      9. associate-*l* 92.7%

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

      10. 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 a around 0 66.5%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 350000000:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -5 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot x - t \cdot \left(\left(y \cdot 9\right) \cdot z\right)\right) + b \cdot \left(27 \cdot a\right)\\ \end{array} \end{array} \]

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) -5e+172)
   (* y (- (+ (* 2.0 (/ x y)) (* 27.0 (/ (* a b) y))) (* 9.0 (* t z))))
   (+ (- (* 2.0 x) (* t (* (* y 9.0) z))) (* b (* 27.0 a)))))

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) <= -5e+172) {
		tmp = y * (((2.0 * (x / y)) + (27.0 * ((a * b) / y))) - (9.0 * (t * z)));
	} else {
		tmp = ((2.0 * x) - (t * ((y * 9.0) * z))) + (b * (27.0 * a));
	}
	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) <= (-5d+172)) then
        tmp = y * (((2.0d0 * (x / y)) + (27.0d0 * ((a * b) / y))) - (9.0d0 * (t * z)))
    else
        tmp = ((2.0d0 * x) - (t * ((y * 9.0d0) * z))) + (b * (27.0d0 * a))
    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) <= -5e+172) {
		tmp = y * (((2.0 * (x / y)) + (27.0 * ((a * b) / y))) - (9.0 * (t * z)));
	} else {
		tmp = ((2.0 * x) - (t * ((y * 9.0) * z))) + (b * (27.0 * a));
	}
	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) <= -5e+172:
		tmp = y * (((2.0 * (x / y)) + (27.0 * ((a * b) / y))) - (9.0 * (t * z)))
	else:
		tmp = ((2.0 * x) - (t * ((y * 9.0) * z))) + (b * (27.0 * a))
	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) <= -5e+172)
		tmp = Float64(y * Float64(Float64(Float64(2.0 * Float64(x / y)) + Float64(27.0 * Float64(Float64(a * b) / y))) - Float64(9.0 * Float64(t * z))));
	else
		tmp = Float64(Float64(Float64(2.0 * x) - Float64(t * Float64(Float64(y * 9.0) * z))) + Float64(b * Float64(27.0 * a)));
	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) <= -5e+172)
		tmp = y * (((2.0 * (x / y)) + (27.0 * ((a * b) / y))) - (9.0 * (t * z)));
	else
		tmp = ((2.0 * x) - (t * ((y * 9.0) * z))) + (b * (27.0 * a));
	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], -5e+172], N[(y * N[(N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 * x), $MachinePrecision] - N[(t * N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y #s(literal 9 binary64)) < -5.0000000000000001e172

   1. Initial program 71.5%

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

      1. associate-+l- 71.5%

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

      2. *-commutative 71.5%

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

      3. *-commutative 71.5%

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

      4. associate-*l* 71.6%

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

      5. associate-+l- 71.6%

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

      6. associate-*l* 71.5%

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

      7. *-commutative 71.5%

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

      8. *-commutative 71.5%

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

      9. associate-*l* 97.1%

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

      10. associate-*l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in y around inf 97.1%

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

   if -5.0000000000000001e172 < (*.f64 y #s(literal 9 binary64))

   1. Initial program 93.7%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -5 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot x - t \cdot \left(\left(y \cdot 9\right) \cdot z\right)\right) + b \cdot \left(27 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-242}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-293}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;z \leq 10^{-58}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* -9.0 (* t (* y z)))))
   (if (<= z -3.1e-40)
     t_1
     (if (<= z -8.5e-242)
       (* 2.0 x)
       (if (<= z -1.5e-293)
         (* b (* 27.0 a))
         (if (<= z 1e-58) (* 2.0 x) 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 = -9.0 * (t * (y * z));
	double tmp;
	if (z <= -3.1e-40) {
		tmp = t_1;
	} else if (z <= -8.5e-242) {
		tmp = 2.0 * x;
	} else if (z <= -1.5e-293) {
		tmp = b * (27.0 * a);
	} else if (z <= 1e-58) {
		tmp = 2.0 * x;
	} 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) :: tmp
    t_1 = (-9.0d0) * (t * (y * z))
    if (z <= (-3.1d-40)) then
        tmp = t_1
    else if (z <= (-8.5d-242)) then
        tmp = 2.0d0 * x
    else if (z <= (-1.5d-293)) then
        tmp = b * (27.0d0 * a)
    else if (z <= 1d-58) then
        tmp = 2.0d0 * x
    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 = -9.0 * (t * (y * z));
	double tmp;
	if (z <= -3.1e-40) {
		tmp = t_1;
	} else if (z <= -8.5e-242) {
		tmp = 2.0 * x;
	} else if (z <= -1.5e-293) {
		tmp = b * (27.0 * a);
	} else if (z <= 1e-58) {
		tmp = 2.0 * x;
	} 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 = -9.0 * (t * (y * z))
	tmp = 0
	if z <= -3.1e-40:
		tmp = t_1
	elif z <= -8.5e-242:
		tmp = 2.0 * x
	elif z <= -1.5e-293:
		tmp = b * (27.0 * a)
	elif z <= 1e-58:
		tmp = 2.0 * x
	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(-9.0 * Float64(t * Float64(y * z)))
	tmp = 0.0
	if (z <= -3.1e-40)
		tmp = t_1;
	elseif (z <= -8.5e-242)
		tmp = Float64(2.0 * x);
	elseif (z <= -1.5e-293)
		tmp = Float64(b * Float64(27.0 * a));
	elseif (z <= 1e-58)
		tmp = Float64(2.0 * x);
	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 = -9.0 * (t * (y * z));
	tmp = 0.0;
	if (z <= -3.1e-40)
		tmp = t_1;
	elseif (z <= -8.5e-242)
		tmp = 2.0 * x;
	elseif (z <= -1.5e-293)
		tmp = b * (27.0 * a);
	elseif (z <= 1e-58)
		tmp = 2.0 * x;
	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[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e-40], t$95$1, If[LessEqual[z, -8.5e-242], N[(2.0 * x), $MachinePrecision], If[LessEqual[z, -1.5e-293], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-58], N[(2.0 * x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.10000000000000011e-40 or 1e-58 < z

   1. Initial program 86.6%

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

      1. associate-+l- 86.6%

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

      2. *-commutative 86.6%

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

      3. *-commutative 86.6%

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

      4. associate-*l* 86.6%

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

      5. associate-+l- 86.6%

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

      6. associate-*l* 86.6%

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

      7. *-commutative 86.6%

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

      8. *-commutative 86.6%

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

      9. associate-*l* 93.4%

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

      10. 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 inf 45.3%

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

   if -3.10000000000000011e-40 < z < -8.4999999999999997e-242 or -1.5000000000000001e-293 < z < 1e-58

   1. Initial program 97.6%

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

      1. associate-+l- 97.6%

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

      2. *-commutative 97.6%

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

      3. *-commutative 97.6%

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

      4. associate-*l* 97.6%

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

      5. associate-+l- 97.6%

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

      6. associate-*l* 97.6%

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

      7. *-commutative 97.6%

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

      8. *-commutative 97.6%

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

      9. associate-*l* 97.7%

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

      10. associate-*l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around inf 51.5%

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

   if -8.4999999999999997e-242 < z < -1.5000000000000001e-293

   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. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*l* 100.0%

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

      5. associate-+l- 100.0%

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

      6. associate-*l* 100.0%

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

      7. *-commutative 100.0%

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

      8. *-commutative 100.0%

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

      9. associate-*l* 100.0%

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

      10. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 75.1%

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

      1. associate-*r* 75.8%

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

   7. Simplified 75.8%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-40}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-242}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-293}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;z \leq 10^{-58}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-241}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-291}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* t (* -9.0 (* y z)))))
   (if (<= z -5e-40)
     t_1
     (if (<= z -1.16e-241)
       (* 2.0 x)
       (if (<= z -1.9e-291)
         (* b (* 27.0 a))
         (if (<= z 3.4e-58) (* 2.0 x) 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 = t * (-9.0 * (y * z));
	double tmp;
	if (z <= -5e-40) {
		tmp = t_1;
	} else if (z <= -1.16e-241) {
		tmp = 2.0 * x;
	} else if (z <= -1.9e-291) {
		tmp = b * (27.0 * a);
	} else if (z <= 3.4e-58) {
		tmp = 2.0 * x;
	} 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) :: tmp
    t_1 = t * ((-9.0d0) * (y * z))
    if (z <= (-5d-40)) then
        tmp = t_1
    else if (z <= (-1.16d-241)) then
        tmp = 2.0d0 * x
    else if (z <= (-1.9d-291)) then
        tmp = b * (27.0d0 * a)
    else if (z <= 3.4d-58) then
        tmp = 2.0d0 * x
    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 = t * (-9.0 * (y * z));
	double tmp;
	if (z <= -5e-40) {
		tmp = t_1;
	} else if (z <= -1.16e-241) {
		tmp = 2.0 * x;
	} else if (z <= -1.9e-291) {
		tmp = b * (27.0 * a);
	} else if (z <= 3.4e-58) {
		tmp = 2.0 * x;
	} 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 = t * (-9.0 * (y * z))
	tmp = 0
	if z <= -5e-40:
		tmp = t_1
	elif z <= -1.16e-241:
		tmp = 2.0 * x
	elif z <= -1.9e-291:
		tmp = b * (27.0 * a)
	elif z <= 3.4e-58:
		tmp = 2.0 * x
	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(t * Float64(-9.0 * Float64(y * z)))
	tmp = 0.0
	if (z <= -5e-40)
		tmp = t_1;
	elseif (z <= -1.16e-241)
		tmp = Float64(2.0 * x);
	elseif (z <= -1.9e-291)
		tmp = Float64(b * Float64(27.0 * a));
	elseif (z <= 3.4e-58)
		tmp = Float64(2.0 * x);
	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 = t * (-9.0 * (y * z));
	tmp = 0.0;
	if (z <= -5e-40)
		tmp = t_1;
	elseif (z <= -1.16e-241)
		tmp = 2.0 * x;
	elseif (z <= -1.9e-291)
		tmp = b * (27.0 * a);
	elseif (z <= 3.4e-58)
		tmp = 2.0 * x;
	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[(t * N[(-9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e-40], t$95$1, If[LessEqual[z, -1.16e-241], N[(2.0 * x), $MachinePrecision], If[LessEqual[z, -1.9e-291], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-58], N[(2.0 * x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.99999999999999965e-40 or 3.39999999999999973e-58 < z

   1. Initial program 86.6%

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

   3. Taylor expanded in y around 0 86.6%

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

   4. Taylor expanded in y around inf 45.3%

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

      1. *-commutative 45.3%

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

      2. associate-*l* 45.3%

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

      3. associate-*l* 45.3%

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

   6. Simplified 45.3%

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

   7. Taylor expanded in y around 0 45.3%

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

   if -4.99999999999999965e-40 < z < -1.16e-241 or -1.8999999999999999e-291 < z < 3.39999999999999973e-58

   1. Initial program 97.6%

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

      1. associate-+l- 97.6%

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

      2. *-commutative 97.6%

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

      3. *-commutative 97.6%

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

      4. associate-*l* 97.6%

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

      5. associate-+l- 97.6%

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

      6. associate-*l* 97.6%

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

      7. *-commutative 97.6%

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

      8. *-commutative 97.6%

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

      9. associate-*l* 97.7%

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

      10. associate-*l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around inf 51.5%

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

   if -1.16e-241 < z < -1.8999999999999999e-291

   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. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*l* 100.0%

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

      5. associate-+l- 100.0%

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

      6. associate-*l* 100.0%

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

      7. *-commutative 100.0%

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

      8. *-commutative 100.0%

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

      9. associate-*l* 100.0%

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

      10. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 75.1%

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

      1. associate-*r* 75.8%

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

   7. Simplified 75.8%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-241}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-291}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-242}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-290}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* t (* y (* z -9.0)))))
   (if (<= z -2.8e-40)
     t_1
     (if (<= z -4.8e-242)
       (* 2.0 x)
       (if (<= z -1.12e-290)
         (* b (* 27.0 a))
         (if (<= z 1.85e-58) (* 2.0 x) 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 = t * (y * (z * -9.0));
	double tmp;
	if (z <= -2.8e-40) {
		tmp = t_1;
	} else if (z <= -4.8e-242) {
		tmp = 2.0 * x;
	} else if (z <= -1.12e-290) {
		tmp = b * (27.0 * a);
	} else if (z <= 1.85e-58) {
		tmp = 2.0 * x;
	} 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) :: tmp
    t_1 = t * (y * (z * (-9.0d0)))
    if (z <= (-2.8d-40)) then
        tmp = t_1
    else if (z <= (-4.8d-242)) then
        tmp = 2.0d0 * x
    else if (z <= (-1.12d-290)) then
        tmp = b * (27.0d0 * a)
    else if (z <= 1.85d-58) then
        tmp = 2.0d0 * x
    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 = t * (y * (z * -9.0));
	double tmp;
	if (z <= -2.8e-40) {
		tmp = t_1;
	} else if (z <= -4.8e-242) {
		tmp = 2.0 * x;
	} else if (z <= -1.12e-290) {
		tmp = b * (27.0 * a);
	} else if (z <= 1.85e-58) {
		tmp = 2.0 * x;
	} 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 = t * (y * (z * -9.0))
	tmp = 0
	if z <= -2.8e-40:
		tmp = t_1
	elif z <= -4.8e-242:
		tmp = 2.0 * x
	elif z <= -1.12e-290:
		tmp = b * (27.0 * a)
	elif z <= 1.85e-58:
		tmp = 2.0 * x
	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(t * Float64(y * Float64(z * -9.0)))
	tmp = 0.0
	if (z <= -2.8e-40)
		tmp = t_1;
	elseif (z <= -4.8e-242)
		tmp = Float64(2.0 * x);
	elseif (z <= -1.12e-290)
		tmp = Float64(b * Float64(27.0 * a));
	elseif (z <= 1.85e-58)
		tmp = Float64(2.0 * x);
	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 = t * (y * (z * -9.0));
	tmp = 0.0;
	if (z <= -2.8e-40)
		tmp = t_1;
	elseif (z <= -4.8e-242)
		tmp = 2.0 * x;
	elseif (z <= -1.12e-290)
		tmp = b * (27.0 * a);
	elseif (z <= 1.85e-58)
		tmp = 2.0 * x;
	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[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e-40], t$95$1, If[LessEqual[z, -4.8e-242], N[(2.0 * x), $MachinePrecision], If[LessEqual[z, -1.12e-290], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-58], N[(2.0 * x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e-40 or 1.8500000000000001e-58 < z

   1. Initial program 86.6%

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

   3. Taylor expanded in y around 0 86.6%

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

   4. Taylor expanded in y around inf 45.3%

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

      1. *-commutative 45.3%

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

      2. associate-*l* 45.3%

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

      3. associate-*l* 45.3%

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

   6. Simplified 45.3%

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

   if -2.8e-40 < z < -4.8000000000000002e-242 or -1.12e-290 < z < 1.8500000000000001e-58

   1. Initial program 97.6%

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

      1. associate-+l- 97.6%

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

      2. *-commutative 97.6%

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

      3. *-commutative 97.6%

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

      4. associate-*l* 97.6%

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

      5. associate-+l- 97.6%

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

      6. associate-*l* 97.6%

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

      7. *-commutative 97.6%

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

      8. *-commutative 97.6%

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

      9. associate-*l* 97.7%

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

      10. associate-*l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around inf 51.5%

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

   if -4.8000000000000002e-242 < z < -1.12e-290

   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. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*l* 100.0%

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

      5. associate-+l- 100.0%

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

      6. associate-*l* 100.0%

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

      7. *-commutative 100.0%

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

      8. *-commutative 100.0%

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

      9. associate-*l* 100.0%

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

      10. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 75.1%

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

      1. associate-*r* 75.8%

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

   7. Simplified 75.8%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-242}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-290}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(\left(t \cdot z\right) \cdot -9\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-241}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-291}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

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 (<= z -3.4e-40)
   (* y (* (* t z) -9.0))
   (if (<= z -1.16e-241)
     (* 2.0 x)
     (if (<= z -3e-291)
       (* b (* 27.0 a))
       (if (<= z 4.6e-58) (* 2.0 x) (* 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 <= -3.4e-40) {
		tmp = y * ((t * z) * -9.0);
	} else if (z <= -1.16e-241) {
		tmp = 2.0 * x;
	} else if (z <= -3e-291) {
		tmp = b * (27.0 * a);
	} else if (z <= 4.6e-58) {
		tmp = 2.0 * x;
	} 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 (z <= (-3.4d-40)) then
        tmp = y * ((t * z) * (-9.0d0))
    else if (z <= (-1.16d-241)) then
        tmp = 2.0d0 * x
    else if (z <= (-3d-291)) then
        tmp = b * (27.0d0 * a)
    else if (z <= 4.6d-58) then
        tmp = 2.0d0 * x
    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 (z <= -3.4e-40) {
		tmp = y * ((t * z) * -9.0);
	} else if (z <= -1.16e-241) {
		tmp = 2.0 * x;
	} else if (z <= -3e-291) {
		tmp = b * (27.0 * a);
	} else if (z <= 4.6e-58) {
		tmp = 2.0 * x;
	} 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 z <= -3.4e-40:
		tmp = y * ((t * z) * -9.0)
	elif z <= -1.16e-241:
		tmp = 2.0 * x
	elif z <= -3e-291:
		tmp = b * (27.0 * a)
	elif z <= 4.6e-58:
		tmp = 2.0 * x
	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 (z <= -3.4e-40)
		tmp = Float64(y * Float64(Float64(t * z) * -9.0));
	elseif (z <= -1.16e-241)
		tmp = Float64(2.0 * x);
	elseif (z <= -3e-291)
		tmp = Float64(b * Float64(27.0 * a));
	elseif (z <= 4.6e-58)
		tmp = Float64(2.0 * x);
	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 (z <= -3.4e-40)
		tmp = y * ((t * z) * -9.0);
	elseif (z <= -1.16e-241)
		tmp = 2.0 * x;
	elseif (z <= -3e-291)
		tmp = b * (27.0 * a);
	elseif (z <= 4.6e-58)
		tmp = 2.0 * x;
	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[z, -3.4e-40], N[(y * N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.16e-241], N[(2.0 * x), $MachinePrecision], If[LessEqual[z, -3e-291], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e-58], N[(2.0 * x), $MachinePrecision], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.39999999999999984e-40

   1. Initial program 84.7%

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

      1. associate-+l- 84.7%

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

      2. *-commutative 84.7%

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

      3. *-commutative 84.7%

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

      4. associate-*l* 84.7%

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

      5. associate-+l- 84.7%

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

      6. associate-*l* 84.7%

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

      7. *-commutative 84.7%

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

      8. *-commutative 84.7%

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

      9. associate-*l* 92.1%

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

      10. 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. Taylor expanded in y around inf 79.6%

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

   6. Taylor expanded in y around inf 45.9%

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

   if -3.39999999999999984e-40 < z < -1.16e-241 or -3.0000000000000001e-291 < z < 4.5999999999999998e-58

   1. Initial program 97.6%

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

      1. associate-+l- 97.6%

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

      2. *-commutative 97.6%

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

      3. *-commutative 97.6%

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

      4. associate-*l* 97.6%

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

      5. associate-+l- 97.6%

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

      6. associate-*l* 97.6%

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

      7. *-commutative 97.6%

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

      8. *-commutative 97.6%

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

      9. associate-*l* 97.7%

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

      10. associate-*l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around inf 51.5%

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

   if -1.16e-241 < z < -3.0000000000000001e-291

   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. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*l* 100.0%

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

      5. associate-+l- 100.0%

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

      6. associate-*l* 100.0%

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

      7. *-commutative 100.0%

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

      8. *-commutative 100.0%

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

      9. associate-*l* 100.0%

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

      10. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 75.1%

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

      1. associate-*r* 75.8%

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

   7. Simplified 75.8%

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

   if 4.5999999999999998e-58 < z

   1. Initial program 88.2%

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

   3. Taylor expanded in y around 0 88.2%

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

   4. Taylor expanded in y around inf 51.4%

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

      1. *-commutative 51.4%

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

      2. associate-*l* 51.4%

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

      3. associate-*l* 51.4%

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

   6. Simplified 51.4%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(\left(t \cdot z\right) \cdot -9\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-241}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-291}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-241}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-292}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-59}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

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 (<= z -2.5e-40)
   (* y (* z (* t -9.0)))
   (if (<= z -1e-241)
     (* 2.0 x)
     (if (<= z -1.75e-292)
       (* b (* 27.0 a))
       (if (<= z 7e-59) (* 2.0 x) (* 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 <= -2.5e-40) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= -1e-241) {
		tmp = 2.0 * x;
	} else if (z <= -1.75e-292) {
		tmp = b * (27.0 * a);
	} else if (z <= 7e-59) {
		tmp = 2.0 * x;
	} 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 (z <= (-2.5d-40)) then
        tmp = y * (z * (t * (-9.0d0)))
    else if (z <= (-1d-241)) then
        tmp = 2.0d0 * x
    else if (z <= (-1.75d-292)) then
        tmp = b * (27.0d0 * a)
    else if (z <= 7d-59) then
        tmp = 2.0d0 * x
    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 (z <= -2.5e-40) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= -1e-241) {
		tmp = 2.0 * x;
	} else if (z <= -1.75e-292) {
		tmp = b * (27.0 * a);
	} else if (z <= 7e-59) {
		tmp = 2.0 * x;
	} 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 z <= -2.5e-40:
		tmp = y * (z * (t * -9.0))
	elif z <= -1e-241:
		tmp = 2.0 * x
	elif z <= -1.75e-292:
		tmp = b * (27.0 * a)
	elif z <= 7e-59:
		tmp = 2.0 * x
	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 (z <= -2.5e-40)
		tmp = Float64(y * Float64(z * Float64(t * -9.0)));
	elseif (z <= -1e-241)
		tmp = Float64(2.0 * x);
	elseif (z <= -1.75e-292)
		tmp = Float64(b * Float64(27.0 * a));
	elseif (z <= 7e-59)
		tmp = Float64(2.0 * x);
	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 (z <= -2.5e-40)
		tmp = y * (z * (t * -9.0));
	elseif (z <= -1e-241)
		tmp = 2.0 * x;
	elseif (z <= -1.75e-292)
		tmp = b * (27.0 * a);
	elseif (z <= 7e-59)
		tmp = 2.0 * x;
	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[z, -2.5e-40], N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1e-241], N[(2.0 * x), $MachinePrecision], If[LessEqual[z, -1.75e-292], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-59], N[(2.0 * x), $MachinePrecision], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.49999999999999982e-40

   1. Initial program 84.7%

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

      1. associate-+l- 84.7%

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

      2. *-commutative 84.7%

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

      3. *-commutative 84.7%

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

      4. associate-*l* 84.7%

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

      5. associate-+l- 84.7%

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

      6. associate-*l* 84.7%

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

      7. *-commutative 84.7%

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

      8. *-commutative 84.7%

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

      9. associate-*l* 92.1%

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

      10. 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. Taylor expanded in y around inf 79.6%

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

   6. Taylor expanded in y around inf 45.9%

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

      1. *-commutative 45.9%

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

      2. *-commutative 45.9%

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

      3. associate-*r* 45.9%

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

      4. *-commutative 45.9%

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

   8. Simplified 45.9%

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

   if -2.49999999999999982e-40 < z < -9.9999999999999997e-242 or -1.75e-292 < z < 7.0000000000000002e-59

   1. Initial program 97.6%

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

      1. associate-+l- 97.6%

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

      2. *-commutative 97.6%

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

      3. *-commutative 97.6%

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

      4. associate-*l* 97.6%

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

      5. associate-+l- 97.6%

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

      6. associate-*l* 97.6%

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

      7. *-commutative 97.6%

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

      8. *-commutative 97.6%

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

      9. associate-*l* 97.7%

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

      10. associate-*l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around inf 51.5%

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

   if -9.9999999999999997e-242 < z < -1.75e-292

   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. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*l* 100.0%

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

      5. associate-+l- 100.0%

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

      6. associate-*l* 100.0%

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

      7. *-commutative 100.0%

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

      8. *-commutative 100.0%

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

      9. associate-*l* 100.0%

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

      10. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 75.1%

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

      1. associate-*r* 75.8%

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

   7. Simplified 75.8%

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

   if 7.0000000000000002e-59 < z

   1. Initial program 88.2%

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

   3. Taylor expanded in y around 0 88.2%

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

   4. Taylor expanded in y around inf 51.4%

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

      1. *-commutative 51.4%

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

      2. associate-*l* 51.4%

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

      3. associate-*l* 51.4%

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

   6. Simplified 51.4%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-241}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-292}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-59}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 2 \cdot 10^{+285}:\\ \;\;\;\;\left(2 \cdot x - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right) + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(27 \cdot \frac{a \cdot b}{y} - 9 \cdot \left(t \cdot z\right)\right)\\ \end{array} \end{array} \]

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) z) 2e+285)
   (+ (- (* 2.0 x) (* t (* 9.0 (* y z)))) (* b (* 27.0 a)))
   (* y (- (* 27.0 (/ (* a b) y)) (* 9.0 (* t z))))))

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) * z) <= 2e+285) {
		tmp = ((2.0 * x) - (t * (9.0 * (y * z)))) + (b * (27.0 * a));
	} else {
		tmp = y * ((27.0 * ((a * b) / y)) - (9.0 * (t * z)));
	}
	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) * z) <= 2d+285) then
        tmp = ((2.0d0 * x) - (t * (9.0d0 * (y * z)))) + (b * (27.0d0 * a))
    else
        tmp = y * ((27.0d0 * ((a * b) / y)) - (9.0d0 * (t * z)))
    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) * z) <= 2e+285) {
		tmp = ((2.0 * x) - (t * (9.0 * (y * z)))) + (b * (27.0 * a));
	} else {
		tmp = y * ((27.0 * ((a * b) / y)) - (9.0 * (t * z)));
	}
	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) * z) <= 2e+285:
		tmp = ((2.0 * x) - (t * (9.0 * (y * z)))) + (b * (27.0 * a))
	else:
		tmp = y * ((27.0 * ((a * b) / y)) - (9.0 * (t * z)))
	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(Float64(y * 9.0) * z) <= 2e+285)
		tmp = Float64(Float64(Float64(2.0 * x) - Float64(t * Float64(9.0 * Float64(y * z)))) + Float64(b * Float64(27.0 * a)));
	else
		tmp = Float64(y * Float64(Float64(27.0 * Float64(Float64(a * b) / y)) - Float64(9.0 * Float64(t * z))));
	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) * z) <= 2e+285)
		tmp = ((2.0 * x) - (t * (9.0 * (y * z)))) + (b * (27.0 * a));
	else
		tmp = y * ((27.0 * ((a * b) / y)) - (9.0 * (t * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 2e+285], N[(N[(N[(2.0 * x), $MachinePrecision] - N[(t * N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(27.0 * N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 2e285

   1. Initial program 94.8%

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

   3. Taylor expanded in y around 0 94.8%

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

   if 2e285 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 50.6%

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

      1. associate-+l- 50.6%

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

      2. *-commutative 50.6%

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

      3. *-commutative 50.6%

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

      4. associate-*l* 50.6%

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

      5. associate-+l- 50.6%

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

      6. associate-*l* 50.6%

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

      7. *-commutative 50.6%

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

      8. *-commutative 50.6%

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

      9. associate-*l* 95.8%

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

      10. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in y around inf 95.7%

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

   6. Taylor expanded in x around 0 92.0%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 2 \cdot 10^{+285}:\\ \;\;\;\;\left(2 \cdot x - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right) + b \cdot \left(27 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(27 \cdot \frac{a \cdot b}{y} - 9 \cdot \left(t \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-59}:\\ \;\;\;\;2 \cdot x + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

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))))
   (if (<= z -2.5e-40)
     (+ (* y (* t (* z -9.0))) (* b (* 27.0 a)))
     (if (<= z 7.6e-59) (+ (* 2.0 x) t_1) (- t_1 (* 9.0 (* t (* y z))))))))

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 tmp;
	if (z <= -2.5e-40) {
		tmp = (y * (t * (z * -9.0))) + (b * (27.0 * a));
	} else if (z <= 7.6e-59) {
		tmp = (2.0 * x) + t_1;
	} else {
		tmp = t_1 - (9.0 * (t * (y * z)));
	}
	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)
    if (z <= (-2.5d-40)) then
        tmp = (y * (t * (z * (-9.0d0)))) + (b * (27.0d0 * a))
    else if (z <= 7.6d-59) then
        tmp = (2.0d0 * x) + t_1
    else
        tmp = t_1 - (9.0d0 * (t * (y * z)))
    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 tmp;
	if (z <= -2.5e-40) {
		tmp = (y * (t * (z * -9.0))) + (b * (27.0 * a));
	} else if (z <= 7.6e-59) {
		tmp = (2.0 * x) + t_1;
	} else {
		tmp = t_1 - (9.0 * (t * (y * z)));
	}
	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)
	tmp = 0
	if z <= -2.5e-40:
		tmp = (y * (t * (z * -9.0))) + (b * (27.0 * a))
	elif z <= 7.6e-59:
		tmp = (2.0 * x) + t_1
	else:
		tmp = t_1 - (9.0 * (t * (y * z)))
	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))
	tmp = 0.0
	if (z <= -2.5e-40)
		tmp = Float64(Float64(y * Float64(t * Float64(z * -9.0))) + Float64(b * Float64(27.0 * a)));
	elseif (z <= 7.6e-59)
		tmp = Float64(Float64(2.0 * x) + t_1);
	else
		tmp = Float64(t_1 - Float64(9.0 * Float64(t * Float64(y * z))));
	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);
	tmp = 0.0;
	if (z <= -2.5e-40)
		tmp = (y * (t * (z * -9.0))) + (b * (27.0 * a));
	elseif (z <= 7.6e-59)
		tmp = (2.0 * x) + t_1;
	else
		tmp = t_1 - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e-40], N[(N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e-59], N[(N[(2.0 * x), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999982e-40

   1. Initial program 84.7%

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

      1. associate-+l- 84.7%

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

      2. *-commutative 84.7%

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

      3. *-commutative 84.7%

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

      4. associate-*l* 84.7%

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

      5. associate-+l- 84.7%

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

      6. associate-*l* 84.7%

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

      7. *-commutative 84.7%

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

      8. *-commutative 84.7%

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

      9. associate-*l* 92.1%

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

      10. 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. Taylor expanded in x around 0 65.6%

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

      1. sub-neg 65.6%

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

      2. +-commutative 65.6%

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

      3. distribute-lft-neg-in 65.6%

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

      4. metadata-eval 65.6%

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

      5. *-commutative 65.6%

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

      6. associate-*r* 71.7%

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

      7. associate-*l* 71.7%

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

      8. *-commutative 71.7%

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

      9. *-commutative 71.7%

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

      10. associate-*l* 71.7%

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

      11. associate-*r* 71.7%

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

      12. *-commutative 71.7%

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

   7. Applied egg-rr 71.7%

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

   if -2.49999999999999982e-40 < z < 7.59999999999999966e-59

   1. Initial program 97.7%

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

      1. associate-+l- 97.7%

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

      2. *-commutative 97.7%

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

      3. *-commutative 97.7%

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

      4. associate-*l* 97.7%

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

      5. associate-+l- 97.7%

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

      6. associate-*l* 97.7%

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

      7. *-commutative 97.7%

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

      8. *-commutative 97.7%

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

      9. associate-*l* 97.8%

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

      10. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in y around 0 82.5%

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

   if 7.59999999999999966e-59 < z

   1. Initial program 88.2%

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

      1. associate-+l- 88.2%

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

      2. *-commutative 88.2%

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

      3. *-commutative 88.2%

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

      4. associate-*l* 88.2%

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

      5. associate-+l- 88.2%

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

      6. associate-*l* 88.2%

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

      7. *-commutative 88.2%

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

      8. *-commutative 88.2%

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

      9. associate-*l* 94.4%

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

      10. associate-*l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in x around 0 71.2%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-59}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -3.15 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(27 \cdot \frac{a \cdot b}{y} - 9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-59}:\\ \;\;\;\;2 \cdot x + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

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))))
   (if (<= z -3.15e-40)
     (* y (- (* 27.0 (/ (* a b) y)) (* 9.0 (* t z))))
     (if (<= z 7e-59) (+ (* 2.0 x) t_1) (- t_1 (* 9.0 (* t (* y z))))))))

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 tmp;
	if (z <= -3.15e-40) {
		tmp = y * ((27.0 * ((a * b) / y)) - (9.0 * (t * z)));
	} else if (z <= 7e-59) {
		tmp = (2.0 * x) + t_1;
	} else {
		tmp = t_1 - (9.0 * (t * (y * z)));
	}
	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)
    if (z <= (-3.15d-40)) then
        tmp = y * ((27.0d0 * ((a * b) / y)) - (9.0d0 * (t * z)))
    else if (z <= 7d-59) then
        tmp = (2.0d0 * x) + t_1
    else
        tmp = t_1 - (9.0d0 * (t * (y * z)))
    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 tmp;
	if (z <= -3.15e-40) {
		tmp = y * ((27.0 * ((a * b) / y)) - (9.0 * (t * z)));
	} else if (z <= 7e-59) {
		tmp = (2.0 * x) + t_1;
	} else {
		tmp = t_1 - (9.0 * (t * (y * z)));
	}
	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)
	tmp = 0
	if z <= -3.15e-40:
		tmp = y * ((27.0 * ((a * b) / y)) - (9.0 * (t * z)))
	elif z <= 7e-59:
		tmp = (2.0 * x) + t_1
	else:
		tmp = t_1 - (9.0 * (t * (y * z)))
	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))
	tmp = 0.0
	if (z <= -3.15e-40)
		tmp = Float64(y * Float64(Float64(27.0 * Float64(Float64(a * b) / y)) - Float64(9.0 * Float64(t * z))));
	elseif (z <= 7e-59)
		tmp = Float64(Float64(2.0 * x) + t_1);
	else
		tmp = Float64(t_1 - Float64(9.0 * Float64(t * Float64(y * z))));
	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);
	tmp = 0.0;
	if (z <= -3.15e-40)
		tmp = y * ((27.0 * ((a * b) / y)) - (9.0 * (t * z)));
	elseif (z <= 7e-59)
		tmp = (2.0 * x) + t_1;
	else
		tmp = t_1 - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.15e-40], N[(y * N[(N[(27.0 * N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-59], N[(N[(2.0 * x), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1500000000000001e-40

   1. Initial program 84.7%

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

      1. associate-+l- 84.7%

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

      2. *-commutative 84.7%

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

      3. *-commutative 84.7%

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

      4. associate-*l* 84.7%

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

      5. associate-+l- 84.7%

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

      6. associate-*l* 84.7%

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

      7. *-commutative 84.7%

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

      8. *-commutative 84.7%

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

      9. associate-*l* 92.1%

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

      10. 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. Taylor expanded in y around inf 79.6%

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

   6. Taylor expanded in x around 0 67.0%

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

   if -3.1500000000000001e-40 < z < 7.0000000000000002e-59

   1. Initial program 97.7%

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

      1. associate-+l- 97.7%

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

      2. *-commutative 97.7%

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

      3. *-commutative 97.7%

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

      4. associate-*l* 97.7%

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

      5. associate-+l- 97.7%

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

      6. associate-*l* 97.7%

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

      7. *-commutative 97.7%

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

      8. *-commutative 97.7%

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

      9. associate-*l* 97.8%

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

      10. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in y around 0 82.5%

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

   if 7.0000000000000002e-59 < z

   1. Initial program 88.2%

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

      1. associate-+l- 88.2%

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

      2. *-commutative 88.2%

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

      3. *-commutative 88.2%

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

      4. associate-*l* 88.2%

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

      5. associate-+l- 88.2%

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

      6. associate-*l* 88.2%

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

      7. *-commutative 88.2%

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

      8. *-commutative 88.2%

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

      9. associate-*l* 94.4%

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

      10. associate-*l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in x around 0 71.2%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(27 \cdot \frac{a \cdot b}{y} - 9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-59}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 96.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 220000000000:\\ \;\;\;\;\left(2 \cdot x + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

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 220000000000.0)
   (+ (+ (* 2.0 x) (* y (* z (* t -9.0)))) (* a (* 27.0 b)))
   (- (* 2.0 x) (* 9.0 (* t (* y z))))))

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 <= 220000000000.0) {
		tmp = ((2.0 * x) + (y * (z * (t * -9.0)))) + (a * (27.0 * b));
	} else {
		tmp = (2.0 * x) - (9.0 * (t * (y * z)));
	}
	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 <= 220000000000.0d0) then
        tmp = ((2.0d0 * x) + (y * (z * (t * (-9.0d0))))) + (a * (27.0d0 * b))
    else
        tmp = (2.0d0 * x) - (9.0d0 * (t * (y * z)))
    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 <= 220000000000.0) {
		tmp = ((2.0 * x) + (y * (z * (t * -9.0)))) + (a * (27.0 * b));
	} else {
		tmp = (2.0 * x) - (9.0 * (t * (y * z)));
	}
	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 <= 220000000000.0:
		tmp = ((2.0 * x) + (y * (z * (t * -9.0)))) + (a * (27.0 * b))
	else:
		tmp = (2.0 * x) - (9.0 * (t * (y * z)))
	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 <= 220000000000.0)
		tmp = Float64(Float64(Float64(2.0 * x) + Float64(y * Float64(z * Float64(t * -9.0)))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(2.0 * x) - Float64(9.0 * Float64(t * Float64(y * z))));
	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 <= 220000000000.0)
		tmp = ((2.0 * x) + (y * (z * (t * -9.0)))) + (a * (27.0 * b));
	else
		tmp = (2.0 * x) - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 220000000000.0], N[(N[(N[(2.0 * x), $MachinePrecision] + N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.2e11

   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. associate-+l- 92.7%

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

      2. *-commutative 92.7%

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

      3. *-commutative 92.7%

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

      4. associate-*l* 92.7%

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

      5. associate-+l- 92.7%

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

      6. associate-*l* 92.7%

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

      7. *-commutative 92.7%

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

      8. *-commutative 92.7%

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

      9. associate-*l* 95.7%

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

      10. associate-*l* 96.1%

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

   3. Simplified 96.1%

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

      1. sub-neg 96.1%

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

      2. *-commutative 96.1%

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

      3. distribute-rgt-neg-in 96.1%

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

      4. *-commutative 96.1%

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

      5. distribute-lft-neg-in 96.1%

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

      6. metadata-eval 96.1%

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

      7. associate-*l* 96.1%

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

      8. associate-*r* 95.6%

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

      9. *-commutative 95.6%

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

   6. Applied egg-rr 95.6%

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

   if 2.2e11 < z

   1. Initial program 84.5%

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

      1. associate-+l- 84.5%

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

      2. *-commutative 84.5%

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

      3. *-commutative 84.5%

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

      4. associate-*l* 84.5%

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

      5. associate-+l- 84.5%

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

      6. associate-*l* 84.5%

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

      7. *-commutative 84.5%

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

      8. *-commutative 84.5%

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

      9. associate-*l* 92.7%

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

      10. 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 a around 0 66.5%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 220000000000:\\ \;\;\;\;\left(2 \cdot x + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 76.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-72}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

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 -4e-40)
   (* y (* z (* t -9.0)))
   (if (<= z 1.85e-72)
     (+ (* 2.0 x) (* 27.0 (* a b)))
     (- (* 2.0 x) (* 9.0 (* t (* y z)))))))

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 <= -4e-40) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 1.85e-72) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} else {
		tmp = (2.0 * x) - (9.0 * (t * (y * z)));
	}
	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 <= (-4d-40)) then
        tmp = y * (z * (t * (-9.0d0)))
    else if (z <= 1.85d-72) then
        tmp = (2.0d0 * x) + (27.0d0 * (a * b))
    else
        tmp = (2.0d0 * x) - (9.0d0 * (t * (y * z)))
    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 <= -4e-40) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 1.85e-72) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} else {
		tmp = (2.0 * x) - (9.0 * (t * (y * z)));
	}
	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 <= -4e-40:
		tmp = y * (z * (t * -9.0))
	elif z <= 1.85e-72:
		tmp = (2.0 * x) + (27.0 * (a * b))
	else:
		tmp = (2.0 * x) - (9.0 * (t * (y * z)))
	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 <= -4e-40)
		tmp = Float64(y * Float64(z * Float64(t * -9.0)));
	elseif (z <= 1.85e-72)
		tmp = Float64(Float64(2.0 * x) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(2.0 * x) - Float64(9.0 * Float64(t * Float64(y * z))));
	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 <= -4e-40)
		tmp = y * (z * (t * -9.0));
	elseif (z <= 1.85e-72)
		tmp = (2.0 * x) + (27.0 * (a * b));
	else
		tmp = (2.0 * x) - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4e-40], N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-72], N[(N[(2.0 * x), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9999999999999997e-40

   1. Initial program 84.7%

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

      1. associate-+l- 84.7%

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

      2. *-commutative 84.7%

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

      3. *-commutative 84.7%

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

      4. associate-*l* 84.7%

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

      5. associate-+l- 84.7%

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

      6. associate-*l* 84.7%

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

      7. *-commutative 84.7%

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

      8. *-commutative 84.7%

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

      9. associate-*l* 92.1%

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

      10. 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. Taylor expanded in y around inf 79.6%

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

   6. Taylor expanded in y around inf 45.9%

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

      1. *-commutative 45.9%

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

      2. *-commutative 45.9%

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

      3. associate-*r* 45.9%

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

      4. *-commutative 45.9%

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

   8. Simplified 45.9%

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

   if -3.9999999999999997e-40 < z < 1.8499999999999999e-72

   1. Initial program 97.7%

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

      1. associate-+l- 97.7%

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

      2. *-commutative 97.7%

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

      3. *-commutative 97.7%

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

      4. associate-*l* 97.7%

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

      5. associate-+l- 97.7%

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

      6. associate-*l* 97.7%

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

      7. *-commutative 97.7%

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

      8. *-commutative 97.7%

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

      9. associate-*l* 97.7%

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

      10. associate-*l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around 0 82.3%

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

   if 1.8499999999999999e-72 < z

   1. Initial program 88.3%

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

      1. associate-+l- 88.3%

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

      2. *-commutative 88.3%

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

      3. *-commutative 88.3%

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

      4. associate-*l* 88.3%

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

      5. associate-+l- 88.3%

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

      6. associate-*l* 88.3%

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

      7. *-commutative 88.3%

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

      8. *-commutative 88.3%

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

      9. associate-*l* 94.5%

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

      10. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in a around 0 68.8%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-72}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(2 \cdot \frac{x}{y} + z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-69}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

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 -4.6e-40)
   (* y (+ (* 2.0 (/ x y)) (* z (* t -9.0))))
   (if (<= z 1.02e-69)
     (+ (* 2.0 x) (* 27.0 (* a b)))
     (- (* 2.0 x) (* 9.0 (* t (* y z)))))))

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 <= -4.6e-40) {
		tmp = y * ((2.0 * (x / y)) + (z * (t * -9.0)));
	} else if (z <= 1.02e-69) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} else {
		tmp = (2.0 * x) - (9.0 * (t * (y * z)));
	}
	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 <= (-4.6d-40)) then
        tmp = y * ((2.0d0 * (x / y)) + (z * (t * (-9.0d0))))
    else if (z <= 1.02d-69) then
        tmp = (2.0d0 * x) + (27.0d0 * (a * b))
    else
        tmp = (2.0d0 * x) - (9.0d0 * (t * (y * z)))
    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 <= -4.6e-40) {
		tmp = y * ((2.0 * (x / y)) + (z * (t * -9.0)));
	} else if (z <= 1.02e-69) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} else {
		tmp = (2.0 * x) - (9.0 * (t * (y * z)));
	}
	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 <= -4.6e-40:
		tmp = y * ((2.0 * (x / y)) + (z * (t * -9.0)))
	elif z <= 1.02e-69:
		tmp = (2.0 * x) + (27.0 * (a * b))
	else:
		tmp = (2.0 * x) - (9.0 * (t * (y * z)))
	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 <= -4.6e-40)
		tmp = Float64(y * Float64(Float64(2.0 * Float64(x / y)) + Float64(z * Float64(t * -9.0))));
	elseif (z <= 1.02e-69)
		tmp = Float64(Float64(2.0 * x) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(2.0 * x) - Float64(9.0 * Float64(t * Float64(y * z))));
	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 <= -4.6e-40)
		tmp = y * ((2.0 * (x / y)) + (z * (t * -9.0)));
	elseif (z <= 1.02e-69)
		tmp = (2.0 * x) + (27.0 * (a * b));
	else
		tmp = (2.0 * x) - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.6e-40], N[(y * N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-69], N[(N[(2.0 * x), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6e-40

   1. Initial program 84.7%

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

      1. associate-+l- 84.7%

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

      2. *-commutative 84.7%

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

      3. *-commutative 84.7%

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

      4. associate-*l* 84.7%

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

      5. associate-+l- 84.7%

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

      6. associate-*l* 84.7%

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

      7. *-commutative 84.7%

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

      8. *-commutative 84.7%

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

      9. associate-*l* 92.1%

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

      10. 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. Taylor expanded in a around 0 55.9%

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

   6. Taylor expanded in y around inf 60.3%

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

      1. cancel-sign-sub-inv 60.3%

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

      2. metadata-eval 60.3%

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

      3. associate-*r* 60.3%

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

   8. Simplified 60.3%

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

   if -4.6e-40 < z < 1.02000000000000005e-69

   1. Initial program 97.7%

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

      1. associate-+l- 97.7%

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

      2. *-commutative 97.7%

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

      3. *-commutative 97.7%

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

      4. associate-*l* 97.7%

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

      5. associate-+l- 97.7%

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

      6. associate-*l* 97.7%

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

      7. *-commutative 97.7%

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

      8. *-commutative 97.7%

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

      9. associate-*l* 97.7%

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

      10. associate-*l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around 0 82.3%

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

   if 1.02000000000000005e-69 < z

   1. Initial program 88.3%

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

      1. associate-+l- 88.3%

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

      2. *-commutative 88.3%

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

      3. *-commutative 88.3%

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

      4. associate-*l* 88.3%

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

      5. associate-+l- 88.3%

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

      6. associate-*l* 88.3%

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

      7. *-commutative 88.3%

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

      8. *-commutative 88.3%

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

      9. associate-*l* 94.5%

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

      10. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in a around 0 68.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(2 \cdot \frac{x}{y} + z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-69}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 73.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

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 (<= z -4.6e-40)
   (* y (* z (* t -9.0)))
   (if (<= z 9.5e-58) (+ (* 2.0 x) (* 27.0 (* a b))) (* 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 <= -4.6e-40) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 9.5e-58) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} 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 (z <= (-4.6d-40)) then
        tmp = y * (z * (t * (-9.0d0)))
    else if (z <= 9.5d-58) then
        tmp = (2.0d0 * x) + (27.0d0 * (a * b))
    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 (z <= -4.6e-40) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 9.5e-58) {
		tmp = (2.0 * x) + (27.0 * (a * b));
	} 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 z <= -4.6e-40:
		tmp = y * (z * (t * -9.0))
	elif z <= 9.5e-58:
		tmp = (2.0 * x) + (27.0 * (a * b))
	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 (z <= -4.6e-40)
		tmp = Float64(y * Float64(z * Float64(t * -9.0)));
	elseif (z <= 9.5e-58)
		tmp = Float64(Float64(2.0 * x) + Float64(27.0 * Float64(a * b)));
	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 (z <= -4.6e-40)
		tmp = y * (z * (t * -9.0));
	elseif (z <= 9.5e-58)
		tmp = (2.0 * x) + (27.0 * (a * b));
	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[z, -4.6e-40], N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-58], N[(N[(2.0 * x), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6e-40

   1. Initial program 84.7%

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

      1. associate-+l- 84.7%

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

      2. *-commutative 84.7%

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

      3. *-commutative 84.7%

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

      4. associate-*l* 84.7%

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

      5. associate-+l- 84.7%

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

      6. associate-*l* 84.7%

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

      7. *-commutative 84.7%

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

      8. *-commutative 84.7%

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

      9. associate-*l* 92.1%

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

      10. 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. Taylor expanded in y around inf 79.6%

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

   6. Taylor expanded in y around inf 45.9%

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

      1. *-commutative 45.9%

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

      2. *-commutative 45.9%

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

      3. associate-*r* 45.9%

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

      4. *-commutative 45.9%

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

   8. Simplified 45.9%

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

   if -4.6e-40 < z < 9.4999999999999994e-58

   1. Initial program 97.7%

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

      1. associate-+l- 97.7%

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

      2. *-commutative 97.7%

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

      3. *-commutative 97.7%

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

      4. associate-*l* 97.7%

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

      5. associate-+l- 97.7%

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

      6. associate-*l* 97.7%

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

      7. *-commutative 97.7%

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

      8. *-commutative 97.7%

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

      9. associate-*l* 97.8%

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

      10. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in y around 0 82.5%

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

   if 9.4999999999999994e-58 < z

   1. Initial program 88.2%

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

   3. Taylor expanded in y around 0 88.2%

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

   4. Taylor expanded in y around inf 51.4%

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

      1. *-commutative 51.4%

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

      2. associate-*l* 51.4%

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

      3. associate-*l* 51.4%

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

   6. Simplified 51.4%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 44.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+125} \lor \neg \left(a \leq 1.5 \cdot 10^{-100}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4e+125) (not (<= a 1.5e-100))) (* 27.0 (* a b)) (* 2.0 x)))

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 <= -4e+125) || !(a <= 1.5e-100)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 <= (-4d+125)) .or. (.not. (a <= 1.5d-100))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = 2.0d0 * x
    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 <= -4e+125) || !(a <= 1.5e-100)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = 2.0 * x;
	}
	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 <= -4e+125) or not (a <= 1.5e-100):
		tmp = 27.0 * (a * b)
	else:
		tmp = 2.0 * x
	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 <= -4e+125) || !(a <= 1.5e-100))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(2.0 * x);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -4e+125) || ~((a <= 1.5e-100)))
		tmp = 27.0 * (a * b);
	else
		tmp = 2.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4e+125], N[Not[LessEqual[a, 1.5e-100]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(2.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.9999999999999997e125 or 1.5e-100 < a

   1. Initial program 85.9%

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

      1. associate-+l- 85.9%

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

      2. *-commutative 85.9%

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

      3. *-commutative 85.9%

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

      4. associate-*l* 85.9%

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

      5. associate-+l- 85.9%

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

      6. associate-*l* 85.9%

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

      7. *-commutative 85.9%

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

      8. *-commutative 85.9%

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

      9. associate-*l* 92.2%

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

      10. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in a around inf 44.0%

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

   if -3.9999999999999997e125 < a < 1.5e-100

   1. Initial program 94.3%

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

      1. associate-+l- 94.3%

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

      2. *-commutative 94.3%

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

      3. *-commutative 94.3%

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

      4. associate-*l* 94.3%

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

      5. associate-+l- 94.3%

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

      6. associate-*l* 94.3%

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

      7. *-commutative 94.3%

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

      8. *-commutative 94.3%

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

      9. associate-*l* 97.1%

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

      10. associate-*l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in x around inf 39.4%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+125} \lor \neg \left(a \leq 1.5 \cdot 10^{-100}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 44.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+126} \lor \neg \left(a \leq 2.1 \cdot 10^{-108}\right):\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.1e+126) (not (<= a 2.1e-108))) (* a (* 27.0 b)) (* 2.0 x)))

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 <= -1.1e+126) || !(a <= 2.1e-108)) {
		tmp = a * (27.0 * b);
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 <= (-1.1d+126)) .or. (.not. (a <= 2.1d-108))) then
        tmp = a * (27.0d0 * b)
    else
        tmp = 2.0d0 * x
    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 <= -1.1e+126) || !(a <= 2.1e-108)) {
		tmp = a * (27.0 * b);
	} else {
		tmp = 2.0 * x;
	}
	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 <= -1.1e+126) or not (a <= 2.1e-108):
		tmp = a * (27.0 * b)
	else:
		tmp = 2.0 * x
	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 <= -1.1e+126) || !(a <= 2.1e-108))
		tmp = Float64(a * Float64(27.0 * b));
	else
		tmp = Float64(2.0 * x);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.1e+126) || ~((a <= 2.1e-108)))
		tmp = a * (27.0 * b);
	else
		tmp = 2.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.1e+126], N[Not[LessEqual[a, 2.1e-108]], $MachinePrecision]], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], N[(2.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.09999999999999999e126 or 2.0999999999999999e-108 < a

   1. Initial program 86.0%

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

      1. associate-+l- 86.0%

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

      2. *-commutative 86.0%

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

      3. *-commutative 86.0%

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

      4. associate-*l* 86.0%

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

      5. associate-+l- 86.0%

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

      6. associate-*l* 86.0%

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

      7. *-commutative 86.0%

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

      8. *-commutative 86.0%

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

      9. associate-*l* 92.3%

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

      10. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in a around inf 44.4%

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

      1. associate-*r* 44.5%

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

      2. *-commutative 44.5%

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

      3. associate-*r* 44.4%

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

   7. Simplified 44.4%

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

   if -1.09999999999999999e126 < a < 2.0999999999999999e-108

   1. Initial program 94.3%

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

      1. associate-+l- 94.3%

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

      2. *-commutative 94.3%

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

      3. *-commutative 94.3%

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

      4. associate-*l* 94.3%

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

      5. associate-+l- 94.3%

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

      6. associate-*l* 94.3%

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

      7. *-commutative 94.3%

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

      8. *-commutative 94.3%

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

      9. associate-*l* 97.1%

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

      10. associate-*l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in x around inf 39.7%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+126} \lor \neg \left(a \leq 2.1 \cdot 10^{-108}\right):\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 44.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+125}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-108}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.8e+125)
   (* b (* 27.0 a))
   (if (<= a 3.5e-108) (* 2.0 x) (* a (* 27.0 b)))))

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 <= -1.8e+125) {
		tmp = b * (27.0 * a);
	} else if (a <= 3.5e-108) {
		tmp = 2.0 * x;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 <= (-1.8d+125)) then
        tmp = b * (27.0d0 * a)
    else if (a <= 3.5d-108) then
        tmp = 2.0d0 * x
    else
        tmp = a * (27.0d0 * b)
    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 <= -1.8e+125) {
		tmp = b * (27.0 * a);
	} else if (a <= 3.5e-108) {
		tmp = 2.0 * x;
	} else {
		tmp = a * (27.0 * b);
	}
	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 <= -1.8e+125:
		tmp = b * (27.0 * a)
	elif a <= 3.5e-108:
		tmp = 2.0 * x
	else:
		tmp = a * (27.0 * b)
	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 <= -1.8e+125)
		tmp = Float64(b * Float64(27.0 * a));
	elseif (a <= 3.5e-108)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(a * Float64(27.0 * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.8e+125)
		tmp = b * (27.0 * a);
	elseif (a <= 3.5e-108)
		tmp = 2.0 * x;
	else
		tmp = a * (27.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.8e+125], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-108], N[(2.0 * x), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8000000000000002e125

   1. Initial program 81.3%

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

      1. associate-+l- 81.3%

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

      2. *-commutative 81.3%

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

      3. *-commutative 81.3%

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

      4. associate-*l* 81.2%

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

      5. associate-+l- 81.2%

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

      6. associate-*l* 81.3%

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

      7. *-commutative 81.3%

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

      8. *-commutative 81.3%

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

      9. associate-*l* 88.8%

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

      10. associate-*l* 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in a around inf 56.7%

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

      1. associate-*r* 56.7%

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

   7. Simplified 56.7%

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

   if -1.8000000000000002e125 < a < 3.4999999999999999e-108

   1. Initial program 94.3%

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

      1. associate-+l- 94.3%

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

      2. *-commutative 94.3%

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

      3. *-commutative 94.3%

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

      4. associate-*l* 94.3%

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

      5. associate-+l- 94.3%

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

      6. associate-*l* 94.3%

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

      7. *-commutative 94.3%

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

      8. *-commutative 94.3%

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

      9. associate-*l* 97.1%

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

      10. associate-*l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in x around inf 39.7%

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

   if 3.4999999999999999e-108 < a

   1. Initial program 88.1%

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

      1. associate-+l- 88.1%

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

      2. *-commutative 88.1%

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

      3. *-commutative 88.1%

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

      4. associate-*l* 88.2%

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

      5. associate-+l- 88.2%

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

      6. associate-*l* 88.1%

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

      7. *-commutative 88.1%

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

      8. *-commutative 88.1%

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

      9. associate-*l* 93.8%

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

      10. 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

   5. Taylor expanded in a around inf 39.0%

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

      1. associate-*r* 39.1%

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

      2. *-commutative 39.1%

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

      3. associate-*r* 39.1%

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

   7. Simplified 39.1%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+125}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-108}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.3% accurate, 5.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ 2 \cdot x \end{array} \]

FPCore

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

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 2.0 * x;
}

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 = 2.0d0 * x
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 2.0 * x;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return 2.0 * x

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = 2.0 * x;
end

Wolfram

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

Derivation

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. associate-+l- 90.5%

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

   2. *-commutative 90.5%

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

   3. *-commutative 90.5%

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

   4. associate-*l* 90.5%

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

   5. associate-+l- 90.5%

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

   6. associate-*l* 90.5%

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

   7. *-commutative 90.5%

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

   8. *-commutative 90.5%

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

   9. associate-*l* 94.9%

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

   10. 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 x around inf 31.3%

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

6. Final simplification 31.3%

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

Developer target: 94.7% 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 2024115 
(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)))