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

Percentage Accurate: 95.4% → 96.2%

Time: 14.5s

Alternatives: 17

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

   1. +-commutative 95.7%

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

   2. associate-+r- 95.7%

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

   3. *-commutative 95.7%

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

   4. cancel-sign-sub-inv 95.7%

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

   5. associate-*r* 94.2%

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

   6. distribute-lft-neg-in 94.2%

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

   7. *-commutative 94.2%

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

   8. cancel-sign-sub-inv 94.2%

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

   9. associate-+r- 94.2%

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

   10. associate-*l* 94.2%

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

   11. fma-def 95.4%

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

   12. cancel-sign-sub-inv 95.4%

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

   13. fma-def 95.4%

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

   14. *-commutative 95.4%

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

   15. distribute-rgt-neg-in 95.4%

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

   16. distribute-lft-neg-out 95.4%

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

   17. associate-*r* 96.8%

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

   18. associate-*l* 96.8%

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

3. Simplified 96.8%

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

4. Final simplification 96.8%

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

Alternative 2: 49.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ t_2 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.11 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-229}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-175}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-69}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))) (t_2 (* -9.0 (* t (* y z)))))
   (if (<= z -1.5e-59)
     t_2
     (if (<= z -1.11e-122)
       t_1
       (if (<= z -2.1e-229)
         (* x 2.0)
         (if (<= z -1.2e-269)
           t_1
           (if (<= z 5.2e-175)
             (* x 2.0)
             (if (<= z 1.6e-69) (* 27.0 (* a b)) t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = -9.0 * (t * (y * z));
	double tmp;
	if (z <= -1.5e-59) {
		tmp = t_2;
	} else if (z <= -1.11e-122) {
		tmp = t_1;
	} else if (z <= -2.1e-229) {
		tmp = x * 2.0;
	} else if (z <= -1.2e-269) {
		tmp = t_1;
	} else if (z <= 5.2e-175) {
		tmp = x * 2.0;
	} else if (z <= 1.6e-69) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    t_2 = (-9.0d0) * (t * (y * z))
    if (z <= (-1.5d-59)) then
        tmp = t_2
    else if (z <= (-1.11d-122)) then
        tmp = t_1
    else if (z <= (-2.1d-229)) then
        tmp = x * 2.0d0
    else if (z <= (-1.2d-269)) then
        tmp = t_1
    else if (z <= 5.2d-175) then
        tmp = x * 2.0d0
    else if (z <= 1.6d-69) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = -9.0 * (t * (y * z));
	double tmp;
	if (z <= -1.5e-59) {
		tmp = t_2;
	} else if (z <= -1.11e-122) {
		tmp = t_1;
	} else if (z <= -2.1e-229) {
		tmp = x * 2.0;
	} else if (z <= -1.2e-269) {
		tmp = t_1;
	} else if (z <= 5.2e-175) {
		tmp = x * 2.0;
	} else if (z <= 1.6e-69) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	t_2 = -9.0 * (t * (y * z))
	tmp = 0
	if z <= -1.5e-59:
		tmp = t_2
	elif z <= -1.11e-122:
		tmp = t_1
	elif z <= -2.1e-229:
		tmp = x * 2.0
	elif z <= -1.2e-269:
		tmp = t_1
	elif z <= 5.2e-175:
		tmp = x * 2.0
	elif z <= 1.6e-69:
		tmp = 27.0 * (a * b)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	t_2 = Float64(-9.0 * Float64(t * Float64(y * z)))
	tmp = 0.0
	if (z <= -1.5e-59)
		tmp = t_2;
	elseif (z <= -1.11e-122)
		tmp = t_1;
	elseif (z <= -2.1e-229)
		tmp = Float64(x * 2.0);
	elseif (z <= -1.2e-269)
		tmp = t_1;
	elseif (z <= 5.2e-175)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.6e-69)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	t_2 = -9.0 * (t * (y * z));
	tmp = 0.0;
	if (z <= -1.5e-59)
		tmp = t_2;
	elseif (z <= -1.11e-122)
		tmp = t_1;
	elseif (z <= -2.1e-229)
		tmp = x * 2.0;
	elseif (z <= -1.2e-269)
		tmp = t_1;
	elseif (z <= 5.2e-175)
		tmp = x * 2.0;
	elseif (z <= 1.6e-69)
		tmp = 27.0 * (a * b);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e-59], t$95$2, If[LessEqual[z, -1.11e-122], t$95$1, If[LessEqual[z, -2.1e-229], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -1.2e-269], t$95$1, If[LessEqual[z, 5.2e-175], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.6e-69], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.5e-59 or 1.59999999999999999e-69 < z

   1. Initial program 93.5%

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

      1. sub-neg 93.5%

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

      2. sub-neg 93.5%

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

      3. associate-*l* 94.2%

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

      4. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in y around inf 44.5%

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

   if -1.5e-59 < z < -1.11e-122 or -2.09999999999999983e-229 < z < -1.20000000000000005e-269

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around inf 56.8%

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

      1. associate-*r* 56.8%

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

      2. *-commutative 56.8%

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

      3. associate-*r* 56.7%

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

   6. Simplified 56.7%

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

   if -1.11e-122 < z < -2.09999999999999983e-229 or -1.20000000000000005e-269 < z < 5.2e-175

   1. Initial program 98.0%

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

      1. sub-neg 98.0%

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

      2. sub-neg 98.0%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 53.0%

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

   if 5.2e-175 < z < 1.59999999999999999e-69

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around inf 46.2%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -1.11 \cdot 10^{-122}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-229}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-269}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-175}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-69}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 3: 49.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-227}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-173}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-65}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= z -2.8e-60)
     (* t (* y (* -9.0 z)))
     (if (<= z -5.4e-132)
       t_1
       (if (<= z -1.4e-227)
         (* x 2.0)
         (if (<= z -3.5e-269)
           t_1
           (if (<= z 2.45e-173)
             (* x 2.0)
             (if (<= z 2.6e-65) (* 27.0 (* a b)) (* -9.0 (* t (* y z)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -2.8e-60) {
		tmp = t * (y * (-9.0 * z));
	} else if (z <= -5.4e-132) {
		tmp = t_1;
	} else if (z <= -1.4e-227) {
		tmp = x * 2.0;
	} else if (z <= -3.5e-269) {
		tmp = t_1;
	} else if (z <= 2.45e-173) {
		tmp = x * 2.0;
	} else if (z <= 2.6e-65) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = -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.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if (z <= (-2.8d-60)) then
        tmp = t * (y * ((-9.0d0) * z))
    else if (z <= (-5.4d-132)) then
        tmp = t_1
    else if (z <= (-1.4d-227)) then
        tmp = x * 2.0d0
    else if (z <= (-3.5d-269)) then
        tmp = t_1
    else if (z <= 2.45d-173) then
        tmp = x * 2.0d0
    else if (z <= 2.6d-65) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = (-9.0d0) * (t * (y * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -2.8e-60) {
		tmp = t * (y * (-9.0 * z));
	} else if (z <= -5.4e-132) {
		tmp = t_1;
	} else if (z <= -1.4e-227) {
		tmp = x * 2.0;
	} else if (z <= -3.5e-269) {
		tmp = t_1;
	} else if (z <= 2.45e-173) {
		tmp = x * 2.0;
	} else if (z <= 2.6e-65) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = -9.0 * (t * (y * z));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if z <= -2.8e-60:
		tmp = t * (y * (-9.0 * z))
	elif z <= -5.4e-132:
		tmp = t_1
	elif z <= -1.4e-227:
		tmp = x * 2.0
	elif z <= -3.5e-269:
		tmp = t_1
	elif z <= 2.45e-173:
		tmp = x * 2.0
	elif z <= 2.6e-65:
		tmp = 27.0 * (a * b)
	else:
		tmp = -9.0 * (t * (y * z))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (z <= -2.8e-60)
		tmp = Float64(t * Float64(y * Float64(-9.0 * z)));
	elseif (z <= -5.4e-132)
		tmp = t_1;
	elseif (z <= -1.4e-227)
		tmp = Float64(x * 2.0);
	elseif (z <= -3.5e-269)
		tmp = t_1;
	elseif (z <= 2.45e-173)
		tmp = Float64(x * 2.0);
	elseif (z <= 2.6e-65)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = 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])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (z <= -2.8e-60)
		tmp = t * (y * (-9.0 * z));
	elseif (z <= -5.4e-132)
		tmp = t_1;
	elseif (z <= -1.4e-227)
		tmp = x * 2.0;
	elseif (z <= -3.5e-269)
		tmp = t_1;
	elseif (z <= 2.45e-173)
		tmp = x * 2.0;
	elseif (z <= 2.6e-65)
		tmp = 27.0 * (a * b);
	else
		tmp = -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.
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[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e-60], N[(t * N[(y * N[(-9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.4e-132], t$95$1, If[LessEqual[z, -1.4e-227], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -3.5e-269], t$95$1, If[LessEqual[z, 2.45e-173], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 2.6e-65], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.8000000000000002e-60

   1. Initial program 94.1%

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

   2. Taylor expanded in y around 0 94.1%

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

   3. Taylor expanded in y around inf 52.6%

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

      1. *-commutative 52.6%

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

      2. associate-*r* 52.6%

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

      3. associate-*l* 52.5%

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

   5. Simplified 52.5%

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

   if -2.8000000000000002e-60 < z < -5.3999999999999998e-132 or -1.3999999999999999e-227 < z < -3.50000000000000019e-269

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around inf 54.2%

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

      1. associate-*r* 54.1%

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

      2. *-commutative 54.1%

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

      3. associate-*r* 54.0%

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

   6. Simplified 54.0%

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

   if -5.3999999999999998e-132 < z < -1.3999999999999999e-227 or -3.50000000000000019e-269 < z < 2.44999999999999996e-173

   1. Initial program 97.9%

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

      1. sub-neg 97.9%

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

      2. sub-neg 97.9%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 51.9%

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

   if 2.44999999999999996e-173 < z < 2.6000000000000001e-65

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around inf 47.7%

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

   if 2.6000000000000001e-65 < z

   1. Initial program 92.9%

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

      1. sub-neg 92.9%

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

      2. sub-neg 92.9%

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

      3. associate-*l* 94.3%

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

      4. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in y around inf 38.5%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-132}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-227}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-269}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-173}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-65}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 4: 49.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-225}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-174}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-66}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= z -9e-60)
     (* t (* y (* -9.0 z)))
     (if (<= z -3.2e-130)
       t_1
       (if (<= z -3e-225)
         (* x 2.0)
         (if (<= z -3.2e-268)
           t_1
           (if (<= z 9.6e-174)
             (* x 2.0)
             (if (<= z 6e-66) (* 27.0 (* a b)) (* t (* z (* y -9.0)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -9e-60) {
		tmp = t * (y * (-9.0 * z));
	} else if (z <= -3.2e-130) {
		tmp = t_1;
	} else if (z <= -3e-225) {
		tmp = x * 2.0;
	} else if (z <= -3.2e-268) {
		tmp = t_1;
	} else if (z <= 9.6e-174) {
		tmp = x * 2.0;
	} else if (z <= 6e-66) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t * (z * (y * -9.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if (z <= (-9d-60)) then
        tmp = t * (y * ((-9.0d0) * z))
    else if (z <= (-3.2d-130)) then
        tmp = t_1
    else if (z <= (-3d-225)) then
        tmp = x * 2.0d0
    else if (z <= (-3.2d-268)) then
        tmp = t_1
    else if (z <= 9.6d-174) then
        tmp = x * 2.0d0
    else if (z <= 6d-66) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = t * (z * (y * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -9e-60) {
		tmp = t * (y * (-9.0 * z));
	} else if (z <= -3.2e-130) {
		tmp = t_1;
	} else if (z <= -3e-225) {
		tmp = x * 2.0;
	} else if (z <= -3.2e-268) {
		tmp = t_1;
	} else if (z <= 9.6e-174) {
		tmp = x * 2.0;
	} else if (z <= 6e-66) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t * (z * (y * -9.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if z <= -9e-60:
		tmp = t * (y * (-9.0 * z))
	elif z <= -3.2e-130:
		tmp = t_1
	elif z <= -3e-225:
		tmp = x * 2.0
	elif z <= -3.2e-268:
		tmp = t_1
	elif z <= 9.6e-174:
		tmp = x * 2.0
	elif z <= 6e-66:
		tmp = 27.0 * (a * b)
	else:
		tmp = t * (z * (y * -9.0))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (z <= -9e-60)
		tmp = Float64(t * Float64(y * Float64(-9.0 * z)));
	elseif (z <= -3.2e-130)
		tmp = t_1;
	elseif (z <= -3e-225)
		tmp = Float64(x * 2.0);
	elseif (z <= -3.2e-268)
		tmp = t_1;
	elseif (z <= 9.6e-174)
		tmp = Float64(x * 2.0);
	elseif (z <= 6e-66)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(t * Float64(z * Float64(y * -9.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (z <= -9e-60)
		tmp = t * (y * (-9.0 * z));
	elseif (z <= -3.2e-130)
		tmp = t_1;
	elseif (z <= -3e-225)
		tmp = x * 2.0;
	elseif (z <= -3.2e-268)
		tmp = t_1;
	elseif (z <= 9.6e-174)
		tmp = x * 2.0;
	elseif (z <= 6e-66)
		tmp = 27.0 * (a * b);
	else
		tmp = t * (z * (y * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e-60], N[(t * N[(y * N[(-9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.2e-130], t$95$1, If[LessEqual[z, -3e-225], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -3.2e-268], t$95$1, If[LessEqual[z, 9.6e-174], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 6e-66], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9.00000000000000001e-60

   1. Initial program 94.1%

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

   2. Taylor expanded in y around 0 94.1%

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

   3. Taylor expanded in y around inf 52.6%

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

      1. *-commutative 52.6%

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

      2. associate-*r* 52.6%

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

      3. associate-*l* 52.5%

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

   5. Simplified 52.5%

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

   if -9.00000000000000001e-60 < z < -3.2e-130 or -3.00000000000000018e-225 < z < -3.1999999999999999e-268

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around inf 56.8%

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

      1. associate-*r* 56.8%

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

      2. *-commutative 56.8%

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

      3. associate-*r* 56.7%

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

   6. Simplified 56.7%

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

   if -3.2e-130 < z < -3.00000000000000018e-225 or -3.1999999999999999e-268 < z < 9.6e-174

   1. Initial program 98.0%

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

      1. sub-neg 98.0%

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

      2. sub-neg 98.0%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 53.0%

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

   if 9.6e-174 < z < 6.0000000000000004e-66

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around inf 47.7%

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

   if 6.0000000000000004e-66 < z

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 92.9%

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

   3. Taylor expanded in y around inf 38.5%

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

      1. *-commutative 38.5%

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

      2. associate-*r* 38.5%

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

      3. associate-*l* 38.6%

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

   5. Simplified 38.6%

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

   6. Taylor expanded in y around 0 38.5%

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

      1. *-commutative 38.5%

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

      2. *-commutative 38.5%

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

      3. associate-*l* 38.6%

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

   8. Simplified 38.6%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-130}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-225}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-268}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-174}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-66}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 5: 50.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{-59}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-228}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-175}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-69}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= z -1.55e-59)
     (* z (* -9.0 (* t y)))
     (if (<= z -2.3e-125)
       t_1
       (if (<= z -1.7e-228)
         (* x 2.0)
         (if (<= z -1.36e-269)
           t_1
           (if (<= z 7.5e-175)
             (* x 2.0)
             (if (<= z 3.1e-69) (* 27.0 (* a b)) (* t (* z (* y -9.0)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -1.55e-59) {
		tmp = z * (-9.0 * (t * y));
	} else if (z <= -2.3e-125) {
		tmp = t_1;
	} else if (z <= -1.7e-228) {
		tmp = x * 2.0;
	} else if (z <= -1.36e-269) {
		tmp = t_1;
	} else if (z <= 7.5e-175) {
		tmp = x * 2.0;
	} else if (z <= 3.1e-69) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t * (z * (y * -9.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if (z <= (-1.55d-59)) then
        tmp = z * ((-9.0d0) * (t * y))
    else if (z <= (-2.3d-125)) then
        tmp = t_1
    else if (z <= (-1.7d-228)) then
        tmp = x * 2.0d0
    else if (z <= (-1.36d-269)) then
        tmp = t_1
    else if (z <= 7.5d-175) then
        tmp = x * 2.0d0
    else if (z <= 3.1d-69) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = t * (z * (y * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -1.55e-59) {
		tmp = z * (-9.0 * (t * y));
	} else if (z <= -2.3e-125) {
		tmp = t_1;
	} else if (z <= -1.7e-228) {
		tmp = x * 2.0;
	} else if (z <= -1.36e-269) {
		tmp = t_1;
	} else if (z <= 7.5e-175) {
		tmp = x * 2.0;
	} else if (z <= 3.1e-69) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t * (z * (y * -9.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if z <= -1.55e-59:
		tmp = z * (-9.0 * (t * y))
	elif z <= -2.3e-125:
		tmp = t_1
	elif z <= -1.7e-228:
		tmp = x * 2.0
	elif z <= -1.36e-269:
		tmp = t_1
	elif z <= 7.5e-175:
		tmp = x * 2.0
	elif z <= 3.1e-69:
		tmp = 27.0 * (a * b)
	else:
		tmp = t * (z * (y * -9.0))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (z <= -1.55e-59)
		tmp = Float64(z * Float64(-9.0 * Float64(t * y)));
	elseif (z <= -2.3e-125)
		tmp = t_1;
	elseif (z <= -1.7e-228)
		tmp = Float64(x * 2.0);
	elseif (z <= -1.36e-269)
		tmp = t_1;
	elseif (z <= 7.5e-175)
		tmp = Float64(x * 2.0);
	elseif (z <= 3.1e-69)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(t * Float64(z * Float64(y * -9.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (z <= -1.55e-59)
		tmp = z * (-9.0 * (t * y));
	elseif (z <= -2.3e-125)
		tmp = t_1;
	elseif (z <= -1.7e-228)
		tmp = x * 2.0;
	elseif (z <= -1.36e-269)
		tmp = t_1;
	elseif (z <= 7.5e-175)
		tmp = x * 2.0;
	elseif (z <= 3.1e-69)
		tmp = 27.0 * (a * b);
	else
		tmp = t * (z * (y * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e-59], N[(z * N[(-9.0 * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-125], t$95$1, If[LessEqual[z, -1.7e-228], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -1.36e-269], t$95$1, If[LessEqual[z, 7.5e-175], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 3.1e-69], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.55e-59

   1. Initial program 94.1%

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

   2. Taylor expanded in y around 0 94.1%

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

   3. Taylor expanded in y around inf 52.6%

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

      1. *-commutative 52.6%

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

      2. *-commutative 52.6%

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

      3. *-commutative 52.6%

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

      4. associate-*r* 53.9%

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

      5. associate-*l* 53.9%

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

      6. *-commutative 53.9%

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

   5. Simplified 53.9%

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

   if -1.55e-59 < z < -2.2999999999999999e-125 or -1.69999999999999995e-228 < z < -1.36e-269

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around inf 56.8%

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

      1. associate-*r* 56.8%

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

      2. *-commutative 56.8%

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

      3. associate-*r* 56.7%

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

   6. Simplified 56.7%

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

   if -2.2999999999999999e-125 < z < -1.69999999999999995e-228 or -1.36e-269 < z < 7.50000000000000053e-175

   1. Initial program 98.0%

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

      1. sub-neg 98.0%

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

      2. sub-neg 98.0%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 53.0%

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

   if 7.50000000000000053e-175 < z < 3.0999999999999999e-69

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around inf 46.2%

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

   if 3.0999999999999999e-69 < z

   1. Initial program 93.0%

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

   2. Taylor expanded in y around 0 93.0%

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

   3. Taylor expanded in y around inf 38.1%

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

      1. *-commutative 38.1%

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

      2. associate-*r* 38.1%

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

      3. associate-*l* 38.2%

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

   5. Simplified 38.2%

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

   6. Taylor expanded in y around 0 38.1%

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

      1. *-commutative 38.1%

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

      2. *-commutative 38.1%

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

      3. associate-*l* 38.2%

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

   8. Simplified 38.2%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-59}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-125}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-228}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-269}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-175}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-69}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 6: 78.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-209}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+68}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+255}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(y \cdot z\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -8.2e-209)
   (- (* x 2.0) (* 9.0 (* z (* t y))))
   (if (<= t 6e+68)
     (- (* x 2.0) (* b (* a -27.0)))
     (if (<= t 5.2e+255)
       (+ (* t (* -9.0 (* y z))) (* a (* 27.0 b)))
       (- (* x 2.0) (* 9.0 (* t (* y z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.2e-209) {
		tmp = (x * 2.0) - (9.0 * (z * (t * y)));
	} else if (t <= 6e+68) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else if (t <= 5.2e+255) {
		tmp = (t * (-9.0 * (y * z))) + (a * (27.0 * b));
	} else {
		tmp = (x * 2.0) - (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.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-8.2d-209)) then
        tmp = (x * 2.0d0) - (9.0d0 * (z * (t * y)))
    else if (t <= 6d+68) then
        tmp = (x * 2.0d0) - (b * (a * (-27.0d0)))
    else if (t <= 5.2d+255) then
        tmp = (t * ((-9.0d0) * (y * z))) + (a * (27.0d0 * b))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.2e-209) {
		tmp = (x * 2.0) - (9.0 * (z * (t * y)));
	} else if (t <= 6e+68) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else if (t <= 5.2e+255) {
		tmp = (t * (-9.0 * (y * z))) + (a * (27.0 * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -8.2e-209:
		tmp = (x * 2.0) - (9.0 * (z * (t * y)))
	elif t <= 6e+68:
		tmp = (x * 2.0) - (b * (a * -27.0))
	elif t <= 5.2e+255:
		tmp = (t * (-9.0 * (y * z))) + (a * (27.0 * b))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -8.2e-209)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(z * Float64(t * y))));
	elseif (t <= 6e+68)
		tmp = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)));
	elseif (t <= 5.2e+255)
		tmp = Float64(Float64(t * Float64(-9.0 * Float64(y * z))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(x * 2.0) - 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])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -8.2e-209)
		tmp = (x * 2.0) - (9.0 * (z * (t * y)));
	elseif (t <= 6e+68)
		tmp = (x * 2.0) - (b * (a * -27.0));
	elseif (t <= 5.2e+255)
		tmp = (t * (-9.0 * (y * z))) + (a * (27.0 * b));
	else
		tmp = (x * 2.0) - (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.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -8.2e-209], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+68], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+255], N[(N[(t * N[(-9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.19999999999999955e-209

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. sub-neg 95.0%

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

      3. associate-*l* 96.9%

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

      4. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in a around 0 60.4%

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

      1. expm1-log1p-u 40.5%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-udef 39.6%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 39.6%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y \cdot z\right) \cdot t}\right)} - 1\right) \]

      4. *-commutative 39.6%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(z \cdot y\right)} \cdot t\right)} - 1\right) \]

      5. associate-*l* 38.9%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{z \cdot \left(y \cdot t\right)}\right)} - 1\right) \]

   6. Applied egg-rr 38.9%

      \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(z \cdot \left(y \cdot t\right)\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 40.3%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(z \cdot \left(y \cdot t\right)\right)\right)} \]

      2. expm1-log1p 61.8%

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

      3. *-commutative 61.8%

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

   8. Simplified 61.8%

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

   if -8.19999999999999955e-209 < t < 6.0000000000000004e68

   1. Initial program 95.7%

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

      1. sub-neg 95.7%

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

      2. sub-neg 95.7%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 86.2%

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

      1. flip-+ 48.1%

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

      2. *-commutative 48.1%

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

      3. fma-neg 48.1%

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

      4. *-commutative 48.1%

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

      5. clear-num 48.1%

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

      6. *-commutative 48.1%

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

      7. fma-neg 48.1%

         \[\leadsto \frac{1}{\frac{\color{blue}{x \cdot 2 - 27 \cdot \left(a \cdot b\right)}}{\left(2 \cdot x\right) \cdot \left(2 \cdot x\right) - \left(27 \cdot \left(a \cdot b\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} \]

      8. cancel-sign-sub-inv 48.1%

         \[\leadsto \frac{1}{\frac{\color{blue}{x \cdot 2 + \left(-27\right) \cdot \left(a \cdot b\right)}}{\left(2 \cdot x\right) \cdot \left(2 \cdot x\right) - \left(27 \cdot \left(a \cdot b\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} \]

      9. metadata-eval 48.1%

         \[\leadsto \frac{1}{\frac{x \cdot 2 + \color{blue}{-27} \cdot \left(a \cdot b\right)}{\left(2 \cdot x\right) \cdot \left(2 \cdot x\right) - \left(27 \cdot \left(a \cdot b\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} \]

      10. *-commutative 48.1%

          \[\leadsto \frac{1}{\frac{x \cdot 2 + -27 \cdot \left(a \cdot b\right)}{\left(2 \cdot x\right) \cdot \color{blue}{\left(x \cdot 2\right)} - \left(27 \cdot \left(a \cdot b\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} \]

      11. *-commutative 48.1%

          \[\leadsto \frac{1}{\frac{x \cdot 2 + -27 \cdot \left(a \cdot b\right)}{\color{blue}{\left(x \cdot 2\right)} \cdot \left(x \cdot 2\right) - \left(27 \cdot \left(a \cdot b\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} \]

      12. pow2 48.1%

          \[\leadsto \frac{1}{\frac{x \cdot 2 + -27 \cdot \left(a \cdot b\right)}{\color{blue}{{\left(x \cdot 2\right)}^{2}} - \left(27 \cdot \left(a \cdot b\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} \]

      13. *-commutative 48.1%

          \[\leadsto \frac{1}{\frac{x \cdot 2 + -27 \cdot \left(a \cdot b\right)}{{\left(x \cdot 2\right)}^{2} - \color{blue}{\left(\left(a \cdot b\right) \cdot 27\right)} \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} \]

   6. Applied egg-rr 48.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot 2 + -27 \cdot \left(a \cdot b\right)}{{\left(x \cdot 2\right)}^{2} - {\left(a \cdot b\right)}^{2} \cdot 729}}} \]
   7. Step-by-step derivation

      1. clear-num 48.0%

         \[\leadsto \color{blue}{\frac{{\left(x \cdot 2\right)}^{2} - {\left(a \cdot b\right)}^{2} \cdot 729}{x \cdot 2 + -27 \cdot \left(a \cdot b\right)}} \]

      2. unpow2 48.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)} - {\left(a \cdot b\right)}^{2} \cdot 729}{x \cdot 2 + -27 \cdot \left(a \cdot b\right)} \]

      3. *-commutative 48.0%

         \[\leadsto \frac{\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) - \color{blue}{729 \cdot {\left(a \cdot b\right)}^{2}}}{x \cdot 2 + -27 \cdot \left(a \cdot b\right)} \]

      4. metadata-eval 48.0%

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

      5. unpow2 48.0%

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

      6. swap-sqr 48.1%

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

      7. flip-- 86.2%

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

      8. associate-*r* 86.2%

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

      9. cancel-sign-sub-inv 86.2%

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

   8. Applied egg-rr 86.2%

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

   if 6.0000000000000004e68 < t < 5.20000000000000019e255

   1. Initial program 97.5%

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

      1. sub-neg 97.5%

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

      2. sub-neg 97.5%

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

      3. associate-*l* 95.3%

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

      4. associate-*l* 95.2%

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

   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. Taylor expanded in x around 0 86.8%

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

      1. *-commutative 86.8%

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

      2. associate-*l* 86.9%

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

      3. sub-neg 86.9%

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

      4. +-commutative 86.9%

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

      5. *-commutative 86.9%

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

      6. distribute-rgt-neg-in 86.9%

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

      7. *-commutative 86.9%

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

      8. distribute-rgt-neg-in 86.9%

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

      9. metadata-eval 86.9%

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

      10. associate-*r* 86.8%

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

      11. *-commutative 86.8%

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

      12. associate-*l* 86.8%

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

   6. Applied egg-rr 86.8%

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

   if 5.20000000000000019e255 < t

   1. Initial program 94.1%

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

      1. sub-neg 94.1%

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

      2. sub-neg 94.1%

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

      3. associate-*l* 77.4%

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

      4. associate-*l* 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in a around 0 92.9%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-209}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+68}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+255}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(y \cdot z\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 7: 78.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{-209}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+67}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+255}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 9.0 (* t (* y z)))))
   (if (<= t -8.2e-209)
     (- (* x 2.0) (* 9.0 (* z (* t y))))
     (if (<= t 8.2e+67)
       (- (* x 2.0) (* b (* a -27.0)))
       (if (<= t 3.8e+255) (- (* 27.0 (* a b)) t_1) (- (* x 2.0) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 9.0 * (t * (y * z));
	double tmp;
	if (t <= -8.2e-209) {
		tmp = (x * 2.0) - (9.0 * (z * (t * y)));
	} else if (t <= 8.2e+67) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else if (t <= 3.8e+255) {
		tmp = (27.0 * (a * b)) - t_1;
	} else {
		tmp = (x * 2.0) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 9.0d0 * (t * (y * z))
    if (t <= (-8.2d-209)) then
        tmp = (x * 2.0d0) - (9.0d0 * (z * (t * y)))
    else if (t <= 8.2d+67) then
        tmp = (x * 2.0d0) - (b * (a * (-27.0d0)))
    else if (t <= 3.8d+255) then
        tmp = (27.0d0 * (a * b)) - t_1
    else
        tmp = (x * 2.0d0) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 9.0 * (t * (y * z));
	double tmp;
	if (t <= -8.2e-209) {
		tmp = (x * 2.0) - (9.0 * (z * (t * y)));
	} else if (t <= 8.2e+67) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else if (t <= 3.8e+255) {
		tmp = (27.0 * (a * b)) - t_1;
	} else {
		tmp = (x * 2.0) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 9.0 * (t * (y * z))
	tmp = 0
	if t <= -8.2e-209:
		tmp = (x * 2.0) - (9.0 * (z * (t * y)))
	elif t <= 8.2e+67:
		tmp = (x * 2.0) - (b * (a * -27.0))
	elif t <= 3.8e+255:
		tmp = (27.0 * (a * b)) - t_1
	else:
		tmp = (x * 2.0) - t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(9.0 * Float64(t * Float64(y * z)))
	tmp = 0.0
	if (t <= -8.2e-209)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(z * Float64(t * y))));
	elseif (t <= 8.2e+67)
		tmp = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)));
	elseif (t <= 3.8e+255)
		tmp = Float64(Float64(27.0 * Float64(a * b)) - t_1);
	else
		tmp = Float64(Float64(x * 2.0) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 9.0 * (t * (y * z));
	tmp = 0.0;
	if (t <= -8.2e-209)
		tmp = (x * 2.0) - (9.0 * (z * (t * y)));
	elseif (t <= 8.2e+67)
		tmp = (x * 2.0) - (b * (a * -27.0));
	elseif (t <= 3.8e+255)
		tmp = (27.0 * (a * b)) - t_1;
	else
		tmp = (x * 2.0) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e-209], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+67], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+255], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.19999999999999955e-209

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. sub-neg 95.0%

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

      3. associate-*l* 96.9%

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

      4. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in a around 0 60.4%

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

      1. expm1-log1p-u 40.5%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-udef 39.6%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 39.6%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y \cdot z\right) \cdot t}\right)} - 1\right) \]

      4. *-commutative 39.6%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(z \cdot y\right)} \cdot t\right)} - 1\right) \]

      5. associate-*l* 38.9%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{z \cdot \left(y \cdot t\right)}\right)} - 1\right) \]

   6. Applied egg-rr 38.9%

      \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(z \cdot \left(y \cdot t\right)\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 40.3%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(z \cdot \left(y \cdot t\right)\right)\right)} \]

      2. expm1-log1p 61.8%

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

      3. *-commutative 61.8%

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

   8. Simplified 61.8%

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

   if -8.19999999999999955e-209 < t < 8.19999999999999959e67

   1. Initial program 95.7%

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

      1. sub-neg 95.7%

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

      2. sub-neg 95.7%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 86.2%

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

      1. flip-+ 48.1%

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

      2. *-commutative 48.1%

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

      3. fma-neg 48.1%

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

      4. *-commutative 48.1%

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

      5. clear-num 48.1%

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

      6. *-commutative 48.1%

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

      7. fma-neg 48.1%

         \[\leadsto \frac{1}{\frac{\color{blue}{x \cdot 2 - 27 \cdot \left(a \cdot b\right)}}{\left(2 \cdot x\right) \cdot \left(2 \cdot x\right) - \left(27 \cdot \left(a \cdot b\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} \]

      8. cancel-sign-sub-inv 48.1%

         \[\leadsto \frac{1}{\frac{\color{blue}{x \cdot 2 + \left(-27\right) \cdot \left(a \cdot b\right)}}{\left(2 \cdot x\right) \cdot \left(2 \cdot x\right) - \left(27 \cdot \left(a \cdot b\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} \]

      9. metadata-eval 48.1%

         \[\leadsto \frac{1}{\frac{x \cdot 2 + \color{blue}{-27} \cdot \left(a \cdot b\right)}{\left(2 \cdot x\right) \cdot \left(2 \cdot x\right) - \left(27 \cdot \left(a \cdot b\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} \]

      10. *-commutative 48.1%

          \[\leadsto \frac{1}{\frac{x \cdot 2 + -27 \cdot \left(a \cdot b\right)}{\left(2 \cdot x\right) \cdot \color{blue}{\left(x \cdot 2\right)} - \left(27 \cdot \left(a \cdot b\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} \]

      11. *-commutative 48.1%

          \[\leadsto \frac{1}{\frac{x \cdot 2 + -27 \cdot \left(a \cdot b\right)}{\color{blue}{\left(x \cdot 2\right)} \cdot \left(x \cdot 2\right) - \left(27 \cdot \left(a \cdot b\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} \]

      12. pow2 48.1%

          \[\leadsto \frac{1}{\frac{x \cdot 2 + -27 \cdot \left(a \cdot b\right)}{\color{blue}{{\left(x \cdot 2\right)}^{2}} - \left(27 \cdot \left(a \cdot b\right)\right) \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} \]

      13. *-commutative 48.1%

          \[\leadsto \frac{1}{\frac{x \cdot 2 + -27 \cdot \left(a \cdot b\right)}{{\left(x \cdot 2\right)}^{2} - \color{blue}{\left(\left(a \cdot b\right) \cdot 27\right)} \cdot \left(27 \cdot \left(a \cdot b\right)\right)}} \]

   6. Applied egg-rr 48.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot 2 + -27 \cdot \left(a \cdot b\right)}{{\left(x \cdot 2\right)}^{2} - {\left(a \cdot b\right)}^{2} \cdot 729}}} \]
   7. Step-by-step derivation

      1. clear-num 48.0%

         \[\leadsto \color{blue}{\frac{{\left(x \cdot 2\right)}^{2} - {\left(a \cdot b\right)}^{2} \cdot 729}{x \cdot 2 + -27 \cdot \left(a \cdot b\right)}} \]

      2. unpow2 48.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 2\right) \cdot \left(x \cdot 2\right)} - {\left(a \cdot b\right)}^{2} \cdot 729}{x \cdot 2 + -27 \cdot \left(a \cdot b\right)} \]

      3. *-commutative 48.0%

         \[\leadsto \frac{\left(x \cdot 2\right) \cdot \left(x \cdot 2\right) - \color{blue}{729 \cdot {\left(a \cdot b\right)}^{2}}}{x \cdot 2 + -27 \cdot \left(a \cdot b\right)} \]

      4. metadata-eval 48.0%

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

      5. unpow2 48.0%

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

      6. swap-sqr 48.1%

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

      7. flip-- 86.2%

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

      8. associate-*r* 86.2%

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

      9. cancel-sign-sub-inv 86.2%

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

   8. Applied egg-rr 86.2%

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

   if 8.19999999999999959e67 < t < 3.7999999999999999e255

   1. Initial program 97.5%

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

      1. sub-neg 97.5%

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

      2. sub-neg 97.5%

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

      3. associate-*l* 95.3%

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

      4. associate-*l* 95.2%

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

   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. Taylor expanded in x around 0 86.8%

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

   if 3.7999999999999999e255 < t

   1. Initial program 94.1%

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

      1. sub-neg 94.1%

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

      2. sub-neg 94.1%

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

      3. associate-*l* 77.4%

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

      4. associate-*l* 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in a around 0 92.9%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-209}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+67}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+255}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 8: 96.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 2.3 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 2.3e+51)
   (+ (* y (* z (* t -9.0))) (+ (* 27.0 (* a b)) (* x 2.0)))
   (- (* x 2.0) (* 9.0 (* t (* y z))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2.3e+51) {
		tmp = (y * (z * (t * -9.0))) + ((27.0 * (a * b)) + (x * 2.0));
	} else {
		tmp = (x * 2.0) - (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.
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 <= 2.3d+51) then
        tmp = (y * (z * (t * (-9.0d0)))) + ((27.0d0 * (a * b)) + (x * 2.0d0))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2.3e+51) {
		tmp = (y * (z * (t * -9.0))) + ((27.0 * (a * b)) + (x * 2.0));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 2.3e+51:
		tmp = (y * (z * (t * -9.0))) + ((27.0 * (a * b)) + (x * 2.0))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 2.3e+51)
		tmp = Float64(Float64(y * Float64(z * Float64(t * -9.0))) + Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0)));
	else
		tmp = Float64(Float64(x * 2.0) - 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])){:}
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 <= 2.3e+51)
		tmp = (y * (z * (t * -9.0))) + ((27.0 * (a * b)) + (x * 2.0));
	else
		tmp = (x * 2.0) - (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.
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, 2.3e+51], N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.30000000000000005e51

   1. Initial program 97.0%

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

      1. +-commutative 97.0%

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

      2. associate-+r- 97.0%

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

      3. *-commutative 97.0%

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

      4. cancel-sign-sub-inv 97.0%

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

      5. associate-*r* 93.1%

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

      6. distribute-lft-neg-in 93.1%

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

      7. *-commutative 93.1%

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

      8. cancel-sign-sub-inv 93.1%

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

      9. associate-+r- 93.1%

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

      10. associate-*l* 93.1%

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

      11. fma-def 94.1%

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

      12. cancel-sign-sub-inv 94.1%

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

      13. fma-def 94.1%

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

      14. *-commutative 94.1%

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

      15. distribute-rgt-neg-in 94.1%

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

      16. distribute-lft-neg-out 94.1%

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

      17. associate-*r* 97.9%

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

      18. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

      1. fma-udef 96.9%

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

      2. fma-udef 96.9%

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

      3. associate-+r+ 96.9%

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

      4. associate-*r* 96.9%

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

      5. *-commutative 96.9%

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

      6. associate-*l* 96.9%

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

      7. *-commutative 96.9%

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

      8. associate-*l* 97.9%

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

      9. *-commutative 97.9%

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

      10. associate-*r* 97.8%

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

      11. *-commutative 97.8%

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

   5. Applied egg-rr 97.8%

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

   if 2.30000000000000005e51 < z

   1. Initial program 91.1%

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

      1. sub-neg 91.1%

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

      2. sub-neg 91.1%

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

      3. associate-*l* 91.4%

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

      4. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in a around 0 72.1%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.3 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 9: 95.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (b * (a * 27.0)) + ((x * 2.0) - ((y * z) * (t * 9.0)));
end

Wolfram

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

Derivation

1. Initial program 95.7%

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

2. Taylor expanded in y around 0 95.6%

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

3. Taylor expanded in y around 0 95.6%

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

   1. associate-*r* 95.7%

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

5. Simplified 95.7%

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

6. Final simplification 95.7%

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

Alternative 10: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (y * z))));
end

Wolfram

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

Derivation

1. Initial program 95.7%

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

2. Taylor expanded in y around 0 95.6%

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

3. Final simplification 95.6%

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

Alternative 11: 95.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (t * (z * (y * 9.0)))) + (b * (a * 27.0));
end

Wolfram

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

Derivation

1. Initial program 95.7%

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

2. Final simplification 95.7%

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

Alternative 12: 79.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-61} \lor \neg \left(z \leq 6.5 \cdot 10^{-66}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 (<= z -4.4e-61) (not (<= z 6.5e-66)))
   (- (* x 2.0) (* 9.0 (* t (* y z))))
   (+ (* 27.0 (* a b)) (* x 2.0))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.4e-61) || !(z <= 6.5e-66)) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.4d-61)) .or. (.not. (z <= 6.5d-66))) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    else
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.4e-61) || !(z <= 6.5e-66)) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.4e-61) or not (z <= 6.5e-66):
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	else:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.4e-61) || !(z <= 6.5e-66))
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	else
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.4e-61) || ~((z <= 6.5e-66)))
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	else
		tmp = (27.0 * (a * b)) + (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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[z, -4.4e-61], N[Not[LessEqual[z, 6.5e-66]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000017e-61 or 6.50000000000000024e-66 < z

   1. Initial program 93.5%

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

      1. sub-neg 93.5%

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

      2. sub-neg 93.5%

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

      3. associate-*l* 94.2%

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

      4. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in a around 0 70.9%

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

   if -4.40000000000000017e-61 < z < 6.50000000000000024e-66

   1. Initial program 99.0%

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

      1. sub-neg 99.0%

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

      2. sub-neg 99.0%

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

      3. associate-*l* 99.7%

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

      4. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 83.4%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-61} \lor \neg \left(z \leq 6.5 \cdot 10^{-66}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \end{array} \]

Alternative 13: 80.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-60}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-69}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 -1.2e-60)
   (- (* x 2.0) (* 9.0 (* z (* t y))))
   (if (<= z 8.2e-69)
     (+ (* 27.0 (* a b)) (* x 2.0))
     (- (* x 2.0) (* 9.0 (* t (* y z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.2e-60) {
		tmp = (x * 2.0) - (9.0 * (z * (t * y)));
	} else if (z <= 8.2e-69) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (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.
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 <= (-1.2d-60)) then
        tmp = (x * 2.0d0) - (9.0d0 * (z * (t * y)))
    else if (z <= 8.2d-69) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.2e-60) {
		tmp = (x * 2.0) - (9.0 * (z * (t * y)));
	} else if (z <= 8.2e-69) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.2e-60:
		tmp = (x * 2.0) - (9.0 * (z * (t * y)))
	elif z <= 8.2e-69:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.2e-60)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(z * Float64(t * y))));
	elseif (z <= 8.2e-69)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.2e-60)
		tmp = (x * 2.0) - (9.0 * (z * (t * y)));
	elseif (z <= 8.2e-69)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = (x * 2.0) - (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.
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, -1.2e-60], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-69], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.20000000000000005e-60

   1. Initial program 94.2%

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

      1. sub-neg 94.2%

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

      2. sub-neg 94.2%

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

      3. associate-*l* 94.2%

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

      4. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in a around 0 74.4%

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

      1. expm1-log1p-u 46.0%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-udef 45.9%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 45.9%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y \cdot z\right) \cdot t}\right)} - 1\right) \]

      4. *-commutative 45.9%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(z \cdot y\right)} \cdot t\right)} - 1\right) \]

      5. associate-*l* 45.9%

         \[\leadsto 2 \cdot x - 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{z \cdot \left(y \cdot t\right)}\right)} - 1\right) \]

   6. Applied egg-rr 45.9%

      \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(z \cdot \left(y \cdot t\right)\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 46.0%

         \[\leadsto 2 \cdot x - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(z \cdot \left(y \cdot t\right)\right)\right)} \]

      2. expm1-log1p 77.2%

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

      3. *-commutative 77.2%

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

   8. Simplified 77.2%

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

   if -1.20000000000000005e-60 < z < 8.1999999999999998e-69

   1. Initial program 99.0%

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

      1. sub-neg 99.0%

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

      2. sub-neg 99.0%

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

      3. associate-*l* 99.7%

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

      4. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 83.3%

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

   if 8.1999999999999998e-69 < z

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. sub-neg 93.0%

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

      3. associate-*l* 94.3%

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

      4. associate-*l* 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. Taylor expanded in a around 0 67.3%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-60}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-69}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 14: 75.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-47}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+29}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 -8.8e-47)
   (* z (* -9.0 (* t y)))
   (if (<= z 5.4e+29) (+ (* 27.0 (* a b)) (* x 2.0)) (* -9.0 (* t (* y z))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.8e-47) {
		tmp = z * (-9.0 * (t * y));
	} else if (z <= 5.4e+29) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = -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.
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 <= (-8.8d-47)) then
        tmp = z * ((-9.0d0) * (t * y))
    else if (z <= 5.4d+29) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (-9.0d0) * (t * (y * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.8e-47) {
		tmp = z * (-9.0 * (t * y));
	} else if (z <= 5.4e+29) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = -9.0 * (t * (y * z));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.8e-47:
		tmp = z * (-9.0 * (t * y))
	elif z <= 5.4e+29:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = -9.0 * (t * (y * z))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.8e-47)
		tmp = Float64(z * Float64(-9.0 * Float64(t * y)));
	elseif (z <= 5.4e+29)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = 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])){:}
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 <= -8.8e-47)
		tmp = z * (-9.0 * (t * y));
	elseif (z <= 5.4e+29)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = -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.
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, -8.8e-47], N[(z * N[(-9.0 * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+29], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.80000000000000075e-47

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0 95.4%

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

   3. Taylor expanded in y around inf 52.7%

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

      1. *-commutative 52.7%

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

      2. *-commutative 52.7%

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

      3. *-commutative 52.7%

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

      4. associate-*r* 54.0%

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

      5. associate-*l* 54.0%

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

      6. *-commutative 54.0%

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

   5. Simplified 54.0%

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

   if -8.80000000000000075e-47 < z < 5.4e29

   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. sub-neg 97.6%

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

      2. sub-neg 97.6%

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

      3. associate-*l* 99.0%

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

      4. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 83.9%

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

   if 5.4e29 < z

   1. Initial program 91.9%

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

      1. sub-neg 91.9%

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

      2. sub-neg 91.9%

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

      3. associate-*l* 92.1%

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

      4. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in y around inf 47.5%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-47}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+29}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 15: 48.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+38} \lor \neg \left(a \leq 2.95 \cdot 10^{-74}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 -2.5e+38) (not (<= a 2.95e-74))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.5e+38) || !(a <= 2.95e-74)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 <= (-2.5d+38)) .or. (.not. (a <= 2.95d-74))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
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 <= -2.5e+38) || !(a <= 2.95e-74)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[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 <= -2.5e+38) or not (a <= 2.95e-74):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
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 <= -2.5e+38) || !(a <= 2.95e-74))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
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 <= -2.5e+38) || ~((a <= 2.95e-74)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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, -2.5e+38], N[Not[LessEqual[a, 2.95e-74]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.49999999999999985e38 or 2.94999999999999983e-74 < a

   1. Initial program 93.8%

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

      1. sub-neg 93.8%

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

      2. sub-neg 93.8%

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

      3. associate-*l* 94.7%

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

      4. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in a around inf 54.5%

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

   if -2.49999999999999985e38 < a < 2.94999999999999983e-74

   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. sub-neg 97.6%

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

      2. sub-neg 97.6%

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

      3. associate-*l* 98.2%

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

      4. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around inf 48.4%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+38} \lor \neg \left(a \leq 2.95 \cdot 10^{-74}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 16: 48.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-75}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.55e+35)
   (* a (* 27.0 b))
   (if (<= a 1.3e-75) (* x 2.0) (* 27.0 (* a b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.55e+35) {
		tmp = a * (27.0 * b);
	} else if (a <= 1.3e-75) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.55d+35)) then
        tmp = a * (27.0d0 * b)
    else if (a <= 1.3d-75) then
        tmp = x * 2.0d0
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.55e+35) {
		tmp = a * (27.0 * b);
	} else if (a <= 1.3e-75) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.55e+35:
		tmp = a * (27.0 * b)
	elif a <= 1.3e-75:
		tmp = x * 2.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.55e+35)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (a <= 1.3e-75)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.55e+35)
		tmp = a * (27.0 * b);
	elseif (a <= 1.3e-75)
		tmp = x * 2.0;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.55e+35], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e-75], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.54999999999999993e35

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. sub-neg 96.1%

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

      3. associate-*l* 94.5%

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

      4. 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. Taylor expanded in a around inf 53.9%

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

      1. associate-*r* 53.9%

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

      2. *-commutative 53.9%

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

      3. associate-*r* 53.9%

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

   6. Simplified 53.9%

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

   if -1.54999999999999993e35 < a < 1.3e-75

   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. sub-neg 97.6%

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

      2. sub-neg 97.6%

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

      3. associate-*l* 98.2%

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

      4. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around inf 48.4%

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

   if 1.3e-75 < a

   1. Initial program 92.4%

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

      1. sub-neg 92.4%

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

      2. sub-neg 92.4%

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

      3. associate-*l* 94.9%

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

      4. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in a around inf 54.9%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-75}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 17: 31.4% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * 2.0d0
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

   1. sub-neg 95.7%

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

   2. sub-neg 95.7%

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

   3. associate-*l* 96.4%

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

   4. associate-*l* 96.4%

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

3. Simplified 96.4%

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

4. Taylor expanded in x around inf 35.0%

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

5. Final simplification 35.0%

   \[\leadsto x \cdot 2 \]

Developer target: 94.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (< y 7.590524218811189e-161)
   (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y < 7.590524218811189d-161) then
        tmp = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + (a * (27.0d0 * b))
    else
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (t * z)))) + ((a * 27.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y < 7.590524218811189e-161:
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b))
	else:
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y < 7.590524218811189e-161)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(t * z)))) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y < 7.590524218811189e-161)
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	else
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Less[y, 7.590524218811189e-161], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023322 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (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)))