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

Percentage Accurate: 95.3% → 98.1%

Time: 13.2s

Alternatives: 15

Speedup: 0.8×

• 27.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 4.5 \cdot 10^{-108}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(2 \cdot \frac{x}{t} + 27 \cdot \frac{a \cdot b}{t}\right) - 9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 4.5e-108)
   (+ (* y (* z (* t -9.0))) (+ (* 27.0 (* a b)) (* x 2.0)))
   (* t (- (+ (* 2.0 (/ x t)) (* 27.0 (/ (* a b) t))) (* 9.0 (* z y))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 4.5e-108) {
		tmp = (y * (z * (t * -9.0))) + ((27.0 * (a * b)) + (x * 2.0));
	} else {
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (z * y)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 4.5d-108) then
        tmp = (y * (z * (t * (-9.0d0)))) + ((27.0d0 * (a * b)) + (x * 2.0d0))
    else
        tmp = t * (((2.0d0 * (x / t)) + (27.0d0 * ((a * b) / t))) - (9.0d0 * (z * y)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 4.5e-108) {
		tmp = (y * (z * (t * -9.0))) + ((27.0 * (a * b)) + (x * 2.0));
	} else {
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (z * y)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 4.5e-108:
		tmp = (y * (z * (t * -9.0))) + ((27.0 * (a * b)) + (x * 2.0))
	else:
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (z * y)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 4.5e-108)
		tmp = Float64(Float64(y * Float64(z * Float64(t * -9.0))) + Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0)));
	else
		tmp = Float64(t * Float64(Float64(Float64(2.0 * Float64(x / t)) + Float64(27.0 * Float64(Float64(a * b) / t))) - Float64(9.0 * Float64(z * y))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 4.5e-108)
		tmp = (y * (z * (t * -9.0))) + ((27.0 * (a * b)) + (x * 2.0));
	else
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 4.5e-108], 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[(t * N[(N[(N[(2.0 * N[(x / t), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(N[(a * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.4999999999999997e-108

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. associate-+r- 97.4%

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

      3. *-commutative 97.4%

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

      4. cancel-sign-sub-inv 97.4%

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

      5. associate-*r* 90.2%

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

      6. distribute-lft-neg-in 90.2%

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

      7. *-commutative 90.2%

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

      8. cancel-sign-sub-inv 90.2%

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

      9. associate-+r- 90.2%

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

      10. associate-*l* 91.3%

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

      11. fma-define 91.3%

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

      12. cancel-sign-sub-inv 91.3%

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

      13. fma-define 91.3%

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

      14. distribute-lft-neg-in 91.3%

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

      15. distribute-rgt-neg-in 91.3%

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

      16. *-commutative 91.3%

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

      17. associate-*r* 98.6%

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

      18. associate-*l* 98.6%

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

      19. neg-mul-1 98.6%

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

      20. associate-*r* 98.6%

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

   3. Simplified 98.6%

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

      1. fma-undefine 98.6%

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

      2. fma-undefine 98.6%

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

      3. associate-+r+ 98.6%

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

      4. *-commutative 98.6%

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

      5. associate-*l* 97.8%

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

      6. *-commutative 97.8%

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

      7. associate-*r* 97.3%

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

      8. *-commutative 97.3%

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

      9. associate-*r* 96.1%

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

      10. *-commutative 96.1%

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

      11. associate-*l* 97.3%

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

   6. Applied egg-rr 97.3%

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

   if 4.4999999999999997e-108 < z

   1. Initial program 96.5%

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

      1. sub-neg 96.5%

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

      2. sub-neg 96.5%

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

      3. associate-*l* 91.2%

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

      4. associate-*l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in t around inf 85.8%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.5 \cdot 10^{-108}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(2 \cdot \frac{x}{t} + 27 \cdot \frac{a \cdot b}{t}\right) - 9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 49.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+15}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-135}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.02 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= z -4.3e+15)
     (* -9.0 (* z (* y t)))
     (if (<= z -7.5e-246)
       t_1
       (if (<= z 1.7e-135)
         (* x 2.0)
         (if (<= z 2.02e-72) t_1 (* t (* y (* z -9.0)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (z <= -4.3e+15) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= -7.5e-246) {
		tmp = t_1;
	} else if (z <= 1.7e-135) {
		tmp = x * 2.0;
	} else if (z <= 2.02e-72) {
		tmp = t_1;
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (z <= (-4.3d+15)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (z <= (-7.5d-246)) then
        tmp = t_1
    else if (z <= 1.7d-135) then
        tmp = x * 2.0d0
    else if (z <= 2.02d-72) then
        tmp = t_1
    else
        tmp = t * (y * (z * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (z <= -4.3e+15) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= -7.5e-246) {
		tmp = t_1;
	} else if (z <= 1.7e-135) {
		tmp = x * 2.0;
	} else if (z <= 2.02e-72) {
		tmp = t_1;
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if z <= -4.3e+15:
		tmp = -9.0 * (z * (y * t))
	elif z <= -7.5e-246:
		tmp = t_1
	elif z <= 1.7e-135:
		tmp = x * 2.0
	elif z <= 2.02e-72:
		tmp = t_1
	else:
		tmp = t * (y * (z * -9.0))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (z <= -4.3e+15)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (z <= -7.5e-246)
		tmp = t_1;
	elseif (z <= 1.7e-135)
		tmp = Float64(x * 2.0);
	elseif (z <= 2.02e-72)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (z <= -4.3e+15)
		tmp = -9.0 * (z * (y * t));
	elseif (z <= -7.5e-246)
		tmp = t_1;
	elseif (z <= 1.7e-135)
		tmp = x * 2.0;
	elseif (z <= 2.02e-72)
		tmp = t_1;
	else
		tmp = t * (y * (z * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e+15], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-246], t$95$1, If[LessEqual[z, 1.7e-135], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 2.02e-72], t$95$1, N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.3e15

   1. Initial program 96.5%

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

      1. sub-neg 96.5%

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

      2. sub-neg 96.5%

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

      3. associate-*l* 95.4%

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

      4. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in y around inf 48.6%

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

      1. *-commutative 48.6%

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

      2. associate-*r* 48.7%

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

   7. Simplified 48.7%

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

   if -4.3e15 < z < -7.50000000000000049e-246 or 1.69999999999999995e-135 < z < 2.02e-72

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. sub-neg 97.2%

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

      3. associate-*l* 96.5%

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

      4. associate-*l* 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. Add Preprocessing

   5. Taylor expanded in a around inf 51.4%

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

   if -7.50000000000000049e-246 < z < 1.69999999999999995e-135

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 49.8%

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

   if 2.02e-72 < z

   1. Initial program 96.2%

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

      1. sub-neg 96.2%

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

      2. sub-neg 96.2%

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

      3. associate-*l* 90.5%

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

      4. associate-*l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in y around inf 48.8%

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

      1. *-commutative 48.8%

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

      2. associate-*r* 48.8%

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

      3. associate-*r* 48.8%

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

   7. Simplified 48.8%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+15}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-246}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-135}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.02 \cdot 10^{-72}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 45.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-172}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-259}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3e-172)
   (* 27.0 (* a b))
   (if (<= b 1.06e-259)
     (* x 2.0)
     (if (<= b 6.2e-24)
       (* t (* z (* y -9.0)))
       (if (<= b 6.5e+108) (* x 2.0) (* b (* 27.0 a)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-172) {
		tmp = 27.0 * (a * b);
	} else if (b <= 1.06e-259) {
		tmp = x * 2.0;
	} else if (b <= 6.2e-24) {
		tmp = t * (z * (y * -9.0));
	} else if (b <= 6.5e+108) {
		tmp = x * 2.0;
	} else {
		tmp = b * (27.0 * a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3d-172)) then
        tmp = 27.0d0 * (a * b)
    else if (b <= 1.06d-259) then
        tmp = x * 2.0d0
    else if (b <= 6.2d-24) then
        tmp = t * (z * (y * (-9.0d0)))
    else if (b <= 6.5d+108) then
        tmp = x * 2.0d0
    else
        tmp = b * (27.0d0 * a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-172) {
		tmp = 27.0 * (a * b);
	} else if (b <= 1.06e-259) {
		tmp = x * 2.0;
	} else if (b <= 6.2e-24) {
		tmp = t * (z * (y * -9.0));
	} else if (b <= 6.5e+108) {
		tmp = x * 2.0;
	} else {
		tmp = b * (27.0 * a);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3e-172:
		tmp = 27.0 * (a * b)
	elif b <= 1.06e-259:
		tmp = x * 2.0
	elif b <= 6.2e-24:
		tmp = t * (z * (y * -9.0))
	elif b <= 6.5e+108:
		tmp = x * 2.0
	else:
		tmp = b * (27.0 * a)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3e-172)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (b <= 1.06e-259)
		tmp = Float64(x * 2.0);
	elseif (b <= 6.2e-24)
		tmp = Float64(t * Float64(z * Float64(y * -9.0)));
	elseif (b <= 6.5e+108)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(b * Float64(27.0 * a));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3e-172)
		tmp = 27.0 * (a * b);
	elseif (b <= 1.06e-259)
		tmp = x * 2.0;
	elseif (b <= 6.2e-24)
		tmp = t * (z * (y * -9.0));
	elseif (b <= 6.5e+108)
		tmp = x * 2.0;
	else
		tmp = b * (27.0 * a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3e-172], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.06e-259], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 6.2e-24], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+108], N[(x * 2.0), $MachinePrecision], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.99999999999999984e-172

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. sub-neg 96.7%

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

      3. associate-*l* 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* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in a around inf 49.5%

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

   if -2.99999999999999984e-172 < b < 1.06e-259 or 6.2000000000000001e-24 < b < 6.4999999999999996e108

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. sub-neg 97.2%

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

      3. associate-*l* 93.4%

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

      4. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in x around inf 46.0%

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

   if 1.06e-259 < b < 6.2000000000000001e-24

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 93.8%

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

      4. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around inf 56.3%

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

      1. *-commutative 56.3%

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

      2. associate-*r* 56.2%

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

      3. associate-*r* 56.2%

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

   7. Simplified 56.2%

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

   8. Taylor expanded in y around 0 56.2%

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

      1. *-commutative 56.2%

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

      2. *-commutative 56.2%

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

      3. associate-*l* 56.3%

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

   10. Simplified 56.3%

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

   if 6.4999999999999996e108 < b

   1. Initial program 95.3%

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

      1. sub-neg 95.3%

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

      2. sub-neg 95.3%

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

      3. associate-*l* 93.2%

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

      4. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in a around inf 69.6%

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

      1. associate-*r* 69.7%

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

   7. Simplified 69.7%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-172}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-259}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 45.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-172}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-261}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+109}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3e-172)
   (* 27.0 (* a b))
   (if (<= b 1.45e-261)
     (* x 2.0)
     (if (<= b 4.1e-24)
       (* t (* y (* z -9.0)))
       (if (<= b 1.1e+109) (* x 2.0) (* b (* 27.0 a)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-172) {
		tmp = 27.0 * (a * b);
	} else if (b <= 1.45e-261) {
		tmp = x * 2.0;
	} else if (b <= 4.1e-24) {
		tmp = t * (y * (z * -9.0));
	} else if (b <= 1.1e+109) {
		tmp = x * 2.0;
	} else {
		tmp = b * (27.0 * a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3d-172)) then
        tmp = 27.0d0 * (a * b)
    else if (b <= 1.45d-261) then
        tmp = x * 2.0d0
    else if (b <= 4.1d-24) then
        tmp = t * (y * (z * (-9.0d0)))
    else if (b <= 1.1d+109) then
        tmp = x * 2.0d0
    else
        tmp = b * (27.0d0 * a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-172) {
		tmp = 27.0 * (a * b);
	} else if (b <= 1.45e-261) {
		tmp = x * 2.0;
	} else if (b <= 4.1e-24) {
		tmp = t * (y * (z * -9.0));
	} else if (b <= 1.1e+109) {
		tmp = x * 2.0;
	} else {
		tmp = b * (27.0 * a);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3e-172:
		tmp = 27.0 * (a * b)
	elif b <= 1.45e-261:
		tmp = x * 2.0
	elif b <= 4.1e-24:
		tmp = t * (y * (z * -9.0))
	elif b <= 1.1e+109:
		tmp = x * 2.0
	else:
		tmp = b * (27.0 * a)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3e-172)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (b <= 1.45e-261)
		tmp = Float64(x * 2.0);
	elseif (b <= 4.1e-24)
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	elseif (b <= 1.1e+109)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(b * Float64(27.0 * a));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3e-172)
		tmp = 27.0 * (a * b);
	elseif (b <= 1.45e-261)
		tmp = x * 2.0;
	elseif (b <= 4.1e-24)
		tmp = t * (y * (z * -9.0));
	elseif (b <= 1.1e+109)
		tmp = x * 2.0;
	else
		tmp = b * (27.0 * a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3e-172], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e-261], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 4.1e-24], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e+109], N[(x * 2.0), $MachinePrecision], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.99999999999999984e-172

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. sub-neg 96.7%

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

      3. associate-*l* 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* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in a around inf 49.5%

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

   if -2.99999999999999984e-172 < b < 1.44999999999999993e-261 or 4.10000000000000015e-24 < b < 1.1e109

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. sub-neg 97.2%

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

      3. associate-*l* 93.4%

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

      4. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in x around inf 46.0%

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

   if 1.44999999999999993e-261 < b < 4.10000000000000015e-24

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 93.8%

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

      4. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around inf 56.3%

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

      1. *-commutative 56.3%

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

      2. associate-*r* 56.2%

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

      3. associate-*r* 56.2%

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

   7. Simplified 56.2%

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

   if 1.1e109 < b

   1. Initial program 95.3%

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

      1. sub-neg 95.3%

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

      2. sub-neg 95.3%

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

      3. associate-*l* 93.2%

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

      4. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in a around inf 69.6%

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

      1. associate-*r* 69.7%

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

   7. Simplified 69.7%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-172}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-261}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+109}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 45.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-172}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-268}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{-24}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3e-172)
   (* 27.0 (* a b))
   (if (<= b 7e-268)
     (* x 2.0)
     (if (<= b 2.65e-24)
       (* -9.0 (* t (* z y)))
       (if (<= b 6.5e+108) (* x 2.0) (* b (* 27.0 a)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-172) {
		tmp = 27.0 * (a * b);
	} else if (b <= 7e-268) {
		tmp = x * 2.0;
	} else if (b <= 2.65e-24) {
		tmp = -9.0 * (t * (z * y));
	} else if (b <= 6.5e+108) {
		tmp = x * 2.0;
	} else {
		tmp = b * (27.0 * a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3d-172)) then
        tmp = 27.0d0 * (a * b)
    else if (b <= 7d-268) then
        tmp = x * 2.0d0
    else if (b <= 2.65d-24) then
        tmp = (-9.0d0) * (t * (z * y))
    else if (b <= 6.5d+108) then
        tmp = x * 2.0d0
    else
        tmp = b * (27.0d0 * a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-172) {
		tmp = 27.0 * (a * b);
	} else if (b <= 7e-268) {
		tmp = x * 2.0;
	} else if (b <= 2.65e-24) {
		tmp = -9.0 * (t * (z * y));
	} else if (b <= 6.5e+108) {
		tmp = x * 2.0;
	} else {
		tmp = b * (27.0 * a);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3e-172:
		tmp = 27.0 * (a * b)
	elif b <= 7e-268:
		tmp = x * 2.0
	elif b <= 2.65e-24:
		tmp = -9.0 * (t * (z * y))
	elif b <= 6.5e+108:
		tmp = x * 2.0
	else:
		tmp = b * (27.0 * a)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3e-172)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (b <= 7e-268)
		tmp = Float64(x * 2.0);
	elseif (b <= 2.65e-24)
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	elseif (b <= 6.5e+108)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(b * Float64(27.0 * a));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3e-172)
		tmp = 27.0 * (a * b);
	elseif (b <= 7e-268)
		tmp = x * 2.0;
	elseif (b <= 2.65e-24)
		tmp = -9.0 * (t * (z * y));
	elseif (b <= 6.5e+108)
		tmp = x * 2.0;
	else
		tmp = b * (27.0 * a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3e-172], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e-268], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 2.65e-24], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+108], N[(x * 2.0), $MachinePrecision], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.99999999999999984e-172

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. sub-neg 96.7%

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

      3. associate-*l* 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* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in a around inf 49.5%

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

   if -2.99999999999999984e-172 < b < 7.00000000000000011e-268 or 2.64999999999999984e-24 < b < 6.4999999999999996e108

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. sub-neg 97.2%

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

      3. associate-*l* 93.4%

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

      4. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in x around inf 46.0%

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

   if 7.00000000000000011e-268 < b < 2.64999999999999984e-24

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 93.8%

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

      4. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around inf 56.3%

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

   if 6.4999999999999996e108 < b

   1. Initial program 95.3%

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

      1. sub-neg 95.3%

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

      2. sub-neg 95.3%

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

      3. associate-*l* 93.2%

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

      4. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in a around inf 69.6%

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

      1. associate-*r* 69.7%

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

   7. Simplified 69.7%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-172}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-268}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{-24}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + t\_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-131}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{t\_1}{t} + z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= z -7.5e-53)
     (+ (* y (* z (* t -9.0))) t_1)
     (if (<= z 4.3e-131)
       (+ (* 27.0 (* a b)) (* x 2.0))
       (* t (+ (/ t_1 t) (* z (* y -9.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -7.5e-53) {
		tmp = (y * (z * (t * -9.0))) + t_1;
	} else if (z <= 4.3e-131) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = t * ((t_1 / 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.
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 <= (-7.5d-53)) then
        tmp = (y * (z * (t * (-9.0d0)))) + t_1
    else if (z <= 4.3d-131) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = t * ((t_1 / t) + (z * (y * (-9.0d0))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -7.5e-53) {
		tmp = (y * (z * (t * -9.0))) + t_1;
	} else if (z <= 4.3e-131) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = t * ((t_1 / t) + (z * (y * -9.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if z <= -7.5e-53:
		tmp = (y * (z * (t * -9.0))) + t_1
	elif z <= 4.3e-131:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = t * ((t_1 / t) + (z * (y * -9.0)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (z <= -7.5e-53)
		tmp = Float64(Float64(y * Float64(z * Float64(t * -9.0))) + t_1);
	elseif (z <= 4.3e-131)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(t * Float64(Float64(t_1 / 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])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (z <= -7.5e-53)
		tmp = (y * (z * (t * -9.0))) + t_1;
	elseif (z <= 4.3e-131)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = t * ((t_1 / 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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e-53], N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 4.3e-131], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(t$95$1 / t), $MachinePrecision] + N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5000000000000001e-53

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. sub-neg 96.9%

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

      3. associate-*l* 95.8%

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

      4. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in x around 0 79.9%

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

      1. cancel-sign-sub-inv 79.9%

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

      2. metadata-eval 79.9%

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

      3. *-commutative 79.9%

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

      4. associate-*r* 80.0%

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

      5. +-commutative 80.0%

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

      6. associate-*r* 79.9%

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

      7. *-commutative 79.9%

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

      8. associate-*r* 79.9%

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

      9. associate-*r* 77.4%

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

      10. *-commutative 77.4%

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

      11. associate-*l* 77.4%

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

   7. Applied egg-rr 77.4%

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

   if -7.5000000000000001e-53 < z < 4.30000000000000019e-131

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. sub-neg 98.7%

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

      3. associate-*l* 98.1%

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

      4. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around 0 82.3%

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

   if 4.30000000000000019e-131 < z

   1. Initial program 95.8%

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

      1. sub-neg 95.8%

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

      2. sub-neg 95.8%

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

      3. associate-*l* 91.1%

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

      4. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in x around 0 75.0%

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

   6. Taylor expanded in t around inf 71.2%

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

      1. cancel-sign-sub-inv 71.2%

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

      2. metadata-eval 71.2%

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

      3. associate-*r/ 71.3%

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

      4. *-commutative 71.3%

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

      5. associate-*r* 71.2%

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

      6. *-commutative 71.2%

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

      7. associate-*r* 71.2%

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

   8. Simplified 71.2%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-131}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a \cdot \left(27 \cdot b\right)}{t} + z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+23} \lor \neg \left(z \leq 4.2 \cdot 10^{-131}\right):\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.5e+23) (not (<= z 4.2e-131)))
   (+ (* a (* 27.0 b)) (* -9.0 (* z (* y t))))
   (+ (* 27.0 (* a b)) (* x 2.0))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.5e+23) || !(z <= 4.2e-131)) {
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	} 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.
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 <= (-5.5d+23)) .or. (.not. (z <= 4.2d-131))) then
        tmp = (a * (27.0d0 * b)) + ((-9.0d0) * (z * (y * t)))
    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;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.5e+23) || !(z <= 4.2e-131)) {
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	} 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])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.5e+23) or not (z <= 4.2e-131):
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)))
	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])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.5e+23) || !(z <= 4.2e-131))
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(-9.0 * Float64(z * Float64(y * t))));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.5e+23) || ~((z <= 4.2e-131)))
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	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.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.5e+23], N[Not[LessEqual[z, 4.2e-131]], $MachinePrecision]], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(-9.0 * N[(z * N[(y * t), $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 < -5.50000000000000004e23 or 4.19999999999999994e-131 < z

   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* 92.7%

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

      4. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in x around 0 78.2%

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

      1. cancel-sign-sub-inv 78.2%

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

      2. metadata-eval 78.2%

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

      3. *-commutative 78.2%

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

      4. associate-*r* 77.1%

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

      5. +-commutative 77.1%

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

      6. associate-*r* 78.2%

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

      7. *-commutative 78.2%

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

      8. associate-*r* 77.6%

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

      9. associate-*r* 74.8%

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

      10. *-commutative 74.8%

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

      11. associate-*l* 74.8%

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

   7. Applied egg-rr 74.8%

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

   8. Taylor expanded in y around 0 78.2%

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

      1. associate-*r* 77.1%

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

   10. Simplified 77.1%

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

   if -5.50000000000000004e23 < z < 4.19999999999999994e-131

   1. Initial program 98.8%

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

      1. sub-neg 98.8%

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

      2. sub-neg 98.8%

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

      3. associate-*l* 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* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around 0 81.8%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+23} \lor \neg \left(z \leq 4.2 \cdot 10^{-131}\right):\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-132}:\\ \;\;\;\;t\_1 + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= z -1.15e-52)
     (+ (* y (* z (* t -9.0))) (* a (* 27.0 b)))
     (if (<= z 3.6e-132) (+ t_1 (* x 2.0)) (- t_1 (* 9.0 (* t (* z y))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (z <= -1.15e-52) {
		tmp = (y * (z * (t * -9.0))) + (a * (27.0 * b));
	} else if (z <= 3.6e-132) {
		tmp = t_1 + (x * 2.0);
	} else {
		tmp = t_1 - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (z <= (-1.15d-52)) then
        tmp = (y * (z * (t * (-9.0d0)))) + (a * (27.0d0 * b))
    else if (z <= 3.6d-132) then
        tmp = t_1 + (x * 2.0d0)
    else
        tmp = t_1 - (9.0d0 * (t * (z * y)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (z <= -1.15e-52) {
		tmp = (y * (z * (t * -9.0))) + (a * (27.0 * b));
	} else if (z <= 3.6e-132) {
		tmp = t_1 + (x * 2.0);
	} else {
		tmp = t_1 - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if z <= -1.15e-52:
		tmp = (y * (z * (t * -9.0))) + (a * (27.0 * b))
	elif z <= 3.6e-132:
		tmp = t_1 + (x * 2.0)
	else:
		tmp = t_1 - (9.0 * (t * (z * y)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (z <= -1.15e-52)
		tmp = Float64(Float64(y * Float64(z * Float64(t * -9.0))) + Float64(a * Float64(27.0 * b)));
	elseif (z <= 3.6e-132)
		tmp = Float64(t_1 + Float64(x * 2.0));
	else
		tmp = Float64(t_1 - Float64(9.0 * Float64(t * Float64(z * y))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (z <= -1.15e-52)
		tmp = (y * (z * (t * -9.0))) + (a * (27.0 * b));
	elseif (z <= 3.6e-132)
		tmp = t_1 + (x * 2.0);
	else
		tmp = t_1 - (9.0 * (t * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e-52], N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-132], N[(t$95$1 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.14999999999999997e-52

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. sub-neg 96.9%

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

      3. associate-*l* 95.8%

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

      4. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in x around 0 79.9%

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

      1. cancel-sign-sub-inv 79.9%

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

      2. metadata-eval 79.9%

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

      3. *-commutative 79.9%

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

      4. associate-*r* 80.0%

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

      5. +-commutative 80.0%

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

      6. associate-*r* 79.9%

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

      7. *-commutative 79.9%

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

      8. associate-*r* 79.9%

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

      9. associate-*r* 77.4%

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

      10. *-commutative 77.4%

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

      11. associate-*l* 77.4%

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

   7. Applied egg-rr 77.4%

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

   if -1.14999999999999997e-52 < z < 3.60000000000000007e-132

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. sub-neg 98.7%

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

      3. associate-*l* 98.1%

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

      4. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around 0 82.3%

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

   if 3.60000000000000007e-132 < z

   1. Initial program 95.8%

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

      1. sub-neg 95.8%

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

      2. sub-neg 95.8%

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

      3. associate-*l* 91.1%

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

      4. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in x around 0 75.0%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-132}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-132}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= z -1.85e-49)
     (+ (* y (* z (* t -9.0))) t_1)
     (if (<= z 1.3e-132)
       (+ (* 27.0 (* a b)) (* x 2.0))
       (+ t_1 (* -9.0 (* z (* y t))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -1.85e-49) {
		tmp = (y * (z * (t * -9.0))) + t_1;
	} else if (z <= 1.3e-132) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = t_1 + (-9.0 * (z * (y * t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if (z <= (-1.85d-49)) then
        tmp = (y * (z * (t * (-9.0d0)))) + t_1
    else if (z <= 1.3d-132) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = t_1 + ((-9.0d0) * (z * (y * t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -1.85e-49) {
		tmp = (y * (z * (t * -9.0))) + t_1;
	} else if (z <= 1.3e-132) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = t_1 + (-9.0 * (z * (y * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if z <= -1.85e-49:
		tmp = (y * (z * (t * -9.0))) + t_1
	elif z <= 1.3e-132:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = t_1 + (-9.0 * (z * (y * t)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (z <= -1.85e-49)
		tmp = Float64(Float64(y * Float64(z * Float64(t * -9.0))) + t_1);
	elseif (z <= 1.3e-132)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(t_1 + Float64(-9.0 * Float64(z * Float64(y * t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (z <= -1.85e-49)
		tmp = (y * (z * (t * -9.0))) + t_1;
	elseif (z <= 1.3e-132)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = t_1 + (-9.0 * (z * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e-49], N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 1.3e-132], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.85e-49

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. sub-neg 96.9%

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

      3. associate-*l* 95.8%

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

      4. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in x around 0 79.9%

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

      1. cancel-sign-sub-inv 79.9%

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

      2. metadata-eval 79.9%

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

      3. *-commutative 79.9%

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

      4. associate-*r* 80.0%

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

      5. +-commutative 80.0%

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

      6. associate-*r* 79.9%

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

      7. *-commutative 79.9%

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

      8. associate-*r* 79.9%

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

      9. associate-*r* 77.4%

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

      10. *-commutative 77.4%

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

      11. associate-*l* 77.4%

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

   7. Applied egg-rr 77.4%

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

   if -1.85e-49 < z < 1.3e-132

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. sub-neg 98.7%

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

      3. associate-*l* 98.1%

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

      4. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around 0 82.3%

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

   if 1.3e-132 < z

   1. Initial program 95.8%

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

      1. sub-neg 95.8%

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

      2. sub-neg 95.8%

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

      3. associate-*l* 91.1%

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

      4. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in x around 0 75.0%

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

      1. cancel-sign-sub-inv 75.0%

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

      2. metadata-eval 75.0%

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

      3. *-commutative 75.0%

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

      4. associate-*r* 73.1%

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

      5. +-commutative 73.1%

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

      6. associate-*r* 75.0%

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

      7. *-commutative 75.0%

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

      8. associate-*r* 74.0%

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

      9. associate-*r* 71.3%

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

      10. *-commutative 71.3%

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

      11. associate-*l* 71.2%

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

   7. Applied egg-rr 71.2%

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

   8. Taylor expanded in y around 0 74.9%

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

      1. associate-*r* 73.1%

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

   10. Simplified 73.1%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-132}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 96.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 4.6 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a \cdot \left(27 \cdot b\right)}{t} + z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 4.6e+74)
   (+ (* y (* z (* t -9.0))) (+ (* 27.0 (* a b)) (* x 2.0)))
   (* t (+ (/ (* a (* 27.0 b)) t) (* z (* y -9.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 4.6e+74) {
		tmp = (y * (z * (t * -9.0))) + ((27.0 * (a * b)) + (x * 2.0));
	} else {
		tmp = t * (((a * (27.0 * b)) / 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.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 4.6d+74) then
        tmp = (y * (z * (t * (-9.0d0)))) + ((27.0d0 * (a * b)) + (x * 2.0d0))
    else
        tmp = t * (((a * (27.0d0 * b)) / t) + (z * (y * (-9.0d0))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 4.6e+74) {
		tmp = (y * (z * (t * -9.0))) + ((27.0 * (a * b)) + (x * 2.0));
	} else {
		tmp = t * (((a * (27.0 * b)) / t) + (z * (y * -9.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 4.6e+74:
		tmp = (y * (z * (t * -9.0))) + ((27.0 * (a * b)) + (x * 2.0))
	else:
		tmp = t * (((a * (27.0 * b)) / t) + (z * (y * -9.0)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 4.6e+74)
		tmp = Float64(Float64(y * Float64(z * Float64(t * -9.0))) + Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0)));
	else
		tmp = Float64(t * Float64(Float64(Float64(a * Float64(27.0 * b)) / 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])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 4.6e+74)
		tmp = (y * (z * (t * -9.0))) + ((27.0 * (a * b)) + (x * 2.0));
	else
		tmp = t * (((a * (27.0 * b)) / 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.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 4.6e+74], 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[(t * N[(N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.5999999999999997e74

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. associate-+r- 97.4%

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

      3. *-commutative 97.4%

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

      4. cancel-sign-sub-inv 97.4%

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

      5. associate-*r* 91.2%

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

      6. distribute-lft-neg-in 91.2%

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

      7. *-commutative 91.2%

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

      8. cancel-sign-sub-inv 91.2%

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

      9. associate-+r- 91.2%

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

      10. associate-*l* 92.1%

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

      11. fma-define 92.1%

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

      12. cancel-sign-sub-inv 92.1%

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

      13. fma-define 92.1%

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

      14. distribute-lft-neg-in 92.1%

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

      15. distribute-rgt-neg-in 92.1%

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

      16. *-commutative 92.1%

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

      17. associate-*r* 98.3%

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

      18. associate-*l* 98.3%

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

      19. neg-mul-1 98.3%

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

      20. associate-*r* 98.3%

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

   3. Simplified 98.3%

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

      1. fma-undefine 98.3%

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

      2. fma-undefine 98.3%

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

      3. associate-+r+ 98.3%

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

      4. *-commutative 98.3%

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

      5. associate-*l* 97.3%

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

      6. *-commutative 97.3%

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

      7. associate-*r* 96.8%

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

      8. *-commutative 96.8%

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

      9. associate-*r* 95.9%

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

      10. *-commutative 95.9%

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

      11. associate-*l* 96.9%

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

   6. Applied egg-rr 96.9%

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

   if 4.5999999999999997e74 < z

   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* 88.0%

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

      4. associate-*l* 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in x around 0 84.9%

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

   6. Taylor expanded in t around inf 83.1%

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

      1. cancel-sign-sub-inv 83.1%

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

      2. metadata-eval 83.1%

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

      3. associate-*r/ 83.1%

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

      4. *-commutative 83.1%

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

      5. associate-*r* 83.1%

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

      6. *-commutative 83.1%

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

      7. associate-*r* 83.1%

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

   8. Simplified 83.1%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.6 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a \cdot \left(27 \cdot b\right)}{t} + z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+27}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-72}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.15e+27)
   (* -9.0 (* z (* y t)))
   (if (<= z 1.75e-72)
     (+ (* 27.0 (* a b)) (* x 2.0))
     (- (* x 2.0) (* 9.0 (* t (* z y)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+27) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= 1.75e-72) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.15d+27)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (z <= 1.75d-72) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+27) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= 1.75e-72) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.15e+27:
		tmp = -9.0 * (z * (y * t))
	elif z <= 1.75e-72:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.15e+27)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (z <= 1.75e-72)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.15e+27)
		tmp = -9.0 * (z * (y * t));
	elseif (z <= 1.75e-72)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.15e+27], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-72], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e27

   1. Initial program 96.4%

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

      1. sub-neg 96.4%

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

      2. sub-neg 96.4%

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

      3. associate-*l* 95.2%

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

      4. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around inf 48.6%

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

      1. *-commutative 48.6%

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

      2. associate-*r* 48.6%

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

   7. Simplified 48.6%

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

   if -1.15e27 < z < 1.75e-72

   1. Initial program 98.1%

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

      1. sub-neg 98.1%

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

      2. sub-neg 98.1%

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

      3. associate-*l* 97.7%

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

      4. associate-*l* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 80.2%

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

   if 1.75e-72 < z

   1. Initial program 96.2%

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

      1. sub-neg 96.2%

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

      2. sub-neg 96.2%

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

      3. associate-*l* 90.5%

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

      4. associate-*l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in a around 0 69.5%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+27}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-72}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+32}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+100}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.2e+32)
   (* -9.0 (* z (* y t)))
   (if (<= z 3.45e+100)
     (+ (* 27.0 (* a b)) (* x 2.0))
     (* t (* z (* y -9.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.2e+32) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= 3.45e+100) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} 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.
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 <= (-5.2d+32)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (z <= 3.45d+100) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    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;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.2e+32) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= 3.45e+100) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = t * (z * (y * -9.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.2e+32:
		tmp = -9.0 * (z * (y * t))
	elif z <= 3.45e+100:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = t * (z * (y * -9.0))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.2e+32)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (z <= 3.45e+100)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.2e+32)
		tmp = -9.0 * (z * (y * t));
	elseif (z <= 3.45e+100)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	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.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.2e+32], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.45e+100], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2000000000000004e32

   1. Initial program 96.4%

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

      1. sub-neg 96.4%

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

      2. sub-neg 96.4%

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

      3. associate-*l* 95.2%

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

      4. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around inf 48.6%

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

      1. *-commutative 48.6%

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

      2. associate-*r* 48.6%

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

   7. Simplified 48.6%

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

   if -5.2000000000000004e32 < z < 3.45e100

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. sub-neg 97.2%

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

      3. associate-*l* 95.1%

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

      4. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in y around 0 76.3%

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

   if 3.45e100 < z

   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* 93.3%

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

      4. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in y around inf 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-*r* 60.6%

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

      3. associate-*r* 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in y around 0 60.6%

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

      1. *-commutative 60.6%

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

      2. *-commutative 60.6%

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

      3. associate-*l* 60.6%

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

   10. Simplified 60.6%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+32}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+100}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-172} \lor \neg \left(b \leq 6.5 \cdot 10^{+108}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3e-172) (not (<= b 6.5e+108))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3e-172) || !(b <= 6.5e+108)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3d-172)) .or. (.not. (b <= 6.5d+108))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3e-172) || !(b <= 6.5e+108)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3e-172) or not (b <= 6.5e+108):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3e-172) || !(b <= 6.5e+108))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3e-172) || ~((b <= 6.5e+108)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3e-172], N[Not[LessEqual[b, 6.5e+108]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.99999999999999984e-172 or 6.4999999999999996e108 < b

   1. Initial program 96.3%

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

      1. sub-neg 96.3%

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

      2. sub-neg 96.3%

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

      3. associate-*l* 95.8%

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

      4. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in a around inf 55.6%

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

   if -2.99999999999999984e-172 < b < 6.4999999999999996e108

   1. Initial program 98.2%

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

      1. sub-neg 98.2%

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

      2. sub-neg 98.2%

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

      3. associate-*l* 93.5%

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

      4. associate-*l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in x around inf 38.0%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-172} \lor \neg \left(b \leq 6.5 \cdot 10^{+108}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-172}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+108}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3e-172)
   (* 27.0 (* a b))
   (if (<= b 6.8e+108) (* x 2.0) (* b (* 27.0 a)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-172) {
		tmp = 27.0 * (a * b);
	} else if (b <= 6.8e+108) {
		tmp = x * 2.0;
	} else {
		tmp = b * (27.0 * a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3d-172)) then
        tmp = 27.0d0 * (a * b)
    else if (b <= 6.8d+108) then
        tmp = x * 2.0d0
    else
        tmp = b * (27.0d0 * a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-172) {
		tmp = 27.0 * (a * b);
	} else if (b <= 6.8e+108) {
		tmp = x * 2.0;
	} else {
		tmp = b * (27.0 * a);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3e-172:
		tmp = 27.0 * (a * b)
	elif b <= 6.8e+108:
		tmp = x * 2.0
	else:
		tmp = b * (27.0 * a)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3e-172)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (b <= 6.8e+108)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(b * Float64(27.0 * a));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3e-172)
		tmp = 27.0 * (a * b);
	elseif (b <= 6.8e+108)
		tmp = x * 2.0;
	else
		tmp = b * (27.0 * a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3e-172], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.8e+108], N[(x * 2.0), $MachinePrecision], N[(b * N[(27.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.99999999999999984e-172

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. sub-neg 96.7%

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

      3. associate-*l* 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* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in a around inf 49.5%

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

   if -2.99999999999999984e-172 < b < 6.79999999999999992e108

   1. Initial program 98.2%

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

      1. sub-neg 98.2%

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

      2. sub-neg 98.2%

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

      3. associate-*l* 93.5%

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

      4. associate-*l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in x around inf 38.0%

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

   if 6.79999999999999992e108 < b

   1. Initial program 95.3%

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

      1. sub-neg 95.3%

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

      2. sub-neg 95.3%

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

      3. associate-*l* 93.2%

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

      4. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in a around inf 69.6%

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

      1. associate-*r* 69.7%

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

   7. Simplified 69.7%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-172}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+108}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(27 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.7% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

   1. sub-neg 97.1%

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

   2. sub-neg 97.1%

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

   3. associate-*l* 94.8%

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

   4. associate-*l* 95.5%

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

3. Simplified 95.5%

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

5. Taylor expanded in x around inf 28.4%

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

6. Final simplification 28.4%

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

Developer Target 1: 94.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024137 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y 7590524218811189/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x 2) (* (* (* y 9) z) t)) (* a (* 27 b))) (+ (- (* x 2) (* 9 (* y (* t z)))) (* (* a 27) b))))

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