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

Percentage Accurate: 95.1% → 98.3%

Time: 15.0s

Alternatives: 16

Speedup: 0.8×

• 27.3% 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: 95.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(y \cdot 9\right) \cdot z\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+101}:\\ \;\;\;\;\left(x \cdot 2 - t\_1 \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

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 (* (* y 9.0) z)))
   (if (<= t_1 2e+101)
     (+ (- (* x 2.0) (* t_1 t)) (* (* a 27.0) b))
     (* y (- (+ (* 2.0 (/ x y)) (* 27.0 (/ (* a b) y))) (* 9.0 (* z 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 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 2e+101) {
		tmp = ((x * 2.0) - (t_1 * t)) + ((a * 27.0) * b);
	} else {
		tmp = y * (((2.0 * (x / y)) + (27.0 * ((a * b) / y))) - (9.0 * (z * 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 = (y * 9.0d0) * z
    if (t_1 <= 2d+101) then
        tmp = ((x * 2.0d0) - (t_1 * t)) + ((a * 27.0d0) * b)
    else
        tmp = y * (((2.0d0 * (x / y)) + (27.0d0 * ((a * b) / y))) - (9.0d0 * (z * 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 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 2e+101) {
		tmp = ((x * 2.0) - (t_1 * t)) + ((a * 27.0) * b);
	} else {
		tmp = y * (((2.0 * (x / y)) + (27.0 * ((a * b) / y))) - (9.0 * (z * 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 = (y * 9.0) * z
	tmp = 0
	if t_1 <= 2e+101:
		tmp = ((x * 2.0) - (t_1 * t)) + ((a * 27.0) * b)
	else:
		tmp = y * (((2.0 * (x / y)) + (27.0 * ((a * b) / y))) - (9.0 * (z * 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(Float64(y * 9.0) * z)
	tmp = 0.0
	if (t_1 <= 2e+101)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t_1 * t)) + Float64(Float64(a * 27.0) * b));
	else
		tmp = Float64(y * Float64(Float64(Float64(2.0 * Float64(x / y)) + Float64(27.0 * Float64(Float64(a * b) / y))) - Float64(9.0 * Float64(z * 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 = (y * 9.0) * z;
	tmp = 0.0;
	if (t_1 <= 2e+101)
		tmp = ((x * 2.0) - (t_1 * t)) + ((a * 27.0) * b);
	else
		tmp = y * (((2.0 * (x / y)) + (27.0 * ((a * b) / y))) - (9.0 * (z * 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[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+101], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t$95$1 * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 2e101

   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. Add Preprocessing

   if 2e101 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 81.2%

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

      1. sub-neg 81.2%

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

      2. sub-neg 81.2%

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

      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* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in y around inf 99.8%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 2 \cdot 10^{+101}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 49.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ t_2 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-93}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-153}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-172}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 10^{-230}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-127}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))) (t_2 (* -9.0 (* t (* y z)))))
   (if (<= z -4.2e-93)
     (* -9.0 (* z (* y t)))
     (if (<= z -5.8e-130)
       t_1
       (if (<= z -7.8e-153)
         t_2
         (if (<= z -7.5e-172)
           (* 27.0 (* a b))
           (if (<= z 1e-230)
             (* x 2.0)
             (if (<= z 4.4e-197)
               t_1
               (if (<= z 8.5e-127)
                 (* x 2.0)
                 (if (<= z 6.5e-112) t_1 t_2))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = -9.0 * (t * (y * z));
	double tmp;
	if (z <= -4.2e-93) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= -5.8e-130) {
		tmp = t_1;
	} else if (z <= -7.8e-153) {
		tmp = t_2;
	} else if (z <= -7.5e-172) {
		tmp = 27.0 * (a * b);
	} else if (z <= 1e-230) {
		tmp = x * 2.0;
	} else if (z <= 4.4e-197) {
		tmp = t_1;
	} else if (z <= 8.5e-127) {
		tmp = x * 2.0;
	} else if (z <= 6.5e-112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    t_2 = (-9.0d0) * (t * (y * z))
    if (z <= (-4.2d-93)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (z <= (-5.8d-130)) then
        tmp = t_1
    else if (z <= (-7.8d-153)) then
        tmp = t_2
    else if (z <= (-7.5d-172)) then
        tmp = 27.0d0 * (a * b)
    else if (z <= 1d-230) then
        tmp = x * 2.0d0
    else if (z <= 4.4d-197) then
        tmp = t_1
    else if (z <= 8.5d-127) then
        tmp = x * 2.0d0
    else if (z <= 6.5d-112) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = -9.0 * (t * (y * z));
	double tmp;
	if (z <= -4.2e-93) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= -5.8e-130) {
		tmp = t_1;
	} else if (z <= -7.8e-153) {
		tmp = t_2;
	} else if (z <= -7.5e-172) {
		tmp = 27.0 * (a * b);
	} else if (z <= 1e-230) {
		tmp = x * 2.0;
	} else if (z <= 4.4e-197) {
		tmp = t_1;
	} else if (z <= 8.5e-127) {
		tmp = x * 2.0;
	} else if (z <= 6.5e-112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	t_2 = -9.0 * (t * (y * z))
	tmp = 0
	if z <= -4.2e-93:
		tmp = -9.0 * (z * (y * t))
	elif z <= -5.8e-130:
		tmp = t_1
	elif z <= -7.8e-153:
		tmp = t_2
	elif z <= -7.5e-172:
		tmp = 27.0 * (a * b)
	elif z <= 1e-230:
		tmp = x * 2.0
	elif z <= 4.4e-197:
		tmp = t_1
	elif z <= 8.5e-127:
		tmp = x * 2.0
	elif z <= 6.5e-112:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	t_2 = Float64(-9.0 * Float64(t * Float64(y * z)))
	tmp = 0.0
	if (z <= -4.2e-93)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (z <= -5.8e-130)
		tmp = t_1;
	elseif (z <= -7.8e-153)
		tmp = t_2;
	elseif (z <= -7.5e-172)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (z <= 1e-230)
		tmp = Float64(x * 2.0);
	elseif (z <= 4.4e-197)
		tmp = t_1;
	elseif (z <= 8.5e-127)
		tmp = Float64(x * 2.0);
	elseif (z <= 6.5e-112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	t_2 = -9.0 * (t * (y * z));
	tmp = 0.0;
	if (z <= -4.2e-93)
		tmp = -9.0 * (z * (y * t));
	elseif (z <= -5.8e-130)
		tmp = t_1;
	elseif (z <= -7.8e-153)
		tmp = t_2;
	elseif (z <= -7.5e-172)
		tmp = 27.0 * (a * b);
	elseif (z <= 1e-230)
		tmp = x * 2.0;
	elseif (z <= 4.4e-197)
		tmp = t_1;
	elseif (z <= 8.5e-127)
		tmp = x * 2.0;
	elseif (z <= 6.5e-112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e-93], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8e-130], t$95$1, If[LessEqual[z, -7.8e-153], t$95$2, If[LessEqual[z, -7.5e-172], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-230], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 4.4e-197], t$95$1, If[LessEqual[z, 8.5e-127], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 6.5e-112], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.2000000000000002e-93

   1. Initial program 90.9%

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

      1. sub-neg 90.9%

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

      2. sub-neg 90.9%

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

      3. associate-*l* 91.8%

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

      4. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in t around inf 85.2%

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

   6. Taylor expanded in t around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. *-commutative 52.8%

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

      3. associate-*l* 55.1%

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

      4. *-commutative 55.1%

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

   8. Simplified 55.1%

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

   if -4.2000000000000002e-93 < z < -5.8e-130 or 1.00000000000000005e-230 < z < 4.4000000000000001e-197 or 8.5e-127 < z < 6.49999999999999956e-112

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l* 99.9%

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

      4. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 77.7%

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

      1. associate-*r* 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-*r* 77.7%

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

   7. Simplified 77.7%

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

   if -5.8e-130 < z < -7.8000000000000004e-153 or 6.49999999999999956e-112 < z

   1. Initial program 94.6%

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

      1. sub-neg 94.6%

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

      2. sub-neg 94.6%

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

      3. associate-*l* 93.6%

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

      4. associate-*l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in y around inf 50.6%

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

   if -7.8000000000000004e-153 < z < -7.4999999999999999e-172

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around inf 73.0%

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

   if -7.4999999999999999e-172 < z < 1.00000000000000005e-230 or 4.4000000000000001e-197 < z < 8.5e-127

   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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 60.2%

      \[\leadsto \color{blue}{2 \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-93}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-130}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-153}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-172}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 10^{-230}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-197}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-127}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-112}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-172}:\\ \;\;\;\;\left(t \cdot -9\right) \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-229}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-126}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

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 (* a (* 27.0 b))))
   (if (<= z -4.3e-94)
     (* z (* y (* t -9.0)))
     (if (<= z -1.9e-127)
       t_1
       (if (<= z -7.2e-172)
         (* (* t -9.0) (* y z))
         (if (<= z 1.85e-229)
           (* x 2.0)
           (if (<= z 3.7e-194)
             t_1
             (if (<= z 1.4e-126)
               (* x 2.0)
               (if (<= z 6.8e-112) 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 = a * (27.0 * b);
	double tmp;
	if (z <= -4.3e-94) {
		tmp = z * (y * (t * -9.0));
	} else if (z <= -1.9e-127) {
		tmp = t_1;
	} else if (z <= -7.2e-172) {
		tmp = (t * -9.0) * (y * z);
	} else if (z <= 1.85e-229) {
		tmp = x * 2.0;
	} else if (z <= 3.7e-194) {
		tmp = t_1;
	} else if (z <= 1.4e-126) {
		tmp = x * 2.0;
	} else if (z <= 6.8e-112) {
		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 = a * (27.0d0 * b)
    if (z <= (-4.3d-94)) then
        tmp = z * (y * (t * (-9.0d0)))
    else if (z <= (-1.9d-127)) then
        tmp = t_1
    else if (z <= (-7.2d-172)) then
        tmp = (t * (-9.0d0)) * (y * z)
    else if (z <= 1.85d-229) then
        tmp = x * 2.0d0
    else if (z <= 3.7d-194) then
        tmp = t_1
    else if (z <= 1.4d-126) then
        tmp = x * 2.0d0
    else if (z <= 6.8d-112) 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 = a * (27.0 * b);
	double tmp;
	if (z <= -4.3e-94) {
		tmp = z * (y * (t * -9.0));
	} else if (z <= -1.9e-127) {
		tmp = t_1;
	} else if (z <= -7.2e-172) {
		tmp = (t * -9.0) * (y * z);
	} else if (z <= 1.85e-229) {
		tmp = x * 2.0;
	} else if (z <= 3.7e-194) {
		tmp = t_1;
	} else if (z <= 1.4e-126) {
		tmp = x * 2.0;
	} else if (z <= 6.8e-112) {
		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 = a * (27.0 * b)
	tmp = 0
	if z <= -4.3e-94:
		tmp = z * (y * (t * -9.0))
	elif z <= -1.9e-127:
		tmp = t_1
	elif z <= -7.2e-172:
		tmp = (t * -9.0) * (y * z)
	elif z <= 1.85e-229:
		tmp = x * 2.0
	elif z <= 3.7e-194:
		tmp = t_1
	elif z <= 1.4e-126:
		tmp = x * 2.0
	elif z <= 6.8e-112:
		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(a * Float64(27.0 * b))
	tmp = 0.0
	if (z <= -4.3e-94)
		tmp = Float64(z * Float64(y * Float64(t * -9.0)));
	elseif (z <= -1.9e-127)
		tmp = t_1;
	elseif (z <= -7.2e-172)
		tmp = Float64(Float64(t * -9.0) * Float64(y * z));
	elseif (z <= 1.85e-229)
		tmp = Float64(x * 2.0);
	elseif (z <= 3.7e-194)
		tmp = t_1;
	elseif (z <= 1.4e-126)
		tmp = Float64(x * 2.0);
	elseif (z <= 6.8e-112)
		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 = a * (27.0 * b);
	tmp = 0.0;
	if (z <= -4.3e-94)
		tmp = z * (y * (t * -9.0));
	elseif (z <= -1.9e-127)
		tmp = t_1;
	elseif (z <= -7.2e-172)
		tmp = (t * -9.0) * (y * z);
	elseif (z <= 1.85e-229)
		tmp = x * 2.0;
	elseif (z <= 3.7e-194)
		tmp = t_1;
	elseif (z <= 1.4e-126)
		tmp = x * 2.0;
	elseif (z <= 6.8e-112)
		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[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e-94], N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.9e-127], t$95$1, If[LessEqual[z, -7.2e-172], N[(N[(t * -9.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-229], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 3.7e-194], t$95$1, If[LessEqual[z, 1.4e-126], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 6.8e-112], t$95$1, N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.2999999999999998e-94

   1. Initial program 90.9%

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

   3. Taylor expanded in y around 0 90.8%

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

   4. Taylor expanded in y around inf 52.8%

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

      1. associate-*r* 52.9%

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

      2. associate-*r* 55.2%

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

      3. associate-*r* 55.2%

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

      4. *-commutative 55.2%

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

      5. associate-*r* 55.2%

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

      6. *-commutative 55.2%

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

      7. *-commutative 55.2%

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

   6. Simplified 55.2%

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

   if -4.2999999999999998e-94 < z < -1.90000000000000001e-127 or 1.8499999999999999e-229 < z < 3.70000000000000008e-194 or 1.39999999999999996e-126 < z < 6.7999999999999996e-112

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l* 99.9%

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

      4. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 73.5%

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

      1. associate-*r* 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-*r* 73.5%

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

   7. Simplified 73.5%

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

   if -1.90000000000000001e-127 < z < -7.20000000000000029e-172

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 99.3%

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

   4. Taylor expanded in y around inf 50.8%

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

      1. associate-*r* 51.1%

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

      2. *-commutative 51.1%

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

      3. *-commutative 51.1%

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

   6. Simplified 51.1%

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

   if -7.20000000000000029e-172 < z < 1.8499999999999999e-229 or 3.70000000000000008e-194 < z < 1.39999999999999996e-126

   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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 59.5%

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

   if 6.7999999999999996e-112 < z

   1. Initial program 94.1%

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

      1. sub-neg 94.1%

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

      2. sub-neg 94.1%

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

      3. associate-*l* 93.0%

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

      4. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in y around inf 83.9%

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

   6. Taylor expanded in y around inf 48.3%

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

      1. *-commutative 48.3%

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

      2. associate-*r* 48.3%

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

      3. associate-*l* 48.4%

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

      4. *-commutative 48.4%

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

   8. Simplified 48.4%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-127}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-172}:\\ \;\;\;\;\left(t \cdot -9\right) \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-229}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-194}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-126}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-112}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ t_2 := t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-172}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-230}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-126}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))) (t_2 (* t (* y (* z -9.0)))))
   (if (<= z -3e-94)
     (* z (* y (* t -9.0)))
     (if (<= z -8e-128)
       t_1
       (if (<= z -7.2e-172)
         t_2
         (if (<= z 8.2e-230)
           (* x 2.0)
           (if (<= z 1.45e-196)
             t_1
             (if (<= z 1.5e-126) (* x 2.0) (if (<= z 4.2e-113) t_1 t_2)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = t * (y * (z * -9.0));
	double tmp;
	if (z <= -3e-94) {
		tmp = z * (y * (t * -9.0));
	} else if (z <= -8e-128) {
		tmp = t_1;
	} else if (z <= -7.2e-172) {
		tmp = t_2;
	} else if (z <= 8.2e-230) {
		tmp = x * 2.0;
	} else if (z <= 1.45e-196) {
		tmp = t_1;
	} else if (z <= 1.5e-126) {
		tmp = x * 2.0;
	} else if (z <= 4.2e-113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    t_2 = t * (y * (z * (-9.0d0)))
    if (z <= (-3d-94)) then
        tmp = z * (y * (t * (-9.0d0)))
    else if (z <= (-8d-128)) then
        tmp = t_1
    else if (z <= (-7.2d-172)) then
        tmp = t_2
    else if (z <= 8.2d-230) then
        tmp = x * 2.0d0
    else if (z <= 1.45d-196) then
        tmp = t_1
    else if (z <= 1.5d-126) then
        tmp = x * 2.0d0
    else if (z <= 4.2d-113) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = t * (y * (z * -9.0));
	double tmp;
	if (z <= -3e-94) {
		tmp = z * (y * (t * -9.0));
	} else if (z <= -8e-128) {
		tmp = t_1;
	} else if (z <= -7.2e-172) {
		tmp = t_2;
	} else if (z <= 8.2e-230) {
		tmp = x * 2.0;
	} else if (z <= 1.45e-196) {
		tmp = t_1;
	} else if (z <= 1.5e-126) {
		tmp = x * 2.0;
	} else if (z <= 4.2e-113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	t_2 = t * (y * (z * -9.0))
	tmp = 0
	if z <= -3e-94:
		tmp = z * (y * (t * -9.0))
	elif z <= -8e-128:
		tmp = t_1
	elif z <= -7.2e-172:
		tmp = t_2
	elif z <= 8.2e-230:
		tmp = x * 2.0
	elif z <= 1.45e-196:
		tmp = t_1
	elif z <= 1.5e-126:
		tmp = x * 2.0
	elif z <= 4.2e-113:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	t_2 = Float64(t * Float64(y * Float64(z * -9.0)))
	tmp = 0.0
	if (z <= -3e-94)
		tmp = Float64(z * Float64(y * Float64(t * -9.0)));
	elseif (z <= -8e-128)
		tmp = t_1;
	elseif (z <= -7.2e-172)
		tmp = t_2;
	elseif (z <= 8.2e-230)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.45e-196)
		tmp = t_1;
	elseif (z <= 1.5e-126)
		tmp = Float64(x * 2.0);
	elseif (z <= 4.2e-113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	t_2 = t * (y * (z * -9.0));
	tmp = 0.0;
	if (z <= -3e-94)
		tmp = z * (y * (t * -9.0));
	elseif (z <= -8e-128)
		tmp = t_1;
	elseif (z <= -7.2e-172)
		tmp = t_2;
	elseif (z <= 8.2e-230)
		tmp = x * 2.0;
	elseif (z <= 1.45e-196)
		tmp = t_1;
	elseif (z <= 1.5e-126)
		tmp = x * 2.0;
	elseif (z <= 4.2e-113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e-94], N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8e-128], t$95$1, If[LessEqual[z, -7.2e-172], t$95$2, If[LessEqual[z, 8.2e-230], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.45e-196], t$95$1, If[LessEqual[z, 1.5e-126], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 4.2e-113], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.0000000000000001e-94

   1. Initial program 90.9%

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

   3. Taylor expanded in y around 0 90.8%

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

   4. Taylor expanded in y around inf 52.8%

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

      1. associate-*r* 52.9%

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

      2. associate-*r* 55.2%

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

      3. associate-*r* 55.2%

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

      4. *-commutative 55.2%

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

      5. associate-*r* 55.2%

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

      6. *-commutative 55.2%

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

      7. *-commutative 55.2%

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

   6. Simplified 55.2%

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

   if -3.0000000000000001e-94 < z < -8.00000000000000043e-128 or 8.2000000000000003e-230 < z < 1.44999999999999994e-196 or 1.5000000000000001e-126 < z < 4.2e-113

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l* 99.9%

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

      4. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 77.7%

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

      1. associate-*r* 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-*r* 77.7%

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

   7. Simplified 77.7%

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

   if -8.00000000000000043e-128 < z < -7.20000000000000029e-172 or 4.2e-113 < z

   1. Initial program 94.8%

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

      1. sub-neg 94.8%

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

      2. sub-neg 94.8%

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

      3. associate-*l* 93.9%

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

      4. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in y around inf 84.0%

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

   6. Taylor expanded in y around inf 48.6%

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

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

      3. associate-*l* 48.7%

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

      4. *-commutative 48.7%

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

   8. Simplified 48.7%

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

   if -7.20000000000000029e-172 < z < 8.2000000000000003e-230 or 1.44999999999999994e-196 < z < 1.5000000000000001e-126

   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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 60.2%

      \[\leadsto \color{blue}{2 \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-128}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-172}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-230}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-196}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-126}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ t_2 := t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{-94}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-172}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-232}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-126}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))) (t_2 (* t (* y (* z -9.0)))))
   (if (<= z -8e-94)
     (* -9.0 (* z (* y t)))
     (if (<= z -4.2e-130)
       t_1
       (if (<= z -7.2e-172)
         t_2
         (if (<= z 2.95e-232)
           (* x 2.0)
           (if (<= z 2.25e-197)
             t_1
             (if (<= z 1.2e-126)
               (* x 2.0)
               (if (<= z 1.85e-112) t_1 t_2)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = t * (y * (z * -9.0));
	double tmp;
	if (z <= -8e-94) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= -4.2e-130) {
		tmp = t_1;
	} else if (z <= -7.2e-172) {
		tmp = t_2;
	} else if (z <= 2.95e-232) {
		tmp = x * 2.0;
	} else if (z <= 2.25e-197) {
		tmp = t_1;
	} else if (z <= 1.2e-126) {
		tmp = x * 2.0;
	} else if (z <= 1.85e-112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    t_2 = t * (y * (z * (-9.0d0)))
    if (z <= (-8d-94)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (z <= (-4.2d-130)) then
        tmp = t_1
    else if (z <= (-7.2d-172)) then
        tmp = t_2
    else if (z <= 2.95d-232) then
        tmp = x * 2.0d0
    else if (z <= 2.25d-197) then
        tmp = t_1
    else if (z <= 1.2d-126) then
        tmp = x * 2.0d0
    else if (z <= 1.85d-112) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = t * (y * (z * -9.0));
	double tmp;
	if (z <= -8e-94) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= -4.2e-130) {
		tmp = t_1;
	} else if (z <= -7.2e-172) {
		tmp = t_2;
	} else if (z <= 2.95e-232) {
		tmp = x * 2.0;
	} else if (z <= 2.25e-197) {
		tmp = t_1;
	} else if (z <= 1.2e-126) {
		tmp = x * 2.0;
	} else if (z <= 1.85e-112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	t_2 = t * (y * (z * -9.0))
	tmp = 0
	if z <= -8e-94:
		tmp = -9.0 * (z * (y * t))
	elif z <= -4.2e-130:
		tmp = t_1
	elif z <= -7.2e-172:
		tmp = t_2
	elif z <= 2.95e-232:
		tmp = x * 2.0
	elif z <= 2.25e-197:
		tmp = t_1
	elif z <= 1.2e-126:
		tmp = x * 2.0
	elif z <= 1.85e-112:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	t_2 = Float64(t * Float64(y * Float64(z * -9.0)))
	tmp = 0.0
	if (z <= -8e-94)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (z <= -4.2e-130)
		tmp = t_1;
	elseif (z <= -7.2e-172)
		tmp = t_2;
	elseif (z <= 2.95e-232)
		tmp = Float64(x * 2.0);
	elseif (z <= 2.25e-197)
		tmp = t_1;
	elseif (z <= 1.2e-126)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.85e-112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	t_2 = t * (y * (z * -9.0));
	tmp = 0.0;
	if (z <= -8e-94)
		tmp = -9.0 * (z * (y * t));
	elseif (z <= -4.2e-130)
		tmp = t_1;
	elseif (z <= -7.2e-172)
		tmp = t_2;
	elseif (z <= 2.95e-232)
		tmp = x * 2.0;
	elseif (z <= 2.25e-197)
		tmp = t_1;
	elseif (z <= 1.2e-126)
		tmp = x * 2.0;
	elseif (z <= 1.85e-112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e-94], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-130], t$95$1, If[LessEqual[z, -7.2e-172], t$95$2, If[LessEqual[z, 2.95e-232], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 2.25e-197], t$95$1, If[LessEqual[z, 1.2e-126], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.85e-112], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.9999999999999996e-94

   1. Initial program 90.9%

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

      1. sub-neg 90.9%

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

      2. sub-neg 90.9%

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

      3. associate-*l* 91.8%

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

      4. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in t around inf 85.2%

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

   6. Taylor expanded in t around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. *-commutative 52.8%

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

      3. associate-*l* 55.1%

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

      4. *-commutative 55.1%

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

   8. Simplified 55.1%

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

   if -7.9999999999999996e-94 < z < -4.20000000000000004e-130 or 2.95000000000000008e-232 < z < 2.25e-197 or 1.20000000000000003e-126 < z < 1.8499999999999999e-112

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l* 99.9%

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

      4. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 77.7%

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

      1. associate-*r* 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-*r* 77.7%

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

   7. Simplified 77.7%

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

   if -4.20000000000000004e-130 < z < -7.20000000000000029e-172 or 1.8499999999999999e-112 < z

   1. Initial program 94.8%

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

      1. sub-neg 94.8%

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

      2. sub-neg 94.8%

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

      3. associate-*l* 93.9%

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

      4. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in y around inf 84.0%

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

   6. Taylor expanded in y around inf 48.6%

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

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

      3. associate-*l* 48.7%

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

      4. *-commutative 48.7%

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

   8. Simplified 48.7%

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

   if -7.20000000000000029e-172 < z < 2.95000000000000008e-232 or 2.25e-197 < z < 1.20000000000000003e-126

   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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 60.2%

      \[\leadsto \color{blue}{2 \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-94}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-130}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-172}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-232}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-197}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-126}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-112}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ t_2 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{-93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-172}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-232}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-126}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))) (t_2 (* -9.0 (* t (* y z)))))
   (if (<= z -5.4e-93)
     t_2
     (if (<= z -1.85e-128)
       t_1
       (if (<= z -7e-172)
         t_2
         (if (<= z 1.7e-232)
           (* x 2.0)
           (if (<= z 8.8e-193)
             t_1
             (if (<= z 2.4e-126)
               (* x 2.0)
               (if (<= z 2.55e-113) t_1 t_2)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = -9.0 * (t * (y * z));
	double tmp;
	if (z <= -5.4e-93) {
		tmp = t_2;
	} else if (z <= -1.85e-128) {
		tmp = t_1;
	} else if (z <= -7e-172) {
		tmp = t_2;
	} else if (z <= 1.7e-232) {
		tmp = x * 2.0;
	} else if (z <= 8.8e-193) {
		tmp = t_1;
	} else if (z <= 2.4e-126) {
		tmp = x * 2.0;
	} else if (z <= 2.55e-113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    t_2 = (-9.0d0) * (t * (y * z))
    if (z <= (-5.4d-93)) then
        tmp = t_2
    else if (z <= (-1.85d-128)) then
        tmp = t_1
    else if (z <= (-7d-172)) then
        tmp = t_2
    else if (z <= 1.7d-232) then
        tmp = x * 2.0d0
    else if (z <= 8.8d-193) then
        tmp = t_1
    else if (z <= 2.4d-126) then
        tmp = x * 2.0d0
    else if (z <= 2.55d-113) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = -9.0 * (t * (y * z));
	double tmp;
	if (z <= -5.4e-93) {
		tmp = t_2;
	} else if (z <= -1.85e-128) {
		tmp = t_1;
	} else if (z <= -7e-172) {
		tmp = t_2;
	} else if (z <= 1.7e-232) {
		tmp = x * 2.0;
	} else if (z <= 8.8e-193) {
		tmp = t_1;
	} else if (z <= 2.4e-126) {
		tmp = x * 2.0;
	} else if (z <= 2.55e-113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	t_2 = -9.0 * (t * (y * z))
	tmp = 0
	if z <= -5.4e-93:
		tmp = t_2
	elif z <= -1.85e-128:
		tmp = t_1
	elif z <= -7e-172:
		tmp = t_2
	elif z <= 1.7e-232:
		tmp = x * 2.0
	elif z <= 8.8e-193:
		tmp = t_1
	elif z <= 2.4e-126:
		tmp = x * 2.0
	elif z <= 2.55e-113:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	t_2 = Float64(-9.0 * Float64(t * Float64(y * z)))
	tmp = 0.0
	if (z <= -5.4e-93)
		tmp = t_2;
	elseif (z <= -1.85e-128)
		tmp = t_1;
	elseif (z <= -7e-172)
		tmp = t_2;
	elseif (z <= 1.7e-232)
		tmp = Float64(x * 2.0);
	elseif (z <= 8.8e-193)
		tmp = t_1;
	elseif (z <= 2.4e-126)
		tmp = Float64(x * 2.0);
	elseif (z <= 2.55e-113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	t_2 = -9.0 * (t * (y * z));
	tmp = 0.0;
	if (z <= -5.4e-93)
		tmp = t_2;
	elseif (z <= -1.85e-128)
		tmp = t_1;
	elseif (z <= -7e-172)
		tmp = t_2;
	elseif (z <= 1.7e-232)
		tmp = x * 2.0;
	elseif (z <= 8.8e-193)
		tmp = t_1;
	elseif (z <= 2.4e-126)
		tmp = x * 2.0;
	elseif (z <= 2.55e-113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e-93], t$95$2, If[LessEqual[z, -1.85e-128], t$95$1, If[LessEqual[z, -7e-172], t$95$2, If[LessEqual[z, 1.7e-232], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 8.8e-193], t$95$1, If[LessEqual[z, 2.4e-126], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 2.55e-113], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000002e-93 or -1.85e-128 < z < -7.00000000000000057e-172 or 2.54999999999999989e-113 < z

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. sub-neg 93.0%

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

      3. associate-*l* 92.9%

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

      4. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in y around inf 50.6%

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

   if -5.4000000000000002e-93 < z < -1.85e-128 or 1.7000000000000001e-232 < z < 8.79999999999999906e-193 or 2.40000000000000007e-126 < z < 2.54999999999999989e-113

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. sub-neg 99.9%

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

      3. associate-*l* 99.9%

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

      4. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 73.5%

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

      1. associate-*r* 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-*r* 73.5%

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

   7. Simplified 73.5%

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

   if -7.00000000000000057e-172 < z < 1.7000000000000001e-232 or 8.79999999999999906e-193 < z < 2.40000000000000007e-126

   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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 59.5%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-93}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-128}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-172}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-232}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-193}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-126}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-113}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+115}:\\ \;\;\;\;\left(t \cdot -9\right) \cdot \left(y \cdot z\right) + x \cdot 2\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+136} \lor \neg \left(b \leq 2.8 \cdot 10^{+188}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

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
 (if (<= b -2.9e+32)
   (* a (* 27.0 b))
   (if (<= b 2e+115)
     (+ (* (* t -9.0) (* y z)) (* x 2.0))
     (if (or (<= b 3e+136) (not (<= b 2.8e+188)))
       (+ (* 27.0 (* a b)) (* x 2.0))
       (- (* x 2.0) (* 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 tmp;
	if (b <= -2.9e+32) {
		tmp = a * (27.0 * b);
	} else if (b <= 2e+115) {
		tmp = ((t * -9.0) * (y * z)) + (x * 2.0);
	} else if ((b <= 3e+136) || !(b <= 2.8e+188)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (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) :: tmp
    if (b <= (-2.9d+32)) then
        tmp = a * (27.0d0 * b)
    else if (b <= 2d+115) then
        tmp = ((t * (-9.0d0)) * (y * z)) + (x * 2.0d0)
    else if ((b <= 3d+136) .or. (.not. (b <= 2.8d+188))) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (x * 2.0d0) - (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 tmp;
	if (b <= -2.9e+32) {
		tmp = a * (27.0 * b);
	} else if (b <= 2e+115) {
		tmp = ((t * -9.0) * (y * z)) + (x * 2.0);
	} else if ((b <= 3e+136) || !(b <= 2.8e+188)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (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):
	tmp = 0
	if b <= -2.9e+32:
		tmp = a * (27.0 * b)
	elif b <= 2e+115:
		tmp = ((t * -9.0) * (y * z)) + (x * 2.0)
	elif (b <= 3e+136) or not (b <= 2.8e+188):
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = (x * 2.0) - (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)
	tmp = 0.0
	if (b <= -2.9e+32)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (b <= 2e+115)
		tmp = Float64(Float64(Float64(t * -9.0) * Float64(y * z)) + Float64(x * 2.0));
	elseif ((b <= 3e+136) || !(b <= 2.8e+188))
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(x * 2.0) - 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)
	tmp = 0.0;
	if (b <= -2.9e+32)
		tmp = a * (27.0 * b);
	elseif (b <= 2e+115)
		tmp = ((t * -9.0) * (y * z)) + (x * 2.0);
	elseif ((b <= 3e+136) || ~((b <= 2.8e+188)))
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = (x * 2.0) - (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_] := If[LessEqual[b, -2.9e+32], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e+115], N[(N[(N[(t * -9.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 3e+136], N[Not[LessEqual[b, 2.8e+188]], $MachinePrecision]], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.90000000000000003e32

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. sub-neg 98.3%

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

      3. associate-*l* 92.0%

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

      4. associate-*l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in a around inf 53.0%

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

      1. associate-*r* 53.0%

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

      2. *-commutative 53.0%

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

      3. associate-*r* 53.0%

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

   7. Simplified 53.0%

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

   if -2.90000000000000003e32 < b < 2e115

   1. Initial program 94.7%

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

      1. sub-neg 94.7%

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

      2. sub-neg 94.7%

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

      3. associate-*l* 96.4%

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

      4. associate-*l* 96.9%

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

   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 0 79.3%

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

      1. cancel-sign-sub-inv 79.3%

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

      2. *-commutative 79.3%

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

      3. associate-*r* 79.4%

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

      4. metadata-eval 79.4%

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

   7. Applied egg-rr 79.4%

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

   if 2e115 < b < 2.99999999999999979e136 or 2.7999999999999998e188 < b

   1. Initial program 90.3%

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

      1. sub-neg 90.3%

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

      2. sub-neg 90.3%

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

      3. associate-*l* 90.4%

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

      4. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in y around 0 93.0%

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

   if 2.99999999999999979e136 < b < 2.7999999999999998e188

   1. Initial program 91.2%

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

      1. sub-neg 91.2%

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

      2. sub-neg 91.2%

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

      3. associate-*l* 99.4%

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

      4. associate-*l* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around 0 73.8%

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

      1. pow1 73.8%

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

      2. *-commutative 73.8%

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

   7. Applied egg-rr 73.8%

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

      1. unpow1 73.8%

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

      2. *-commutative 73.8%

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

      3. associate-*r* 73.5%

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

      4. *-commutative 73.5%

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

   9. Simplified 73.5%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+115}:\\ \;\;\;\;\left(t \cdot -9\right) \cdot \left(y \cdot z\right) + x \cdot 2\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+136} \lor \neg \left(b \leq 2.8 \cdot 10^{+188}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.95 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+114}:\\ \;\;\;\;\left(t \cdot -9\right) \cdot \left(y \cdot z\right) + x \cdot 2\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+136} \lor \neg \left(b \leq 7.5 \cdot 10^{+161}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(z \cdot t\right) \cdot -9\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.95e+32)
   (* a (* 27.0 b))
   (if (<= b 4.2e+114)
     (+ (* (* t -9.0) (* y z)) (* x 2.0))
     (if (or (<= b 2.4e+136) (not (<= b 7.5e+161)))
       (+ (* 27.0 (* a b)) (* x 2.0))
       (* y (* (* z t) -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 (b <= -2.95e+32) {
		tmp = a * (27.0 * b);
	} else if (b <= 4.2e+114) {
		tmp = ((t * -9.0) * (y * z)) + (x * 2.0);
	} else if ((b <= 2.4e+136) || !(b <= 7.5e+161)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = y * ((z * t) * -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 (b <= (-2.95d+32)) then
        tmp = a * (27.0d0 * b)
    else if (b <= 4.2d+114) then
        tmp = ((t * (-9.0d0)) * (y * z)) + (x * 2.0d0)
    else if ((b <= 2.4d+136) .or. (.not. (b <= 7.5d+161))) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = y * ((z * t) * (-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 (b <= -2.95e+32) {
		tmp = a * (27.0 * b);
	} else if (b <= 4.2e+114) {
		tmp = ((t * -9.0) * (y * z)) + (x * 2.0);
	} else if ((b <= 2.4e+136) || !(b <= 7.5e+161)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = y * ((z * t) * -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 b <= -2.95e+32:
		tmp = a * (27.0 * b)
	elif b <= 4.2e+114:
		tmp = ((t * -9.0) * (y * z)) + (x * 2.0)
	elif (b <= 2.4e+136) or not (b <= 7.5e+161):
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = y * ((z * t) * -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 (b <= -2.95e+32)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (b <= 4.2e+114)
		tmp = Float64(Float64(Float64(t * -9.0) * Float64(y * z)) + Float64(x * 2.0));
	elseif ((b <= 2.4e+136) || !(b <= 7.5e+161))
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(y * Float64(Float64(z * t) * -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 (b <= -2.95e+32)
		tmp = a * (27.0 * b);
	elseif (b <= 4.2e+114)
		tmp = ((t * -9.0) * (y * z)) + (x * 2.0);
	elseif ((b <= 2.4e+136) || ~((b <= 7.5e+161)))
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = y * ((z * t) * -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[b, -2.95e+32], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e+114], N[(N[(N[(t * -9.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 2.4e+136], N[Not[LessEqual[b, 7.5e+161]], $MachinePrecision]], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.94999999999999983e32

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. sub-neg 98.3%

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

      3. associate-*l* 92.0%

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

      4. associate-*l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in a around inf 53.0%

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

      1. associate-*r* 53.0%

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

      2. *-commutative 53.0%

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

      3. associate-*r* 53.0%

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

   7. Simplified 53.0%

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

   if -2.94999999999999983e32 < b < 4.2000000000000001e114

   1. Initial program 94.7%

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

      1. sub-neg 94.7%

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

      2. sub-neg 94.7%

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

      3. associate-*l* 96.4%

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

      4. associate-*l* 96.9%

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

   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 0 79.3%

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

      1. cancel-sign-sub-inv 79.3%

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

      2. *-commutative 79.3%

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

      3. associate-*r* 79.4%

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

      4. metadata-eval 79.4%

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

   7. Applied egg-rr 79.4%

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

   if 4.2000000000000001e114 < b < 2.4e136 or 7.4999999999999995e161 < b

   1. Initial program 92.1%

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

      1. sub-neg 92.1%

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

      2. sub-neg 92.1%

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

      3. associate-*l* 92.2%

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

      4. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in y around 0 90.5%

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

   if 2.4e136 < b < 7.4999999999999995e161

   1. Initial program 84.1%

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

      1. sub-neg 84.1%

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

      2. sub-neg 84.1%

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

      3. associate-*l* 99.2%

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

      4. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around 0 84.4%

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

   6. Taylor expanded in y around inf 100.0%

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

   7. Taylor expanded in x around 0 100.0%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.95 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+114}:\\ \;\;\;\;\left(t \cdot -9\right) \cdot \left(y \cdot z\right) + x \cdot 2\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+136} \lor \neg \left(b \leq 7.5 \cdot 10^{+161}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(z \cdot t\right) \cdot -9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := t\_1 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{-55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+50}:\\ \;\;\;\;\left(t \cdot -9\right) \cdot \left(y \cdot z\right) + x \cdot 2\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+212}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))) (t_2 (- t_1 (* 9.0 (* t (* y z))))))
   (if (<= b -3.1e-55)
     t_2
     (if (<= b 9e+50)
       (+ (* (* t -9.0) (* y z)) (* x 2.0))
       (if (<= b 9.5e+212) t_2 (+ t_1 (* x 2.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = t_1 - (9.0 * (t * (y * z)));
	double tmp;
	if (b <= -3.1e-55) {
		tmp = t_2;
	} else if (b <= 9e+50) {
		tmp = ((t * -9.0) * (y * z)) + (x * 2.0);
	} else if (b <= 9.5e+212) {
		tmp = t_2;
	} else {
		tmp = t_1 + (x * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = t_1 - (9.0d0 * (t * (y * z)))
    if (b <= (-3.1d-55)) then
        tmp = t_2
    else if (b <= 9d+50) then
        tmp = ((t * (-9.0d0)) * (y * z)) + (x * 2.0d0)
    else if (b <= 9.5d+212) then
        tmp = t_2
    else
        tmp = t_1 + (x * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = t_1 - (9.0 * (t * (y * z)));
	double tmp;
	if (b <= -3.1e-55) {
		tmp = t_2;
	} else if (b <= 9e+50) {
		tmp = ((t * -9.0) * (y * z)) + (x * 2.0);
	} else if (b <= 9.5e+212) {
		tmp = t_2;
	} else {
		tmp = t_1 + (x * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = t_1 - (9.0 * (t * (y * z)))
	tmp = 0
	if b <= -3.1e-55:
		tmp = t_2
	elif b <= 9e+50:
		tmp = ((t * -9.0) * (y * z)) + (x * 2.0)
	elif b <= 9.5e+212:
		tmp = t_2
	else:
		tmp = t_1 + (x * 2.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(t_1 - Float64(9.0 * Float64(t * Float64(y * z))))
	tmp = 0.0
	if (b <= -3.1e-55)
		tmp = t_2;
	elseif (b <= 9e+50)
		tmp = Float64(Float64(Float64(t * -9.0) * Float64(y * z)) + Float64(x * 2.0));
	elseif (b <= 9.5e+212)
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(x * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = t_1 - (9.0 * (t * (y * z)));
	tmp = 0.0;
	if (b <= -3.1e-55)
		tmp = t_2;
	elseif (b <= 9e+50)
		tmp = ((t * -9.0) * (y * z)) + (x * 2.0);
	elseif (b <= 9.5e+212)
		tmp = t_2;
	else
		tmp = t_1 + (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e-55], t$95$2, If[LessEqual[b, 9e+50], N[(N[(N[(t * -9.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+212], t$95$2, N[(t$95$1 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.09999999999999997e-55 or 9.00000000000000027e50 < b < 9.4999999999999993e212

   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* 93.0%

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

      4. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around 0 78.6%

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

   if -3.09999999999999997e-55 < b < 9.00000000000000027e50

   1. Initial program 94.0%

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

      1. sub-neg 94.0%

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

      2. sub-neg 94.0%

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

      3. associate-*l* 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 0 79.5%

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

      1. cancel-sign-sub-inv 79.5%

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

      2. *-commutative 79.5%

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

      3. associate-*r* 79.6%

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

      4. metadata-eval 79.6%

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

   7. Applied egg-rr 79.6%

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

   if 9.4999999999999993e212 < b

   1. Initial program 93.3%

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

      1. sub-neg 93.3%

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

      2. sub-neg 93.3%

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

      3. associate-*l* 93.3%

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

      4. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in y around 0 100.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{-55}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+50}:\\ \;\;\;\;\left(t \cdot -9\right) \cdot \left(y \cdot z\right) + x \cdot 2\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+212}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.1% accurate, 0.7× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 8.2e+27)
   (+ (+ (* x 2.0) (* z (* y (* t -9.0)))) (* a (* 27.0 b)))
   (* t (- (+ (* 2.0 (/ x t)) (* 27.0 (/ (* a b) t))) (* 9.0 (* y z))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 8.2e+27) {
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b));
	} else {
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 8.2d+27) then
        tmp = ((x * 2.0d0) + (z * (y * (t * (-9.0d0))))) + (a * (27.0d0 * b))
    else
        tmp = t * (((2.0d0 * (x / t)) + (27.0d0 * ((a * b) / t))) - (9.0d0 * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 8.2e+27) {
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b));
	} else {
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 8.2e+27:
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b))
	else:
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (y * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 8.2e+27)
		tmp = Float64(Float64(Float64(x * 2.0) + Float64(z * Float64(y * Float64(t * -9.0)))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(t * Float64(Float64(Float64(2.0 * Float64(x / t)) + Float64(27.0 * Float64(Float64(a * b) / t))) - Float64(9.0 * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 8.2e+27)
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b));
	else
		tmp = t * (((2.0 * (x / t)) + (27.0 * ((a * b) / t))) - (9.0 * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 8.2e+27], N[(N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $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[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 8.2000000000000005e27

   1. Initial program 94.2%

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

      1. sub-neg 94.2%

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

      2. sub-neg 94.2%

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

      3. associate-*l* 97.4%

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

      4. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

      1. sub-neg 97.9%

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

      2. *-commutative 97.9%

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

      3. distribute-rgt-neg-in 97.9%

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

      4. *-commutative 97.9%

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

      5. distribute-lft-neg-in 97.9%

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

      6. metadata-eval 97.9%

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

      7. associate-*l* 98.3%

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

      8. associate-*r* 98.3%

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

      9. associate-*l* 96.0%

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

   6. Applied egg-rr 96.0%

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

   if 8.2000000000000005e27 < t

   1. Initial program 97.9%

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

      1. sub-neg 97.9%

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

      2. sub-neg 97.9%

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

      3. associate-*l* 86.4%

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

      4. associate-*l* 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in t around inf 99.7%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 8.2 \cdot 10^{+27}:\\ \;\;\;\;\left(x \cdot 2 + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(2 \cdot \frac{x}{t} + 27 \cdot \frac{a \cdot b}{t}\right) - 9 \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(y \cdot 9\right) \cdot z\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+101}:\\ \;\;\;\;\left(x \cdot 2 - t\_1 \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* y 9.0) z)))
   (if (<= t_1 2e+101)
     (+ (- (* x 2.0) (* t_1 t)) (* (* a 27.0) b))
     (+ (+ (* x 2.0) (* z (* y (* t -9.0)))) (* a (* 27.0 b))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 2e+101) {
		tmp = ((x * 2.0) - (t_1 * t)) + ((a * 27.0) * b);
	} else {
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * 9.0d0) * z
    if (t_1 <= 2d+101) then
        tmp = ((x * 2.0d0) - (t_1 * t)) + ((a * 27.0d0) * b)
    else
        tmp = ((x * 2.0d0) + (z * (y * (t * (-9.0d0))))) + (a * (27.0d0 * b))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 2e+101) {
		tmp = ((x * 2.0) - (t_1 * t)) + ((a * 27.0) * b);
	} else {
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (y * 9.0) * z
	tmp = 0
	if t_1 <= 2e+101:
		tmp = ((x * 2.0) - (t_1 * t)) + ((a * 27.0) * b)
	else:
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * 9.0) * z)
	tmp = 0.0
	if (t_1 <= 2e+101)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t_1 * t)) + Float64(Float64(a * 27.0) * b));
	else
		tmp = Float64(Float64(Float64(x * 2.0) + Float64(z * Float64(y * Float64(t * -9.0)))) + Float64(a * Float64(27.0 * b)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * 9.0) * z;
	tmp = 0.0;
	if (t_1 <= 2e+101)
		tmp = ((x * 2.0) - (t_1 * t)) + ((a * 27.0) * b);
	else
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+101], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t$95$1 * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 2e101

   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. Add Preprocessing

   if 2e101 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 81.2%

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

      1. sub-neg 81.2%

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

      2. sub-neg 81.2%

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

      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* 95.0%

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

   3. Simplified 95.0%

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

      1. sub-neg 95.0%

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

      2. *-commutative 95.0%

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

      3. distribute-rgt-neg-in 95.0%

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

      4. *-commutative 95.0%

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

      5. distribute-lft-neg-in 95.0%

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

      6. metadata-eval 95.0%

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

      7. associate-*l* 97.2%

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

      8. associate-*r* 97.1%

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

      9. associate-*l* 97.3%

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

   6. Applied egg-rr 97.3%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 2 \cdot 10^{+101}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-127}:\\ \;\;\;\;\left(x \cdot 2 + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.5e-127)
   (+ (+ (* x 2.0) (* z (* y (* t -9.0)))) (* a (* 27.0 b)))
   (+ (* (* a 27.0) b) (- (* x 2.0) (* t (* 9.0 (* y z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.5e-127) {
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b));
	} else {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t * (9.0 * (y * z))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.5d-127)) then
        tmp = ((x * 2.0d0) + (z * (y * (t * (-9.0d0))))) + (a * (27.0d0 * b))
    else
        tmp = ((a * 27.0d0) * b) + ((x * 2.0d0) - (t * (9.0d0 * (y * z))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.5e-127) {
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b));
	} else {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t * (9.0 * (y * z))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.5e-127:
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b))
	else:
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t * (9.0 * (y * z))))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.5e-127)
		tmp = Float64(Float64(Float64(x * 2.0) + Float64(z * Float64(y * Float64(t * -9.0)))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(a * 27.0) * b) + Float64(Float64(x * 2.0) - Float64(t * Float64(9.0 * Float64(y * z)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.5e-127)
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b));
	else
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t * (9.0 * (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.5e-127], N[(N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.49999999999999989e-127

   1. Initial program 91.3%

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

      1. sub-neg 91.3%

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

      2. sub-neg 91.3%

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

      3. associate-*l* 92.3%

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

      4. associate-*l* 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. Step-by-step derivation

      1. sub-neg 93.3%

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

      2. *-commutative 93.3%

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

      3. distribute-rgt-neg-in 93.3%

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

      4. *-commutative 93.3%

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

      5. distribute-lft-neg-in 93.3%

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

      6. metadata-eval 93.3%

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

      7. associate-*l* 94.3%

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

      8. associate-*r* 94.2%

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

      9. associate-*l* 95.4%

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

   6. Applied egg-rr 95.4%

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

   if -3.49999999999999989e-127 < z

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0 97.0%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-127}:\\ \;\;\;\;\left(x \cdot 2 + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 90.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3.25 \cdot 10^{+153}:\\ \;\;\;\;\left(x \cdot 2 + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -9\right) \cdot \left(y \cdot z\right) + x \cdot 2\\ \end{array} \end{array} \]

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 (<= t 3.25e+153)
   (+ (+ (* x 2.0) (* z (* y (* t -9.0)))) (* a (* 27.0 b)))
   (+ (* (* t -9.0) (* y z)) (* 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 (t <= 3.25e+153) {
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b));
	} else {
		tmp = ((t * -9.0) * (y * z)) + (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 (t <= 3.25d+153) then
        tmp = ((x * 2.0d0) + (z * (y * (t * (-9.0d0))))) + (a * (27.0d0 * b))
    else
        tmp = ((t * (-9.0d0)) * (y * z)) + (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 (t <= 3.25e+153) {
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b));
	} else {
		tmp = ((t * -9.0) * (y * z)) + (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 t <= 3.25e+153:
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b))
	else:
		tmp = ((t * -9.0) * (y * z)) + (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 (t <= 3.25e+153)
		tmp = Float64(Float64(Float64(x * 2.0) + Float64(z * Float64(y * Float64(t * -9.0)))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(t * -9.0) * Float64(y * z)) + 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 (t <= 3.25e+153)
		tmp = ((x * 2.0) + (z * (y * (t * -9.0)))) + (a * (27.0 * b));
	else
		tmp = ((t * -9.0) * (y * z)) + (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 3.25e+153], N[(N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * -9.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.24999999999999986e153

   1. Initial program 94.9%

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

      1. sub-neg 94.9%

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

      2. sub-neg 94.9%

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

      3. associate-*l* 96.9%

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

      4. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

      1. sub-neg 97.3%

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

      2. *-commutative 97.3%

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

      3. distribute-rgt-neg-in 97.3%

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

      4. *-commutative 97.3%

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

      5. distribute-lft-neg-in 97.3%

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

      6. metadata-eval 97.3%

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

      7. associate-*l* 97.7%

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

      8. associate-*r* 97.7%

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

      9. associate-*l* 96.0%

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

   6. Applied egg-rr 96.0%

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

   if 3.24999999999999986e153 < t

   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* 78.6%

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

      4. associate-*l* 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in a around 0 82.0%

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

      1. cancel-sign-sub-inv 82.0%

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

      2. *-commutative 82.0%

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

      3. associate-*r* 82.2%

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

      4. metadata-eval 82.2%

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

   7. Applied egg-rr 82.2%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.25 \cdot 10^{+153}:\\ \;\;\;\;\left(x \cdot 2 + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -9\right) \cdot \left(y \cdot z\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 74.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+28}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-65}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \end{array} \end{array} \]

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 -4.4e+28)
   (* -9.0 (* z (* y t)))
   (if (<= z 4.2e-65) (+ (* 27.0 (* a b)) (* x 2.0)) (* z (* y (* t -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 <= -4.4e+28) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= 4.2e-65) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = z * (y * (t * -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 <= (-4.4d+28)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (z <= 4.2d-65) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = z * (y * (t * (-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 <= -4.4e+28) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= 4.2e-65) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = z * (y * (t * -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 <= -4.4e+28:
		tmp = -9.0 * (z * (y * t))
	elif z <= 4.2e-65:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = z * (y * (t * -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 <= -4.4e+28)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (z <= 4.2e-65)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(z * Float64(y * Float64(t * -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 <= -4.4e+28)
		tmp = -9.0 * (z * (y * t));
	elseif (z <= 4.2e-65)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = z * (y * (t * -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, -4.4e+28], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-65], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.39999999999999973e28

   1. Initial program 89.0%

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

      1. sub-neg 89.0%

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

      2. sub-neg 89.0%

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

      3. associate-*l* 90.3%

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

      4. associate-*l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in t around inf 84.2%

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

   6. Taylor expanded in t around inf 64.6%

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

      1. *-commutative 64.6%

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

      2. *-commutative 64.6%

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

      3. associate-*l* 67.8%

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

      4. *-commutative 67.8%

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

   8. Simplified 67.8%

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

   if -4.39999999999999973e28 < z < 4.20000000000000006e-65

   1. Initial program 98.9%

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

      1. sub-neg 98.9%

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

      2. sub-neg 98.9%

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

      3. associate-*l* 99.0%

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

      4. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in y around 0 83.4%

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

   if 4.20000000000000006e-65 < z

   1. Initial program 93.6%

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

   3. Taylor expanded in y around 0 93.6%

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

   4. Taylor expanded in y around inf 50.6%

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

      1. associate-*r* 50.6%

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

      2. associate-*r* 54.2%

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

      3. associate-*r* 54.2%

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

      4. *-commutative 54.2%

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

      5. associate-*r* 54.2%

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

      6. *-commutative 54.2%

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

      7. *-commutative 54.2%

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

   6. Simplified 54.2%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+28}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-65}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+97} \lor \neg \left(a \leq 2.9 \cdot 10^{-75}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -7.2e+97) (not (<= a 2.9e-75))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7.2e+97) || !(a <= 2.9e-75)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-7.2d+97)) .or. (.not. (a <= 2.9d-75))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7.2e+97) || !(a <= 2.9e-75)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -7.2e+97) or not (a <= 2.9e-75):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -7.2e+97) || !(a <= 2.9e-75))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -7.2e+97) || ~((a <= 2.9e-75)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -7.2e+97], N[Not[LessEqual[a, 2.9e-75]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.19999999999999932e97 or 2.9000000000000002e-75 < a

   1. Initial program 94.1%

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

      1. sub-neg 94.1%

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

      2. sub-neg 94.1%

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

      3. associate-*l* 94.1%

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

      4. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in a around inf 53.6%

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

   if -7.19999999999999932e97 < a < 2.9000000000000002e-75

   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* 95.7%

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

      4. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in x around inf 40.8%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+97} \lor \neg \left(a \leq 2.9 \cdot 10^{-75}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.8% 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 95.0%

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

   1. sub-neg 95.0%

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

   2. sub-neg 95.0%

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

   3. associate-*l* 95.0%

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

   4. associate-*l* 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 x around inf 32.3%

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

6. Final simplification 32.3%

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

Developer target: 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 2024092 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

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

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