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

Percentage Accurate: 94.9% → 97.5%

Time: 14.3s

Alternatives: 16

Speedup: 0.8×

• 26.8% 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: 94.9% 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: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -4 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(\left(z \cdot t\right) \cdot -9\right) + \left(x \cdot 2 - \left(b \cdot -27\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(t \cdot y\right) \cdot \left(z \cdot 9\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* y 9.0) -4e+71)
   (+ (* y (* (* z t) -9.0)) (- (* x 2.0) (* (* b -27.0) a)))
   (+ (- (* x 2.0) (* (* t y) (* z 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 tmp;
	if ((y * 9.0) <= -4e+71) {
		tmp = (y * ((z * t) * -9.0)) + ((x * 2.0) - ((b * -27.0) * a));
	} else {
		tmp = ((x * 2.0) - ((t * y) * (z * 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) :: tmp
    if ((y * 9.0d0) <= (-4d+71)) then
        tmp = (y * ((z * t) * (-9.0d0))) + ((x * 2.0d0) - ((b * (-27.0d0)) * a))
    else
        tmp = ((x * 2.0d0) - ((t * y) * (z * 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 tmp;
	if ((y * 9.0) <= -4e+71) {
		tmp = (y * ((z * t) * -9.0)) + ((x * 2.0) - ((b * -27.0) * a));
	} else {
		tmp = ((x * 2.0) - ((t * y) * (z * 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):
	tmp = 0
	if (y * 9.0) <= -4e+71:
		tmp = (y * ((z * t) * -9.0)) + ((x * 2.0) - ((b * -27.0) * a))
	else:
		tmp = ((x * 2.0) - ((t * y) * (z * 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)
	tmp = 0.0
	if (Float64(y * 9.0) <= -4e+71)
		tmp = Float64(Float64(y * Float64(Float64(z * t) * -9.0)) + Float64(Float64(x * 2.0) - Float64(Float64(b * -27.0) * a)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(t * y) * Float64(z * 9.0))) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y * 9.0) <= -4e+71)
		tmp = (y * ((z * t) * -9.0)) + ((x * 2.0) - ((b * -27.0) * a));
	else
		tmp = ((x * 2.0) - ((t * y) * (z * 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_] := If[LessEqual[N[(y * 9.0), $MachinePrecision], -4e+71], N[(N[(y * N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(b * -27.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(t * y), $MachinePrecision] * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y #s(literal 9 binary64)) < -4.0000000000000002e71

   1. Initial program 90.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   if -4.0000000000000002e71 < (*.f64 y #s(literal 9 binary64))

   1. Initial program 96.9%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 46.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{if}\;a \cdot 27 \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;a \cdot 27 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 27 \leq -1 \cdot 10^{-175}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;a \cdot 27 \leq 2 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 27 \leq 5 \cdot 10^{-118}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

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 (* z t)) -9.0)))
   (if (<= (* a 27.0) -5e+104)
     (* (* a b) 27.0)
     (if (<= (* a 27.0) -2e+14)
       t_1
       (if (<= (* a 27.0) -1e-175)
         (* 2.0 x)
         (if (<= (* a 27.0) 2e-300)
           t_1
           (if (<= (* a 27.0) 5e-118) (* 2.0 x) (* b (* a 27.0)))))))))

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 = (y * (z * t)) * -9.0;
	double tmp;
	if ((a * 27.0) <= -5e+104) {
		tmp = (a * b) * 27.0;
	} else if ((a * 27.0) <= -2e+14) {
		tmp = t_1;
	} else if ((a * 27.0) <= -1e-175) {
		tmp = 2.0 * x;
	} else if ((a * 27.0) <= 2e-300) {
		tmp = t_1;
	} else if ((a * 27.0) <= 5e-118) {
		tmp = 2.0 * x;
	} else {
		tmp = b * (a * 27.0);
	}
	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 = (y * (z * t)) * (-9.0d0)
    if ((a * 27.0d0) <= (-5d+104)) then
        tmp = (a * b) * 27.0d0
    else if ((a * 27.0d0) <= (-2d+14)) then
        tmp = t_1
    else if ((a * 27.0d0) <= (-1d-175)) then
        tmp = 2.0d0 * x
    else if ((a * 27.0d0) <= 2d-300) then
        tmp = t_1
    else if ((a * 27.0d0) <= 5d-118) then
        tmp = 2.0d0 * x
    else
        tmp = b * (a * 27.0d0)
    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 = (y * (z * t)) * -9.0;
	double tmp;
	if ((a * 27.0) <= -5e+104) {
		tmp = (a * b) * 27.0;
	} else if ((a * 27.0) <= -2e+14) {
		tmp = t_1;
	} else if ((a * 27.0) <= -1e-175) {
		tmp = 2.0 * x;
	} else if ((a * 27.0) <= 2e-300) {
		tmp = t_1;
	} else if ((a * 27.0) <= 5e-118) {
		tmp = 2.0 * x;
	} else {
		tmp = b * (a * 27.0);
	}
	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 = (y * (z * t)) * -9.0
	tmp = 0
	if (a * 27.0) <= -5e+104:
		tmp = (a * b) * 27.0
	elif (a * 27.0) <= -2e+14:
		tmp = t_1
	elif (a * 27.0) <= -1e-175:
		tmp = 2.0 * x
	elif (a * 27.0) <= 2e-300:
		tmp = t_1
	elif (a * 27.0) <= 5e-118:
		tmp = 2.0 * x
	else:
		tmp = b * (a * 27.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(z * t)) * -9.0)
	tmp = 0.0
	if (Float64(a * 27.0) <= -5e+104)
		tmp = Float64(Float64(a * b) * 27.0);
	elseif (Float64(a * 27.0) <= -2e+14)
		tmp = t_1;
	elseif (Float64(a * 27.0) <= -1e-175)
		tmp = Float64(2.0 * x);
	elseif (Float64(a * 27.0) <= 2e-300)
		tmp = t_1;
	elseif (Float64(a * 27.0) <= 5e-118)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(b * Float64(a * 27.0));
	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 = (y * (z * t)) * -9.0;
	tmp = 0.0;
	if ((a * 27.0) <= -5e+104)
		tmp = (a * b) * 27.0;
	elseif ((a * 27.0) <= -2e+14)
		tmp = t_1;
	elseif ((a * 27.0) <= -1e-175)
		tmp = 2.0 * x;
	elseif ((a * 27.0) <= 2e-300)
		tmp = t_1;
	elseif ((a * 27.0) <= 5e-118)
		tmp = 2.0 * x;
	else
		tmp = b * (a * 27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision]}, If[LessEqual[N[(a * 27.0), $MachinePrecision], -5e+104], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], -2e+14], t$95$1, If[LessEqual[N[(a * 27.0), $MachinePrecision], -1e-175], N[(2.0 * x), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], 2e-300], t$95$1, If[LessEqual[N[(a * 27.0), $MachinePrecision], 5e-118], N[(2.0 * x), $MachinePrecision], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 27 binary64)) < -4.9999999999999997e104

   1. Initial program 93.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -4.9999999999999997e104 < (*.f64 a #s(literal 27 binary64)) < -2e14 or -1e-175 < (*.f64 a #s(literal 27 binary64)) < 2.00000000000000005e-300

   1. Initial program 94.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -2e14 < (*.f64 a #s(literal 27 binary64)) < -1e-175 or 2.00000000000000005e-300 < (*.f64 a #s(literal 27 binary64)) < 5.00000000000000015e-118

   1. Initial program 98.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 5.00000000000000015e-118 < (*.f64 a #s(literal 27 binary64))

   1. Initial program 95.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 46.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(t \cdot \left(z \cdot -9\right)\right) \cdot y\\ \mathbf{if}\;a \cdot 27 \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;a \cdot 27 \leq -2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 27 \leq -1 \cdot 10^{-175}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;a \cdot 27 \leq 2 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 27 \leq 5 \cdot 10^{-118}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

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 (* (* t (* z -9.0)) y)))
   (if (<= (* a 27.0) -5e+104)
     (* (* a b) 27.0)
     (if (<= (* a 27.0) -2e+14)
       t_1
       (if (<= (* a 27.0) -1e-175)
         (* 2.0 x)
         (if (<= (* a 27.0) 2e-300)
           t_1
           (if (<= (* a 27.0) 5e-118) (* 2.0 x) (* b (* a 27.0)))))))))

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 = (t * (z * -9.0)) * y;
	double tmp;
	if ((a * 27.0) <= -5e+104) {
		tmp = (a * b) * 27.0;
	} else if ((a * 27.0) <= -2e+14) {
		tmp = t_1;
	} else if ((a * 27.0) <= -1e-175) {
		tmp = 2.0 * x;
	} else if ((a * 27.0) <= 2e-300) {
		tmp = t_1;
	} else if ((a * 27.0) <= 5e-118) {
		tmp = 2.0 * x;
	} else {
		tmp = b * (a * 27.0);
	}
	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 = (t * (z * (-9.0d0))) * y
    if ((a * 27.0d0) <= (-5d+104)) then
        tmp = (a * b) * 27.0d0
    else if ((a * 27.0d0) <= (-2d+14)) then
        tmp = t_1
    else if ((a * 27.0d0) <= (-1d-175)) then
        tmp = 2.0d0 * x
    else if ((a * 27.0d0) <= 2d-300) then
        tmp = t_1
    else if ((a * 27.0d0) <= 5d-118) then
        tmp = 2.0d0 * x
    else
        tmp = b * (a * 27.0d0)
    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 = (t * (z * -9.0)) * y;
	double tmp;
	if ((a * 27.0) <= -5e+104) {
		tmp = (a * b) * 27.0;
	} else if ((a * 27.0) <= -2e+14) {
		tmp = t_1;
	} else if ((a * 27.0) <= -1e-175) {
		tmp = 2.0 * x;
	} else if ((a * 27.0) <= 2e-300) {
		tmp = t_1;
	} else if ((a * 27.0) <= 5e-118) {
		tmp = 2.0 * x;
	} else {
		tmp = b * (a * 27.0);
	}
	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 = (t * (z * -9.0)) * y
	tmp = 0
	if (a * 27.0) <= -5e+104:
		tmp = (a * b) * 27.0
	elif (a * 27.0) <= -2e+14:
		tmp = t_1
	elif (a * 27.0) <= -1e-175:
		tmp = 2.0 * x
	elif (a * 27.0) <= 2e-300:
		tmp = t_1
	elif (a * 27.0) <= 5e-118:
		tmp = 2.0 * x
	else:
		tmp = b * (a * 27.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t * Float64(z * -9.0)) * y)
	tmp = 0.0
	if (Float64(a * 27.0) <= -5e+104)
		tmp = Float64(Float64(a * b) * 27.0);
	elseif (Float64(a * 27.0) <= -2e+14)
		tmp = t_1;
	elseif (Float64(a * 27.0) <= -1e-175)
		tmp = Float64(2.0 * x);
	elseif (Float64(a * 27.0) <= 2e-300)
		tmp = t_1;
	elseif (Float64(a * 27.0) <= 5e-118)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(b * Float64(a * 27.0));
	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 = (t * (z * -9.0)) * y;
	tmp = 0.0;
	if ((a * 27.0) <= -5e+104)
		tmp = (a * b) * 27.0;
	elseif ((a * 27.0) <= -2e+14)
		tmp = t_1;
	elseif ((a * 27.0) <= -1e-175)
		tmp = 2.0 * x;
	elseif ((a * 27.0) <= 2e-300)
		tmp = t_1;
	elseif ((a * 27.0) <= 5e-118)
		tmp = 2.0 * x;
	else
		tmp = b * (a * 27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[N[(a * 27.0), $MachinePrecision], -5e+104], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], -2e+14], t$95$1, If[LessEqual[N[(a * 27.0), $MachinePrecision], -1e-175], N[(2.0 * x), $MachinePrecision], If[LessEqual[N[(a * 27.0), $MachinePrecision], 2e-300], t$95$1, If[LessEqual[N[(a * 27.0), $MachinePrecision], 5e-118], N[(2.0 * x), $MachinePrecision], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 27 binary64)) < -4.9999999999999997e104

   1. Initial program 93.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -4.9999999999999997e104 < (*.f64 a #s(literal 27 binary64)) < -2e14 or -1e-175 < (*.f64 a #s(literal 27 binary64)) < 2.00000000000000005e-300

   1. Initial program 94.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -2e14 < (*.f64 a #s(literal 27 binary64)) < -1e-175 or 2.00000000000000005e-300 < (*.f64 a #s(literal 27 binary64)) < 5.00000000000000015e-118

   1. Initial program 98.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 5.00000000000000015e-118 < (*.f64 a #s(literal 27 binary64))

   1. Initial program 95.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 82.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 27\\ t_2 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+163}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+91}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9 + 2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot -9\right) \cdot y\right) \cdot z + t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a b) 27.0)) (t_2 (* (* a 27.0) b)))
   (if (<= t_2 -5e+163)
     (+ (* -9.0 (* t (* y z))) t_1)
     (if (<= t_2 2e+91)
       (+ (* (* y (* z t)) -9.0) (* 2.0 x))
       (+ (* (* (* t -9.0) y) z) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) * 27.0;
	double t_2 = (a * 27.0) * b;
	double tmp;
	if (t_2 <= -5e+163) {
		tmp = (-9.0 * (t * (y * z))) + t_1;
	} else if (t_2 <= 2e+91) {
		tmp = ((y * (z * t)) * -9.0) + (2.0 * x);
	} else {
		tmp = (((t * -9.0) * y) * z) + t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) * 27.0d0
    t_2 = (a * 27.0d0) * b
    if (t_2 <= (-5d+163)) then
        tmp = ((-9.0d0) * (t * (y * z))) + t_1
    else if (t_2 <= 2d+91) then
        tmp = ((y * (z * t)) * (-9.0d0)) + (2.0d0 * x)
    else
        tmp = (((t * (-9.0d0)) * y) * z) + t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) * 27.0;
	double t_2 = (a * 27.0) * b;
	double tmp;
	if (t_2 <= -5e+163) {
		tmp = (-9.0 * (t * (y * z))) + t_1;
	} else if (t_2 <= 2e+91) {
		tmp = ((y * (z * t)) * -9.0) + (2.0 * x);
	} else {
		tmp = (((t * -9.0) * y) * z) + t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * b) * 27.0
	t_2 = (a * 27.0) * b
	tmp = 0
	if t_2 <= -5e+163:
		tmp = (-9.0 * (t * (y * z))) + t_1
	elif t_2 <= 2e+91:
		tmp = ((y * (z * t)) * -9.0) + (2.0 * x)
	else:
		tmp = (((t * -9.0) * y) * z) + t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * b) * 27.0)
	t_2 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_2 <= -5e+163)
		tmp = Float64(Float64(-9.0 * Float64(t * Float64(y * z))) + t_1);
	elseif (t_2 <= 2e+91)
		tmp = Float64(Float64(Float64(y * Float64(z * t)) * -9.0) + Float64(2.0 * x));
	else
		tmp = Float64(Float64(Float64(Float64(t * -9.0) * y) * z) + t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * b) * 27.0;
	t_2 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_2 <= -5e+163)
		tmp = (-9.0 * (t * (y * z))) + t_1;
	elseif (t_2 <= 2e+91)
		tmp = ((y * (z * t)) * -9.0) + (2.0 * x);
	else
		tmp = (((t * -9.0) * y) * z) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+163], N[(N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 2e+91], N[(N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision] + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(t * -9.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -5e163

   1. Initial program 91.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -5e163 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2.00000000000000016e91

   1. Initial program 96.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 2.00000000000000016e91 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 97.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(a \cdot b\right) \cdot 27\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+163}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+91}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9 + 2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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))) (* (* a b) 27.0))))
   (if (<= t_1 -5e+163)
     t_2
     (if (<= t_1 2e+91) (+ (* (* y (* z t)) -9.0) (* 2.0 x)) 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))) + ((a * b) * 27.0);
	double tmp;
	if (t_1 <= -5e+163) {
		tmp = t_2;
	} else if (t_1 <= 2e+91) {
		tmp = ((y * (z * t)) * -9.0) + (2.0 * x);
	} 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))) + ((a * b) * 27.0d0)
    if (t_1 <= (-5d+163)) then
        tmp = t_2
    else if (t_1 <= 2d+91) then
        tmp = ((y * (z * t)) * (-9.0d0)) + (2.0d0 * x)
    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))) + ((a * b) * 27.0);
	double tmp;
	if (t_1 <= -5e+163) {
		tmp = t_2;
	} else if (t_1 <= 2e+91) {
		tmp = ((y * (z * t)) * -9.0) + (2.0 * x);
	} 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))) + ((a * b) * 27.0)
	tmp = 0
	if t_1 <= -5e+163:
		tmp = t_2
	elif t_1 <= 2e+91:
		tmp = ((y * (z * t)) * -9.0) + (2.0 * x)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	t_2 = Float64(Float64(-9.0 * Float64(t * Float64(y * z))) + Float64(Float64(a * b) * 27.0))
	tmp = 0.0
	if (t_1 <= -5e+163)
		tmp = t_2;
	elseif (t_1 <= 2e+91)
		tmp = Float64(Float64(Float64(y * Float64(z * t)) * -9.0) + Float64(2.0 * x));
	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))) + ((a * b) * 27.0);
	tmp = 0.0;
	if (t_1 <= -5e+163)
		tmp = t_2;
	elseif (t_1 <= 2e+91)
		tmp = ((y * (z * t)) * -9.0) + (2.0 * x);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+163], t$95$2, If[LessEqual[t$95$1, 2e+91], N[(N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision] + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -5e163 or 2.00000000000000016e91 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 94.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -5e163 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 2.00000000000000016e91

   1. Initial program 96.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+25}:\\ \;\;\;\;\left(b \cdot 27\right) \cdot a - x \cdot -2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-6}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9 + 2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x + t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= t_1 -2e+25)
     (- (* (* b 27.0) a) (* x -2.0))
     (if (<= t_1 2e-6)
       (+ (* (* y (* z t)) -9.0) (* 2.0 x))
       (+ (* 2.0 x) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -2e+25) {
		tmp = ((b * 27.0) * a) - (x * -2.0);
	} else if (t_1 <= 2e-6) {
		tmp = ((y * (z * t)) * -9.0) + (2.0 * x);
	} else {
		tmp = (2.0 * x) + t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    if (t_1 <= (-2d+25)) then
        tmp = ((b * 27.0d0) * a) - (x * (-2.0d0))
    else if (t_1 <= 2d-6) then
        tmp = ((y * (z * t)) * (-9.0d0)) + (2.0d0 * x)
    else
        tmp = (2.0d0 * x) + t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -2e+25) {
		tmp = ((b * 27.0) * a) - (x * -2.0);
	} else if (t_1 <= 2e-6) {
		tmp = ((y * (z * t)) * -9.0) + (2.0 * x);
	} else {
		tmp = (2.0 * x) + t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -2e+25:
		tmp = ((b * 27.0) * a) - (x * -2.0)
	elif t_1 <= 2e-6:
		tmp = ((y * (z * t)) * -9.0) + (2.0 * x)
	else:
		tmp = (2.0 * x) + t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -2e+25)
		tmp = Float64(Float64(Float64(b * 27.0) * a) - Float64(x * -2.0));
	elseif (t_1 <= 2e-6)
		tmp = Float64(Float64(Float64(y * Float64(z * t)) * -9.0) + Float64(2.0 * x));
	else
		tmp = Float64(Float64(2.0 * x) + t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -2e+25)
		tmp = ((b * 27.0) * a) - (x * -2.0);
	elseif (t_1 <= 2e-6)
		tmp = ((y * (z * t)) * -9.0) + (2.0 * x);
	else
		tmp = (2.0 * x) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+25], N[(N[(N[(b * 27.0), $MachinePrecision] * a), $MachinePrecision] - N[(x * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-6], N[(N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision] + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2.00000000000000018e25

   1. Initial program 94.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -2.00000000000000018e25 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.99999999999999991e-6

   1. Initial program 96.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.99999999999999991e-6 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+25}:\\ \;\;\;\;\left(b \cdot 27\right) \cdot a - x \cdot -2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-6}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + 2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x + t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= t_1 -2e+25)
     (- (* (* b 27.0) a) (* x -2.0))
     (if (<= t_1 2e-6)
       (+ (* -9.0 (* t (* y z))) (* 2.0 x))
       (+ (* 2.0 x) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -2e+25) {
		tmp = ((b * 27.0) * a) - (x * -2.0);
	} else if (t_1 <= 2e-6) {
		tmp = (-9.0 * (t * (y * z))) + (2.0 * x);
	} else {
		tmp = (2.0 * x) + t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    if (t_1 <= (-2d+25)) then
        tmp = ((b * 27.0d0) * a) - (x * (-2.0d0))
    else if (t_1 <= 2d-6) then
        tmp = ((-9.0d0) * (t * (y * z))) + (2.0d0 * x)
    else
        tmp = (2.0d0 * x) + t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -2e+25) {
		tmp = ((b * 27.0) * a) - (x * -2.0);
	} else if (t_1 <= 2e-6) {
		tmp = (-9.0 * (t * (y * z))) + (2.0 * x);
	} else {
		tmp = (2.0 * x) + t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if t_1 <= -2e+25:
		tmp = ((b * 27.0) * a) - (x * -2.0)
	elif t_1 <= 2e-6:
		tmp = (-9.0 * (t * (y * z))) + (2.0 * x)
	else:
		tmp = (2.0 * x) + t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= -2e+25)
		tmp = Float64(Float64(Float64(b * 27.0) * a) - Float64(x * -2.0));
	elseif (t_1 <= 2e-6)
		tmp = Float64(Float64(-9.0 * Float64(t * Float64(y * z))) + Float64(2.0 * x));
	else
		tmp = Float64(Float64(2.0 * x) + t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_1 <= -2e+25)
		tmp = ((b * 27.0) * a) - (x * -2.0);
	elseif (t_1 <= 2e-6)
		tmp = (-9.0 * (t * (y * z))) + (2.0 * x);
	else
		tmp = (2.0 * x) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+25], N[(N[(N[(b * 27.0), $MachinePrecision] * a), $MachinePrecision] - N[(x * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-6], N[(N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -2.00000000000000018e25

   1. Initial program 94.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -2.00000000000000018e25 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.99999999999999991e-6

   1. Initial program 96.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 1.99999999999999991e-6 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 45.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-135}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+74}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+102}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+129}:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3e-135)
   (* (* a b) 27.0)
   (if (<= b 3.2e+74)
     (* 2.0 x)
     (if (<= b 8.6e+102)
       (* -9.0 (* t (* y z)))
       (if (<= b 1.95e+129) (* 2.0 x) (* b (* a 27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-135) {
		tmp = (a * b) * 27.0;
	} else if (b <= 3.2e+74) {
		tmp = 2.0 * x;
	} else if (b <= 8.6e+102) {
		tmp = -9.0 * (t * (y * z));
	} else if (b <= 1.95e+129) {
		tmp = 2.0 * x;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3d-135)) then
        tmp = (a * b) * 27.0d0
    else if (b <= 3.2d+74) then
        tmp = 2.0d0 * x
    else if (b <= 8.6d+102) then
        tmp = (-9.0d0) * (t * (y * z))
    else if (b <= 1.95d+129) then
        tmp = 2.0d0 * x
    else
        tmp = b * (a * 27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3e-135) {
		tmp = (a * b) * 27.0;
	} else if (b <= 3.2e+74) {
		tmp = 2.0 * x;
	} else if (b <= 8.6e+102) {
		tmp = -9.0 * (t * (y * z));
	} else if (b <= 1.95e+129) {
		tmp = 2.0 * x;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3e-135:
		tmp = (a * b) * 27.0
	elif b <= 3.2e+74:
		tmp = 2.0 * x
	elif b <= 8.6e+102:
		tmp = -9.0 * (t * (y * z))
	elif b <= 1.95e+129:
		tmp = 2.0 * x
	else:
		tmp = b * (a * 27.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3e-135)
		tmp = Float64(Float64(a * b) * 27.0);
	elseif (b <= 3.2e+74)
		tmp = Float64(2.0 * x);
	elseif (b <= 8.6e+102)
		tmp = Float64(-9.0 * Float64(t * Float64(y * z)));
	elseif (b <= 1.95e+129)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(b * Float64(a * 27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3e-135)
		tmp = (a * b) * 27.0;
	elseif (b <= 3.2e+74)
		tmp = 2.0 * x;
	elseif (b <= 8.6e+102)
		tmp = -9.0 * (t * (y * z));
	elseif (b <= 1.95e+129)
		tmp = 2.0 * x;
	else
		tmp = b * (a * 27.0);
	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, -3e-135], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], If[LessEqual[b, 3.2e+74], N[(2.0 * x), $MachinePrecision], If[LessEqual[b, 8.6e+102], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.95e+129], N[(2.0 * x), $MachinePrecision], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.00000000000000012e-135

   1. Initial program 95.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -3.00000000000000012e-135 < b < 3.19999999999999995e74 or 8.6000000000000002e102 < b < 1.9499999999999999e129

   1. Initial program 96.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 3.19999999999999995e74 < b < 8.6000000000000002e102

   1. Initial program 88.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 1.9499999999999999e129 < b

   1. Initial program 95.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+238}:\\ \;\;\;\;\left(t \cdot \left(z \cdot -9\right)\right) \cdot y\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+228}:\\ \;\;\;\;2 \cdot x + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+177}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot 27\right) \cdot a - x \cdot -2\\ \end{array} \end{array} \]

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 (<= y -7.6e+238)
   (* (* t (* z -9.0)) y)
   (if (<= y -6.5e+228)
     (+ (* 2.0 x) (* (* a 27.0) b))
     (if (<= y -1.8e+177)
       (* (* y (* z t)) -9.0)
       (- (* (* b 27.0) a) (* 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 (y <= -7.6e+238) {
		tmp = (t * (z * -9.0)) * y;
	} else if (y <= -6.5e+228) {
		tmp = (2.0 * x) + ((a * 27.0) * b);
	} else if (y <= -1.8e+177) {
		tmp = (y * (z * t)) * -9.0;
	} else {
		tmp = ((b * 27.0) * a) - (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 (y <= (-7.6d+238)) then
        tmp = (t * (z * (-9.0d0))) * y
    else if (y <= (-6.5d+228)) then
        tmp = (2.0d0 * x) + ((a * 27.0d0) * b)
    else if (y <= (-1.8d+177)) then
        tmp = (y * (z * t)) * (-9.0d0)
    else
        tmp = ((b * 27.0d0) * a) - (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 (y <= -7.6e+238) {
		tmp = (t * (z * -9.0)) * y;
	} else if (y <= -6.5e+228) {
		tmp = (2.0 * x) + ((a * 27.0) * b);
	} else if (y <= -1.8e+177) {
		tmp = (y * (z * t)) * -9.0;
	} else {
		tmp = ((b * 27.0) * a) - (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 y <= -7.6e+238:
		tmp = (t * (z * -9.0)) * y
	elif y <= -6.5e+228:
		tmp = (2.0 * x) + ((a * 27.0) * b)
	elif y <= -1.8e+177:
		tmp = (y * (z * t)) * -9.0
	else:
		tmp = ((b * 27.0) * a) - (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 (y <= -7.6e+238)
		tmp = Float64(Float64(t * Float64(z * -9.0)) * y);
	elseif (y <= -6.5e+228)
		tmp = Float64(Float64(2.0 * x) + Float64(Float64(a * 27.0) * b));
	elseif (y <= -1.8e+177)
		tmp = Float64(Float64(y * Float64(z * t)) * -9.0);
	else
		tmp = Float64(Float64(Float64(b * 27.0) * a) - 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 (y <= -7.6e+238)
		tmp = (t * (z * -9.0)) * y;
	elseif (y <= -6.5e+228)
		tmp = (2.0 * x) + ((a * 27.0) * b);
	elseif (y <= -1.8e+177)
		tmp = (y * (z * t)) * -9.0;
	else
		tmp = ((b * 27.0) * a) - (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[y, -7.6e+238], N[(N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, -6.5e+228], N[(N[(2.0 * x), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.8e+177], N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision], N[(N[(N[(b * 27.0), $MachinePrecision] * a), $MachinePrecision] - N[(x * -2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.60000000000000049e238

   1. Initial program 76.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -7.60000000000000049e238 < y < -6.5e228

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6.5e228 < y < -1.80000000000000001e177

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -1.80000000000000001e177 < y

   1. Initial program 96.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+238}:\\ \;\;\;\;\left(t \cdot \left(z \cdot -9\right)\right) \cdot y\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{+229}:\\ \;\;\;\;2 \cdot x + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+176}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27 - x \cdot -2\\ \end{array} \end{array} \]

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 (<= y -4.3e+238)
   (* (* t (* z -9.0)) y)
   (if (<= y -1.08e+229)
     (+ (* 2.0 x) (* (* a 27.0) b))
     (if (<= y -6.5e+176)
       (* (* y (* z t)) -9.0)
       (- (* (* a b) 27.0) (* 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 (y <= -4.3e+238) {
		tmp = (t * (z * -9.0)) * y;
	} else if (y <= -1.08e+229) {
		tmp = (2.0 * x) + ((a * 27.0) * b);
	} else if (y <= -6.5e+176) {
		tmp = (y * (z * t)) * -9.0;
	} else {
		tmp = ((a * b) * 27.0) - (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 (y <= (-4.3d+238)) then
        tmp = (t * (z * (-9.0d0))) * y
    else if (y <= (-1.08d+229)) then
        tmp = (2.0d0 * x) + ((a * 27.0d0) * b)
    else if (y <= (-6.5d+176)) then
        tmp = (y * (z * t)) * (-9.0d0)
    else
        tmp = ((a * b) * 27.0d0) - (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 (y <= -4.3e+238) {
		tmp = (t * (z * -9.0)) * y;
	} else if (y <= -1.08e+229) {
		tmp = (2.0 * x) + ((a * 27.0) * b);
	} else if (y <= -6.5e+176) {
		tmp = (y * (z * t)) * -9.0;
	} else {
		tmp = ((a * b) * 27.0) - (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 y <= -4.3e+238:
		tmp = (t * (z * -9.0)) * y
	elif y <= -1.08e+229:
		tmp = (2.0 * x) + ((a * 27.0) * b)
	elif y <= -6.5e+176:
		tmp = (y * (z * t)) * -9.0
	else:
		tmp = ((a * b) * 27.0) - (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 (y <= -4.3e+238)
		tmp = Float64(Float64(t * Float64(z * -9.0)) * y);
	elseif (y <= -1.08e+229)
		tmp = Float64(Float64(2.0 * x) + Float64(Float64(a * 27.0) * b));
	elseif (y <= -6.5e+176)
		tmp = Float64(Float64(y * Float64(z * t)) * -9.0);
	else
		tmp = Float64(Float64(Float64(a * b) * 27.0) - 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 (y <= -4.3e+238)
		tmp = (t * (z * -9.0)) * y;
	elseif (y <= -1.08e+229)
		tmp = (2.0 * x) + ((a * 27.0) * b);
	elseif (y <= -6.5e+176)
		tmp = (y * (z * t)) * -9.0;
	else
		tmp = ((a * b) * 27.0) - (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[y, -4.3e+238], N[(N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, -1.08e+229], N[(N[(2.0 * x), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e+176], N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision], N[(N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision] - N[(x * -2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.29999999999999983e238

   1. Initial program 76.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -4.29999999999999983e238 < y < -1.0800000000000001e229

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.0800000000000001e229 < y < -6.49999999999999949e176

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -6.49999999999999949e176 < y

   1. Initial program 96.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot x + \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;y \leq -4 \cdot 10^{+239}:\\ \;\;\;\;\left(t \cdot \left(z \cdot -9\right)\right) \cdot y\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{+229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+177}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* 2.0 x) (* (* a 27.0) b))))
   (if (<= y -4e+239)
     (* (* t (* z -9.0)) y)
     (if (<= y -2.95e+229)
       t_1
       (if (<= y -1.65e+177) (* (* y (* z t)) -9.0) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (2.0 * x) + ((a * 27.0) * b);
	double tmp;
	if (y <= -4e+239) {
		tmp = (t * (z * -9.0)) * y;
	} else if (y <= -2.95e+229) {
		tmp = t_1;
	} else if (y <= -1.65e+177) {
		tmp = (y * (z * t)) * -9.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 * x) + ((a * 27.0d0) * b)
    if (y <= (-4d+239)) then
        tmp = (t * (z * (-9.0d0))) * y
    else if (y <= (-2.95d+229)) then
        tmp = t_1
    else if (y <= (-1.65d+177)) then
        tmp = (y * (z * t)) * (-9.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (2.0 * x) + ((a * 27.0) * b);
	double tmp;
	if (y <= -4e+239) {
		tmp = (t * (z * -9.0)) * y;
	} else if (y <= -2.95e+229) {
		tmp = t_1;
	} else if (y <= -1.65e+177) {
		tmp = (y * (z * t)) * -9.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (2.0 * x) + ((a * 27.0) * b)
	tmp = 0
	if y <= -4e+239:
		tmp = (t * (z * -9.0)) * y
	elif y <= -2.95e+229:
		tmp = t_1
	elif y <= -1.65e+177:
		tmp = (y * (z * t)) * -9.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(2.0 * x) + Float64(Float64(a * 27.0) * b))
	tmp = 0.0
	if (y <= -4e+239)
		tmp = Float64(Float64(t * Float64(z * -9.0)) * y);
	elseif (y <= -2.95e+229)
		tmp = t_1;
	elseif (y <= -1.65e+177)
		tmp = Float64(Float64(y * Float64(z * t)) * -9.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (2.0 * x) + ((a * 27.0) * b);
	tmp = 0.0;
	if (y <= -4e+239)
		tmp = (t * (z * -9.0)) * y;
	elseif (y <= -2.95e+229)
		tmp = t_1;
	elseif (y <= -1.65e+177)
		tmp = (y * (z * t)) * -9.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(2.0 * x), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e+239], N[(N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, -2.95e+229], t$95$1, If[LessEqual[y, -1.65e+177], N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.99999999999999996e239

   1. Initial program 76.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -3.99999999999999996e239 < y < -2.9499999999999999e229 or -1.6500000000000001e177 < y

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.9499999999999999e229 < y < -1.6500000000000001e177

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 96.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 4.5 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \left(\left(z \cdot t\right) \cdot -9\right) + \left(x \cdot 2 - \left(b \cdot -27\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot -9\right) \cdot y\right) \cdot z + \left(a \cdot b\right) \cdot 27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 4.5e+142)
   (+ (* y (* (* z t) -9.0)) (- (* x 2.0) (* (* b -27.0) a)))
   (+ (* (* (* t -9.0) y) z) (* (* a b) 27.0))))

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 <= 4.5e+142) {
		tmp = (y * ((z * t) * -9.0)) + ((x * 2.0) - ((b * -27.0) * a));
	} else {
		tmp = (((t * -9.0) * y) * z) + ((a * b) * 27.0);
	}
	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 <= 4.5d+142) then
        tmp = (y * ((z * t) * (-9.0d0))) + ((x * 2.0d0) - ((b * (-27.0d0)) * a))
    else
        tmp = (((t * (-9.0d0)) * y) * z) + ((a * b) * 27.0d0)
    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 <= 4.5e+142) {
		tmp = (y * ((z * t) * -9.0)) + ((x * 2.0) - ((b * -27.0) * a));
	} else {
		tmp = (((t * -9.0) * y) * z) + ((a * b) * 27.0);
	}
	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 <= 4.5e+142:
		tmp = (y * ((z * t) * -9.0)) + ((x * 2.0) - ((b * -27.0) * a))
	else:
		tmp = (((t * -9.0) * y) * z) + ((a * b) * 27.0)
	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 <= 4.5e+142)
		tmp = Float64(Float64(y * Float64(Float64(z * t) * -9.0)) + Float64(Float64(x * 2.0) - Float64(Float64(b * -27.0) * a)));
	else
		tmp = Float64(Float64(Float64(Float64(t * -9.0) * y) * z) + Float64(Float64(a * b) * 27.0));
	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 <= 4.5e+142)
		tmp = (y * ((z * t) * -9.0)) + ((x * 2.0) - ((b * -27.0) * a));
	else
		tmp = (((t * -9.0) * y) * z) + ((a * b) * 27.0);
	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, 4.5e+142], N[(N[(y * N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(b * -27.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(t * -9.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.4999999999999999e142

   1. Initial program 97.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   if 4.4999999999999999e142 < z

   1. Initial program 83.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 96.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.05 \cdot 10^{+138}:\\ \;\;\;\;y \cdot \left(\left(z \cdot t\right) \cdot -9\right) + \left(x \cdot 2 - \left(a \cdot b\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t \cdot -9\right) \cdot y\right) \cdot z + \left(a \cdot b\right) \cdot 27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.05e+138)
   (+ (* y (* (* z t) -9.0)) (- (* x 2.0) (* (* a b) -27.0)))
   (+ (* (* (* t -9.0) y) z) (* (* a b) 27.0))))

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 <= 1.05e+138) {
		tmp = (y * ((z * t) * -9.0)) + ((x * 2.0) - ((a * b) * -27.0));
	} else {
		tmp = (((t * -9.0) * y) * z) + ((a * b) * 27.0);
	}
	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 <= 1.05d+138) then
        tmp = (y * ((z * t) * (-9.0d0))) + ((x * 2.0d0) - ((a * b) * (-27.0d0)))
    else
        tmp = (((t * (-9.0d0)) * y) * z) + ((a * b) * 27.0d0)
    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 <= 1.05e+138) {
		tmp = (y * ((z * t) * -9.0)) + ((x * 2.0) - ((a * b) * -27.0));
	} else {
		tmp = (((t * -9.0) * y) * z) + ((a * b) * 27.0);
	}
	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 <= 1.05e+138:
		tmp = (y * ((z * t) * -9.0)) + ((x * 2.0) - ((a * b) * -27.0))
	else:
		tmp = (((t * -9.0) * y) * z) + ((a * b) * 27.0)
	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 <= 1.05e+138)
		tmp = Float64(Float64(y * Float64(Float64(z * t) * -9.0)) + Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0)));
	else
		tmp = Float64(Float64(Float64(Float64(t * -9.0) * y) * z) + Float64(Float64(a * b) * 27.0));
	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 <= 1.05e+138)
		tmp = (y * ((z * t) * -9.0)) + ((x * 2.0) - ((a * b) * -27.0));
	else
		tmp = (((t * -9.0) * y) * z) + ((a * b) * 27.0);
	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, 1.05e+138], N[(N[(y * N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(t * -9.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.05000000000000003e138

   1. Initial program 97.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   if 1.05000000000000003e138 < z

   1. Initial program 84.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 45.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{-137}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;b \leq 5800:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

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 -1.2e-137)
   (* (* a b) 27.0)
   (if (<= b 5800.0) (* 2.0 x) (* b (* a 27.0)))))

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 <= -1.2e-137) {
		tmp = (a * b) * 27.0;
	} else if (b <= 5800.0) {
		tmp = 2.0 * x;
	} else {
		tmp = b * (a * 27.0);
	}
	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 <= (-1.2d-137)) then
        tmp = (a * b) * 27.0d0
    else if (b <= 5800.0d0) then
        tmp = 2.0d0 * x
    else
        tmp = b * (a * 27.0d0)
    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 <= -1.2e-137) {
		tmp = (a * b) * 27.0;
	} else if (b <= 5800.0) {
		tmp = 2.0 * x;
	} else {
		tmp = b * (a * 27.0);
	}
	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 <= -1.2e-137:
		tmp = (a * b) * 27.0
	elif b <= 5800.0:
		tmp = 2.0 * x
	else:
		tmp = b * (a * 27.0)
	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 <= -1.2e-137)
		tmp = Float64(Float64(a * b) * 27.0);
	elseif (b <= 5800.0)
		tmp = Float64(2.0 * x);
	else
		tmp = Float64(b * Float64(a * 27.0));
	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 <= -1.2e-137)
		tmp = (a * b) * 27.0;
	elseif (b <= 5800.0)
		tmp = 2.0 * x;
	else
		tmp = b * (a * 27.0);
	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, -1.2e-137], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], If[LessEqual[b, 5800.0], N[(2.0 * x), $MachinePrecision], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.2e-137

   1. Initial program 95.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.2e-137 < b < 5800

   1. Initial program 98.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 5800 < b

   1. Initial program 92.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 45.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1300:\\ \;\;\;\;2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= b -1.8e-135) t_1 (if (<= b 1300.0) (* 2.0 x) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (b <= -1.8e-135) {
		tmp = t_1;
	} else if (b <= 1300.0) {
		tmp = 2.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    if (b <= (-1.8d-135)) then
        tmp = t_1
    else if (b <= 1300.0d0) then
        tmp = 2.0d0 * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (b <= -1.8e-135) {
		tmp = t_1;
	} else if (b <= 1300.0) {
		tmp = 2.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	tmp = 0
	if b <= -1.8e-135:
		tmp = t_1
	elif b <= 1300.0:
		tmp = 2.0 * x
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (b <= -1.8e-135)
		tmp = t_1;
	elseif (b <= 1300.0)
		tmp = Float64(2.0 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if (b <= -1.8e-135)
		tmp = t_1;
	elseif (b <= 1300.0)
		tmp = 2.0 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.8e-135], t$95$1, If[LessEqual[b, 1300.0], N[(2.0 * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.79999999999999989e-135 or 1300 < b

   1. Initial program 94.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   if -1.79999999999999989e-135 < b < 1300

   1. Initial program 98.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 31.5% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in x around inf 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Developer target: 94.5% 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 2024110 
(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)))