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

Percentage Accurate: 95.6% → 97.6%

Time: 10.7s

Alternatives: 13

Speedup: 0.7×

• 27.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% 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: 97.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + t\_1 \leq 5 \cdot 10^{+295}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(y \cdot -9\right) \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 (<= (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) t_1) 5e+295)
     (+ (- (* x 2.0) (* t (* y (* 9.0 z)))) t_1)
     (fma a (* 27.0 b) (fma x 2.0 (* (* y -9.0) (* z t)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if ((((x * 2.0) - (((y * 9.0) * z) * t)) + t_1) <= 5e+295) {
		tmp = ((x * 2.0) - (t * (y * (9.0 * z)))) + t_1;
	} else {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, ((y * -9.0) * (z * t))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + t_1) <= 5e+295)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(9.0 * z)))) + t_1);
	else
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(Float64(y * -9.0) * Float64(z * t))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], 5e+295], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(N[(y * -9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) (*.f64 (*.f64 a #s(literal 27 binary64)) b)) < 4.99999999999999991e295

   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. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*l* 94.9%

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

      2. *-commutative 94.9%

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

   4. Applied egg-rr 94.9%

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

   if 4.99999999999999991e295 < (+.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)) (*.f64 (*.f64 a #s(literal 27 binary64)) b))

   1. Initial program 87.3%

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

      1. +-commutative 87.3%

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

      2. associate-+r- 87.3%

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

      3. *-commutative 87.3%

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

      4. cancel-sign-sub-inv 87.3%

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

      5. associate-*r* 93.5%

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

      6. distribute-lft-neg-in 93.5%

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

      7. *-commutative 93.5%

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

      8. cancel-sign-sub-inv 93.5%

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

      9. associate-+r- 93.5%

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

      10. associate-*l* 93.5%

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

      11. fma-define 97.8%

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

      12. fma-neg 97.8%

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

      13. associate-*l* 97.8%

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

      14. distribute-lft-neg-in 97.8%

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

      15. *-commutative 97.8%

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

      16. distribute-rgt-neg-in 97.8%

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

      17. metadata-eval 97.8%

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

   3. Simplified 97.8%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + b \cdot \left(a \cdot 27\right) \leq 5 \cdot 10^{+295}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(y \cdot -9\right) \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 48.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;b \leq -1 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-135}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-176}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-215}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-154}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 -1e-46)
     t_1
     (if (<= b -2.9e-135)
       (* x 2.0)
       (if (<= b -1.6e-145)
         t_1
         (if (<= b -1.7e-176)
           (* -9.0 (* t (* y z)))
           (if (<= b 6.4e-215)
             (* x 2.0)
             (if (<= b 4e-154)
               (* (* y z) (* t -9.0))
               (if (<= b 1.55e+24) (* x 2.0) t_1)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (b <= -1e-46) {
		tmp = t_1;
	} else if (b <= -2.9e-135) {
		tmp = x * 2.0;
	} else if (b <= -1.6e-145) {
		tmp = t_1;
	} else if (b <= -1.7e-176) {
		tmp = -9.0 * (t * (y * z));
	} else if (b <= 6.4e-215) {
		tmp = x * 2.0;
	} else if (b <= 4e-154) {
		tmp = (y * z) * (t * -9.0);
	} else if (b <= 1.55e+24) {
		tmp = x * 2.0;
	} 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.
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 <= (-1d-46)) then
        tmp = t_1
    else if (b <= (-2.9d-135)) then
        tmp = x * 2.0d0
    else if (b <= (-1.6d-145)) then
        tmp = t_1
    else if (b <= (-1.7d-176)) then
        tmp = (-9.0d0) * (t * (y * z))
    else if (b <= 6.4d-215) then
        tmp = x * 2.0d0
    else if (b <= 4d-154) then
        tmp = (y * z) * (t * (-9.0d0))
    else if (b <= 1.55d+24) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (b <= -1e-46) {
		tmp = t_1;
	} else if (b <= -2.9e-135) {
		tmp = x * 2.0;
	} else if (b <= -1.6e-145) {
		tmp = t_1;
	} else if (b <= -1.7e-176) {
		tmp = -9.0 * (t * (y * z));
	} else if (b <= 6.4e-215) {
		tmp = x * 2.0;
	} else if (b <= 4e-154) {
		tmp = (y * z) * (t * -9.0);
	} else if (b <= 1.55e+24) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	tmp = 0
	if b <= -1e-46:
		tmp = t_1
	elif b <= -2.9e-135:
		tmp = x * 2.0
	elif b <= -1.6e-145:
		tmp = t_1
	elif b <= -1.7e-176:
		tmp = -9.0 * (t * (y * z))
	elif b <= 6.4e-215:
		tmp = x * 2.0
	elif b <= 4e-154:
		tmp = (y * z) * (t * -9.0)
	elif b <= 1.55e+24:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (b <= -1e-46)
		tmp = t_1;
	elseif (b <= -2.9e-135)
		tmp = Float64(x * 2.0);
	elseif (b <= -1.6e-145)
		tmp = t_1;
	elseif (b <= -1.7e-176)
		tmp = Float64(-9.0 * Float64(t * Float64(y * z)));
	elseif (b <= 6.4e-215)
		tmp = Float64(x * 2.0);
	elseif (b <= 4e-154)
		tmp = Float64(Float64(y * z) * Float64(t * -9.0));
	elseif (b <= 1.55e+24)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if (b <= -1e-46)
		tmp = t_1;
	elseif (b <= -2.9e-135)
		tmp = x * 2.0;
	elseif (b <= -1.6e-145)
		tmp = t_1;
	elseif (b <= -1.7e-176)
		tmp = -9.0 * (t * (y * z));
	elseif (b <= 6.4e-215)
		tmp = x * 2.0;
	elseif (b <= 4e-154)
		tmp = (y * z) * (t * -9.0);
	elseif (b <= 1.55e+24)
		tmp = x * 2.0;
	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.
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, -1e-46], t$95$1, If[LessEqual[b, -2.9e-135], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, -1.6e-145], t$95$1, If[LessEqual[b, -1.7e-176], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.4e-215], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 4e-154], N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e+24], N[(x * 2.0), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.00000000000000002e-46 or -2.9000000000000002e-135 < b < -1.60000000000000004e-145 or 1.55000000000000005e24 < b

   1. Initial program 93.9%

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

   3. Taylor expanded in a around inf 61.8%

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

      1. *-commutative 61.8%

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

      2. *-commutative 61.8%

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

      3. associate-*r* 61.8%

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

      4. *-commutative 61.8%

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

   5. Simplified 61.8%

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

   if -1.00000000000000002e-46 < b < -2.9000000000000002e-135 or -1.6999999999999999e-176 < b < 6.4000000000000003e-215 or 3.9999999999999999e-154 < b < 1.55000000000000005e24

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 49.9%

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

   if -1.60000000000000004e-145 < b < -1.6999999999999999e-176

   1. Initial program 80.3%

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

   3. Taylor expanded in y around inf 41.4%

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

   if 6.4000000000000003e-215 < b < 3.9999999999999999e-154

   1. Initial program 87.8%

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

   3. Taylor expanded in y around inf 48.3%

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

      1. associate-*r* 48.4%

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

   5. Applied egg-rr 48.4%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-135}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-145}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-176}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-215}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-154}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-135}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-177}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-215}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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))) (t_2 (* -9.0 (* t (* y z)))))
   (if (<= b -6e-36)
     t_1
     (if (<= b -2.9e-135)
       (* x 2.0)
       (if (<= b -1.6e-145)
         t_1
         (if (<= b -6.2e-177)
           t_2
           (if (<= b 5.2e-215)
             (* x 2.0)
             (if (<= b 5e-154) t_2 (if (<= b 2.4e+24) (* x 2.0) t_1)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = -9.0 * (t * (y * z));
	double tmp;
	if (b <= -6e-36) {
		tmp = t_1;
	} else if (b <= -2.9e-135) {
		tmp = x * 2.0;
	} else if (b <= -1.6e-145) {
		tmp = t_1;
	} else if (b <= -6.2e-177) {
		tmp = t_2;
	} else if (b <= 5.2e-215) {
		tmp = x * 2.0;
	} else if (b <= 5e-154) {
		tmp = t_2;
	} else if (b <= 2.4e+24) {
		tmp = x * 2.0;
	} 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.
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 = b * (a * 27.0d0)
    t_2 = (-9.0d0) * (t * (y * z))
    if (b <= (-6d-36)) then
        tmp = t_1
    else if (b <= (-2.9d-135)) then
        tmp = x * 2.0d0
    else if (b <= (-1.6d-145)) then
        tmp = t_1
    else if (b <= (-6.2d-177)) then
        tmp = t_2
    else if (b <= 5.2d-215) then
        tmp = x * 2.0d0
    else if (b <= 5d-154) then
        tmp = t_2
    else if (b <= 2.4d+24) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = -9.0 * (t * (y * z));
	double tmp;
	if (b <= -6e-36) {
		tmp = t_1;
	} else if (b <= -2.9e-135) {
		tmp = x * 2.0;
	} else if (b <= -1.6e-145) {
		tmp = t_1;
	} else if (b <= -6.2e-177) {
		tmp = t_2;
	} else if (b <= 5.2e-215) {
		tmp = x * 2.0;
	} else if (b <= 5e-154) {
		tmp = t_2;
	} else if (b <= 2.4e+24) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	t_2 = -9.0 * (t * (y * z))
	tmp = 0
	if b <= -6e-36:
		tmp = t_1
	elif b <= -2.9e-135:
		tmp = x * 2.0
	elif b <= -1.6e-145:
		tmp = t_1
	elif b <= -6.2e-177:
		tmp = t_2
	elif b <= 5.2e-215:
		tmp = x * 2.0
	elif b <= 5e-154:
		tmp = t_2
	elif b <= 2.4e+24:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	t_2 = Float64(-9.0 * Float64(t * Float64(y * z)))
	tmp = 0.0
	if (b <= -6e-36)
		tmp = t_1;
	elseif (b <= -2.9e-135)
		tmp = Float64(x * 2.0);
	elseif (b <= -1.6e-145)
		tmp = t_1;
	elseif (b <= -6.2e-177)
		tmp = t_2;
	elseif (b <= 5.2e-215)
		tmp = Float64(x * 2.0);
	elseif (b <= 5e-154)
		tmp = t_2;
	elseif (b <= 2.4e+24)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	t_2 = -9.0 * (t * (y * z));
	tmp = 0.0;
	if (b <= -6e-36)
		tmp = t_1;
	elseif (b <= -2.9e-135)
		tmp = x * 2.0;
	elseif (b <= -1.6e-145)
		tmp = t_1;
	elseif (b <= -6.2e-177)
		tmp = t_2;
	elseif (b <= 5.2e-215)
		tmp = x * 2.0;
	elseif (b <= 5e-154)
		tmp = t_2;
	elseif (b <= 2.4e+24)
		tmp = x * 2.0;
	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.
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]}, Block[{t$95$2 = N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6e-36], t$95$1, If[LessEqual[b, -2.9e-135], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, -1.6e-145], t$95$1, If[LessEqual[b, -6.2e-177], t$95$2, If[LessEqual[b, 5.2e-215], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 5e-154], t$95$2, If[LessEqual[b, 2.4e+24], N[(x * 2.0), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.0000000000000003e-36 or -2.9000000000000002e-135 < b < -1.60000000000000004e-145 or 2.4000000000000001e24 < b

   1. Initial program 93.9%

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

   3. Taylor expanded in a around inf 62.2%

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

      1. *-commutative 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-*r* 62.2%

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

      4. *-commutative 62.2%

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

   5. Simplified 62.2%

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

   if -6.0000000000000003e-36 < b < -2.9000000000000002e-135 or -6.20000000000000036e-177 < b < 5.2e-215 or 5.0000000000000002e-154 < b < 2.4000000000000001e24

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 50.4%

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

   if -1.60000000000000004e-145 < b < -6.20000000000000036e-177 or 5.2e-215 < b < 5.0000000000000002e-154

   1. Initial program 85.9%

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

   3. Taylor expanded in y around inf 46.6%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{-36}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-135}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-145}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-177}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-215}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-154}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{-99}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 1.58 \cdot 10^{+47}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+98} \lor \neg \left(t \leq 1.14 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 + 27 \cdot \frac{a \cdot b}{x}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.16e-99)
   (- (* x 2.0) (* 9.0 (* y (* z t))))
   (if (<= t 1.58e+47)
     (+ (* 27.0 (* a b)) (* x 2.0))
     (if (or (<= t 9.5e+98) (not (<= t 1.14e+105)))
       (- (* x 2.0) (* 9.0 (* t (* y z))))
       (* x (+ 2.0 (* 27.0 (/ (* a b) x))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.16e-99) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (t <= 1.58e+47) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else if ((t <= 9.5e+98) || !(t <= 1.14e+105)) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else {
		tmp = x * (2.0 + (27.0 * ((a * b) / x)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.16d-99)) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else if (t <= 1.58d+47) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else if ((t <= 9.5d+98) .or. (.not. (t <= 1.14d+105))) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    else
        tmp = x * (2.0d0 + (27.0d0 * ((a * b) / x)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.16e-99) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (t <= 1.58e+47) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else if ((t <= 9.5e+98) || !(t <= 1.14e+105)) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else {
		tmp = x * (2.0 + (27.0 * ((a * b) / x)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.16e-99:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	elif t <= 1.58e+47:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	elif (t <= 9.5e+98) or not (t <= 1.14e+105):
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	else:
		tmp = x * (2.0 + (27.0 * ((a * b) / x)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.16e-99)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	elseif (t <= 1.58e+47)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	elseif ((t <= 9.5e+98) || !(t <= 1.14e+105))
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	else
		tmp = Float64(x * Float64(2.0 + Float64(27.0 * Float64(Float64(a * b) / x))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.16e-99)
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	elseif (t <= 1.58e+47)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	elseif ((t <= 9.5e+98) || ~((t <= 1.14e+105)))
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	else
		tmp = x * (2.0 + (27.0 * ((a * b) / x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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, -1.16e-99], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.58e+47], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 9.5e+98], N[Not[LessEqual[t, 1.14e+105]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 + N[(27.0 * N[(N[(a * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.1599999999999999e-99

   1. Initial program 97.8%

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

   3. Taylor expanded in a around 0 59.0%

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

      1. *-commutative 59.0%

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

      2. associate-*r* 58.9%

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

   5. Applied egg-rr 58.9%

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

   if -1.1599999999999999e-99 < t < 1.5800000000000001e47

   1. Initial program 89.4%

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

   3. Taylor expanded in y around 0 77.0%

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

   if 1.5800000000000001e47 < t < 9.5000000000000001e98 or 1.13999999999999997e105 < t

   1. Initial program 95.7%

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

   3. Taylor expanded in a around 0 82.9%

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

   if 9.5000000000000001e98 < t < 1.13999999999999997e105

   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 y around 0 95.1%

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

   4. Taylor expanded in x around inf 95.1%

      \[\leadsto \color{blue}{x \cdot \left(2 + 27 \cdot \frac{a \cdot b}{x}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{-99}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 1.58 \cdot 10^{+47}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+98} \lor \neg \left(t \leq 1.14 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 + 27 \cdot \frac{a \cdot b}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-98}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+46}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+98} \lor \neg \left(t \leq 1.4 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 + 27 \cdot \frac{a \cdot b}{x}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.15e-98)
   (* (* y t) (* z -9.0))
   (if (<= t 1.65e+46)
     (+ (* 27.0 (* a b)) (* x 2.0))
     (if (or (<= t 9.5e+98) (not (<= t 1.4e+105)))
       (- (* x 2.0) (* 9.0 (* t (* y z))))
       (* x (+ 2.0 (* 27.0 (/ (* a b) x))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.15e-98) {
		tmp = (y * t) * (z * -9.0);
	} else if (t <= 1.65e+46) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else if ((t <= 9.5e+98) || !(t <= 1.4e+105)) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else {
		tmp = x * (2.0 + (27.0 * ((a * b) / x)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.15d-98)) then
        tmp = (y * t) * (z * (-9.0d0))
    else if (t <= 1.65d+46) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else if ((t <= 9.5d+98) .or. (.not. (t <= 1.4d+105))) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    else
        tmp = x * (2.0d0 + (27.0d0 * ((a * b) / x)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.15e-98) {
		tmp = (y * t) * (z * -9.0);
	} else if (t <= 1.65e+46) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else if ((t <= 9.5e+98) || !(t <= 1.4e+105)) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else {
		tmp = x * (2.0 + (27.0 * ((a * b) / x)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.15e-98:
		tmp = (y * t) * (z * -9.0)
	elif t <= 1.65e+46:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	elif (t <= 9.5e+98) or not (t <= 1.4e+105):
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	else:
		tmp = x * (2.0 + (27.0 * ((a * b) / x)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.15e-98)
		tmp = Float64(Float64(y * t) * Float64(z * -9.0));
	elseif (t <= 1.65e+46)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	elseif ((t <= 9.5e+98) || !(t <= 1.4e+105))
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	else
		tmp = Float64(x * Float64(2.0 + Float64(27.0 * Float64(Float64(a * b) / x))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.15e-98)
		tmp = (y * t) * (z * -9.0);
	elseif (t <= 1.65e+46)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	elseif ((t <= 9.5e+98) || ~((t <= 1.4e+105)))
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	else
		tmp = x * (2.0 + (27.0 * ((a * b) / x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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, -2.15e-98], N[(N[(y * t), $MachinePrecision] * N[(z * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e+46], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 9.5e+98], N[Not[LessEqual[t, 1.4e+105]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 + N[(27.0 * N[(N[(a * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.14999999999999994e-98

   1. Initial program 97.8%

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

   3. Taylor expanded in y around inf 35.4%

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

      1. *-commutative 35.4%

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

      2. associate-*r* 34.3%

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

      3. associate-*l* 34.3%

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

   5. Simplified 34.3%

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

   if -2.14999999999999994e-98 < t < 1.6499999999999999e46

   1. Initial program 89.4%

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

   3. Taylor expanded in y around 0 77.0%

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

   if 1.6499999999999999e46 < t < 9.5000000000000001e98 or 1.4000000000000001e105 < t

   1. Initial program 95.7%

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

   3. Taylor expanded in a around 0 82.9%

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

   if 9.5000000000000001e98 < t < 1.4000000000000001e105

   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 y around 0 95.1%

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

   4. Taylor expanded in x around inf 95.1%

      \[\leadsto \color{blue}{x \cdot \left(2 + 27 \cdot \frac{a \cdot b}{x}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-98}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+46}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+98} \lor \neg \left(t \leq 1.4 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 + 27 \cdot \frac{a \cdot b}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(y \cdot 9\right) \cdot z\\ \mathbf{if}\;t\_1 \leq 10^{+280}:\\ \;\;\;\;\left(x \cdot 2 - t\_1 \cdot t\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 1e+280)
     (+ (- (* x 2.0) (* t_1 t)) (* b (* a 27.0)))
     (* 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);
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 <= 1e+280) {
		tmp = ((x * 2.0) - (t_1 * t)) + (b * (a * 27.0));
	} 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.
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 <= 1d+280) then
        tmp = ((x * 2.0d0) - (t_1 * t)) + (b * (a * 27.0d0))
    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;
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 <= 1e+280) {
		tmp = ((x * 2.0) - (t_1 * t)) + (b * (a * 27.0));
	} 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])
[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 <= 1e+280:
		tmp = ((x * 2.0) - (t_1 * t)) + (b * (a * 27.0))
	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])
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 <= 1e+280)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t_1 * t)) + Float64(b * Float64(a * 27.0)));
	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])){:}
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 <= 1e+280)
		tmp = ((x * 2.0) - (t_1 * t)) + (b * (a * 27.0));
	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.
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, 1e+280], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t$95$1 * t), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $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) < 1e280

   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. Add Preprocessing

   if 1e280 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 75.8%

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

   3. Taylor expanded in y around inf 99.9%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 10^{+280}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(2 \cdot \frac{x}{y} + 27 \cdot \frac{a \cdot b}{y}\right) - 9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(y \cdot 9\right) \cdot z\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\left(x \cdot 2 - t\_1 \cdot t\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(27 \cdot \frac{a \cdot b}{y} - 9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 5e+301)
     (+ (- (* x 2.0) (* t_1 t)) (* b (* a 27.0)))
     (* y (- (* 27.0 (/ (* a b) y)) (* 9.0 (* z t)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 5e+301) {
		tmp = ((x * 2.0) - (t_1 * t)) + (b * (a * 27.0));
	} else {
		tmp = 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.
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 <= 5d+301) then
        tmp = ((x * 2.0d0) - (t_1 * t)) + (b * (a * 27.0d0))
    else
        tmp = 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;
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 <= 5e+301) {
		tmp = ((x * 2.0) - (t_1 * t)) + (b * (a * 27.0));
	} else {
		tmp = 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])
[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 <= 5e+301:
		tmp = ((x * 2.0) - (t_1 * t)) + (b * (a * 27.0))
	else:
		tmp = 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])
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 <= 5e+301)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t_1 * t)) + Float64(b * Float64(a * 27.0)));
	else
		tmp = Float64(y * Float64(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])){:}
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 <= 5e+301)
		tmp = ((x * 2.0) - (t_1 * t)) + (b * (a * 27.0));
	else
		tmp = 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.
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, 5e+301], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t$95$1 * t), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(27.0 * N[(N[(a * b), $MachinePrecision] / y), $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) < 5.0000000000000004e301

   1. Initial program 95.1%

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

   if 5.0000000000000004e301 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 71.6%

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

   3. Taylor expanded in y around inf 99.9%

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

   4. Taylor expanded in x around 0 94.3%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(27 \cdot \frac{a \cdot b}{y} - 9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(27 \cdot \frac{a \cdot b}{y} - 9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (* y 9.0) z) 5e+301)
   (+ (- (* x 2.0) (* t (* y (* 9.0 z)))) (* b (* a 27.0)))
   (* y (- (* 27.0 (/ (* a b) y)) (* 9.0 (* z t))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * 9.0) * z) <= 5e+301) {
		tmp = ((x * 2.0) - (t * (y * (9.0 * z)))) + (b * (a * 27.0));
	} else {
		tmp = 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.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((y * 9.0d0) * z) <= 5d+301) then
        tmp = ((x * 2.0d0) - (t * (y * (9.0d0 * z)))) + (b * (a * 27.0d0))
    else
        tmp = 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;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * 9.0) * z) <= 5e+301) {
		tmp = ((x * 2.0) - (t * (y * (9.0 * z)))) + (b * (a * 27.0));
	} else {
		tmp = 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])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if ((y * 9.0) * z) <= 5e+301:
		tmp = ((x * 2.0) - (t * (y * (9.0 * z)))) + (b * (a * 27.0))
	else:
		tmp = 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])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 5e+301)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(9.0 * z)))) + Float64(b * Float64(a * 27.0)));
	else
		tmp = Float64(y * Float64(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])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((y * 9.0) * z) <= 5e+301)
		tmp = ((x * 2.0) - (t * (y * (9.0 * z)))) + (b * (a * 27.0));
	else
		tmp = 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.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 5e+301], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(27.0 * N[(N[(a * b), $MachinePrecision] / y), $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) < 5.0000000000000004e301

   1. Initial program 95.1%

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

      1. associate-*l* 95.1%

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

      2. *-commutative 95.1%

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

   4. Applied egg-rr 95.1%

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

   if 5.0000000000000004e301 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 71.6%

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

   3. Taylor expanded in y around inf 99.9%

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

   4. Taylor expanded in x around 0 94.3%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(27 \cdot \frac{a \cdot b}{y} - 9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{-45} \lor \neg \left(b \leq 2.4 \cdot 10^{+24}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 9.0 (* t (* y z)))))
   (if (or (<= b -5e-45) (not (<= b 2.4e+24)))
     (- (* 27.0 (* a b)) t_1)
     (- (* x 2.0) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 9.0 * (t * (y * z));
	double tmp;
	if ((b <= -5e-45) || !(b <= 2.4e+24)) {
		tmp = (27.0 * (a * b)) - t_1;
	} else {
		tmp = (x * 2.0) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 9.0d0 * (t * (y * z))
    if ((b <= (-5d-45)) .or. (.not. (b <= 2.4d+24))) then
        tmp = (27.0d0 * (a * b)) - t_1
    else
        tmp = (x * 2.0d0) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 9.0 * (t * (y * z));
	double tmp;
	if ((b <= -5e-45) || !(b <= 2.4e+24)) {
		tmp = (27.0 * (a * b)) - t_1;
	} else {
		tmp = (x * 2.0) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 9.0 * (t * (y * z))
	tmp = 0
	if (b <= -5e-45) or not (b <= 2.4e+24):
		tmp = (27.0 * (a * b)) - t_1
	else:
		tmp = (x * 2.0) - t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(9.0 * Float64(t * Float64(y * z)))
	tmp = 0.0
	if ((b <= -5e-45) || !(b <= 2.4e+24))
		tmp = Float64(Float64(27.0 * Float64(a * b)) - t_1);
	else
		tmp = Float64(Float64(x * 2.0) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 9.0 * (t * (y * z));
	tmp = 0.0;
	if ((b <= -5e-45) || ~((b <= 2.4e+24)))
		tmp = (27.0 * (a * b)) - t_1;
	else
		tmp = (x * 2.0) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -5e-45], N[Not[LessEqual[b, 2.4e+24]], $MachinePrecision]], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.99999999999999976e-45 or 2.4000000000000001e24 < b

   1. Initial program 93.8%

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

   3. Taylor expanded in x around 0 77.2%

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

   if -4.99999999999999976e-45 < b < 2.4000000000000001e24

   1. Initial program 93.2%

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

   3. Taylor expanded in a around 0 83.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-45} \lor \neg \left(b \leq 2.4 \cdot 10^{+24}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+65}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-13}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.6e+65)
   (* (* y t) (* z -9.0))
   (if (<= z 2.3e-13) (+ (* 27.0 (* a b)) (* x 2.0)) (* -9.0 (* t (* y z))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.6e+65) {
		tmp = (y * t) * (z * -9.0);
	} else if (z <= 2.3e-13) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = -9.0 * (t * (y * z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-5.6d+65)) then
        tmp = (y * t) * (z * (-9.0d0))
    else if (z <= 2.3d-13) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (-9.0d0) * (t * (y * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.6e+65) {
		tmp = (y * t) * (z * -9.0);
	} else if (z <= 2.3e-13) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = -9.0 * (t * (y * z));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.6e+65:
		tmp = (y * t) * (z * -9.0)
	elif z <= 2.3e-13:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = -9.0 * (t * (y * z))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.6e+65)
		tmp = Float64(Float64(y * t) * Float64(z * -9.0));
	elseif (z <= 2.3e-13)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(-9.0 * Float64(t * Float64(y * z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.6e+65)
		tmp = (y * t) * (z * -9.0);
	elseif (z <= 2.3e-13)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = -9.0 * (t * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.6e+65], N[(N[(y * t), $MachinePrecision] * N[(z * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e-13], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5999999999999998e65

   1. Initial program 87.3%

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

   3. Taylor expanded in y around inf 43.2%

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

      1. *-commutative 43.2%

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

      2. associate-*r* 49.4%

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

      3. associate-*l* 47.5%

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

   5. Simplified 47.5%

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

   if -5.5999999999999998e65 < z < 2.29999999999999979e-13

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0 81.4%

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

   if 2.29999999999999979e-13 < z

   1. Initial program 87.4%

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

   3. Taylor expanded in y around inf 51.1%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+65}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-13}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.16 \cdot 10^{-42} \lor \neg \left(b \leq 1.45 \cdot 10^{+24}\right):\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.16e-42) (not (<= b 1.45e+24))) (* b (* a 27.0)) (* x 2.0)))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.16e-42) || !(b <= 1.45e+24)) {
		tmp = b * (a * 27.0);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.16d-42)) .or. (.not. (b <= 1.45d+24))) then
        tmp = b * (a * 27.0d0)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.16e-42) || !(b <= 1.45e+24)) {
		tmp = b * (a * 27.0);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.16e-42) or not (b <= 1.45e+24):
		tmp = b * (a * 27.0)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.16e-42) || !(b <= 1.45e+24))
		tmp = Float64(b * Float64(a * 27.0));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.16e-42) || ~((b <= 1.45e+24)))
		tmp = b * (a * 27.0);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.16e-42], N[Not[LessEqual[b, 1.45e+24]], $MachinePrecision]], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1600000000000001e-42 or 1.4499999999999999e24 < b

   1. Initial program 93.8%

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

   3. Taylor expanded in a around inf 61.9%

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

      1. *-commutative 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*r* 61.9%

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

      4. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   if -1.1600000000000001e-42 < b < 1.4499999999999999e24

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 46.5%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.16 \cdot 10^{-42} \lor \neg \left(b \leq 1.45 \cdot 10^{+24}\right):\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-46} \lor \neg \left(b \leq 8.5 \cdot 10^{+24}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.5e-46) (not (<= b 8.5e+24))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.5e-46) || !(b <= 8.5e+24)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.5d-46)) .or. (.not. (b <= 8.5d+24))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.5e-46) || !(b <= 8.5e+24)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.5e-46) or not (b <= 8.5e+24):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.5e-46) || !(b <= 8.5e+24))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.5e-46) || ~((b <= 8.5e+24)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.5e-46], N[Not[LessEqual[b, 8.5e+24]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.49999999999999994e-46 or 8.49999999999999959e24 < b

   1. Initial program 93.8%

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

   3. Taylor expanded in a around inf 61.9%

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

   if -1.49999999999999994e-46 < b < 8.49999999999999959e24

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 46.5%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-46} \lor \neg \left(b \leq 8.5 \cdot 10^{+24}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 31.0% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.5%

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

3. Taylor expanded in x around inf 32.5%

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

4. Final simplification 32.5%

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

Developer target: 95.2% 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 2024096 
(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)))