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

Percentage Accurate: 95.6% → 97.0%

Time: 9.6s

Alternatives: 13

Speedup: 1.0×

• 28.0% 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: 97.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.32e+39)
   (+ (* a (* 27.0 b)) (* z (* -9.0 (* y t))))
   (+ (- (* x 2.0) (* t (* 9.0 (* y z)))) (* b (* a 27.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.32e+39) {
		tmp = (a * (27.0 * b)) + (z * (-9.0 * (y * t)));
	} else {
		tmp = ((x * 2.0) - (t * (9.0 * (y * z)))) + (b * (a * 27.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 <= (-1.32d+39)) then
        tmp = (a * (27.0d0 * b)) + (z * ((-9.0d0) * (y * t)))
    else
        tmp = ((x * 2.0d0) - (t * (9.0d0 * (y * z)))) + (b * (a * 27.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.32e+39) {
		tmp = (a * (27.0 * b)) + (z * (-9.0 * (y * t)));
	} else {
		tmp = ((x * 2.0) - (t * (9.0 * (y * z)))) + (b * (a * 27.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.32e+39:
		tmp = (a * (27.0 * b)) + (z * (-9.0 * (y * t)))
	else:
		tmp = ((x * 2.0) - (t * (9.0 * (y * z)))) + (b * (a * 27.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.32e+39)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(z * Float64(-9.0 * Float64(y * t))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(9.0 * Float64(y * z)))) + Float64(b * Float64(a * 27.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.32e+39)
		tmp = (a * (27.0 * b)) + (z * (-9.0 * (y * t)));
	else
		tmp = ((x * 2.0) - (t * (9.0 * (y * z)))) + (b * (a * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.32e+39], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.32e39

   1. Initial program 94.1%

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

      1. sub-neg 94.1%

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

      2. sub-neg 94.1%

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

      3. associate-*l* 86.7%

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

      4. associate-*l* 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in x around 0 72.9%

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

      1. associate-*r* 72.9%

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

      2. *-commutative 72.9%

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

      3. *-commutative 72.9%

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

      4. associate-*l* 73.0%

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

      5. sub-neg 73.0%

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

      6. +-commutative 73.0%

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

      7. associate-*l* 72.9%

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

      8. *-commutative 72.9%

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

      9. distribute-lft-neg-in 72.9%

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

      10. associate-*r* 74.6%

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

      11. associate-*r* 74.6%

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

      12. metadata-eval 74.6%

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

      13. *-commutative 74.6%

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

      14. associate-*l* 74.6%

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

   6. Applied egg-rr 74.6%

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

   if -1.32e39 < z

   1. Initial program 98.4%

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

   2. Taylor expanded in y around 0 98.4%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 2: 96.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Simplified 95.8%

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

4. Final simplification 95.8%

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

Alternative 3: 81.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ t_2 := a \cdot \left(27 \cdot b\right) + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-43}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 (- (* x 2.0) (* 9.0 (* t (* y z)))))
        (t_2 (+ (* a (* 27.0 b)) (* z (* -9.0 (* y t))))))
   (if (<= z -1.75e+36)
     t_2
     (if (<= z -7.5e-20)
       t_1
       (if (<= z -2.8e-45)
         t_2
         (if (<= z 1.55e-43) (+ (* x 2.0) (* 27.0 (* a b))) t_1))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (9.0 * (t * (y * z)));
	double t_2 = (a * (27.0 * b)) + (z * (-9.0 * (y * t)));
	double tmp;
	if (z <= -1.75e+36) {
		tmp = t_2;
	} else if (z <= -7.5e-20) {
		tmp = t_1;
	} else if (z <= -2.8e-45) {
		tmp = t_2;
	} else if (z <= 1.55e-43) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    t_2 = (a * (27.0d0 * b)) + (z * ((-9.0d0) * (y * t)))
    if (z <= (-1.75d+36)) then
        tmp = t_2
    else if (z <= (-7.5d-20)) then
        tmp = t_1
    else if (z <= (-2.8d-45)) then
        tmp = t_2
    else if (z <= 1.55d-43) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (9.0 * (t * (y * z)));
	double t_2 = (a * (27.0 * b)) + (z * (-9.0 * (y * t)));
	double tmp;
	if (z <= -1.75e+36) {
		tmp = t_2;
	} else if (z <= -7.5e-20) {
		tmp = t_1;
	} else if (z <= -2.8e-45) {
		tmp = t_2;
	} else if (z <= 1.55e-43) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (9.0 * (t * (y * z)))
	t_2 = (a * (27.0 * b)) + (z * (-9.0 * (y * t)))
	tmp = 0
	if z <= -1.75e+36:
		tmp = t_2
	elif z <= -7.5e-20:
		tmp = t_1
	elif z <= -2.8e-45:
		tmp = t_2
	elif z <= 1.55e-43:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))))
	t_2 = Float64(Float64(a * Float64(27.0 * b)) + Float64(z * Float64(-9.0 * Float64(y * t))))
	tmp = 0.0
	if (z <= -1.75e+36)
		tmp = t_2;
	elseif (z <= -7.5e-20)
		tmp = t_1;
	elseif (z <= -2.8e-45)
		tmp = t_2;
	elseif (z <= 1.55e-43)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (9.0 * (t * (y * z)));
	t_2 = (a * (27.0 * b)) + (z * (-9.0 * (y * t)));
	tmp = 0.0;
	if (z <= -1.75e+36)
		tmp = t_2;
	elseif (z <= -7.5e-20)
		tmp = t_1;
	elseif (z <= -2.8e-45)
		tmp = t_2;
	elseif (z <= 1.55e-43)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+36], t$95$2, If[LessEqual[z, -7.5e-20], t$95$1, If[LessEqual[z, -2.8e-45], t$95$2, If[LessEqual[z, 1.55e-43], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7499999999999999e36 or -7.49999999999999981e-20 < z < -2.8000000000000001e-45

   1. Initial program 94.7%

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

      1. sub-neg 94.7%

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

      2. sub-neg 94.7%

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

      3. associate-*l* 88.1%

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

      4. associate-*l* 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in x around 0 70.5%

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

      1. associate-*r* 70.6%

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

      2. *-commutative 70.6%

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

      3. *-commutative 70.6%

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

      4. associate-*l* 70.6%

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

      5. sub-neg 70.6%

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

      6. +-commutative 70.6%

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

      7. associate-*l* 70.6%

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

      8. *-commutative 70.6%

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

      9. distribute-lft-neg-in 70.6%

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

      10. associate-*r* 72.0%

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

      11. associate-*r* 72.1%

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

      12. metadata-eval 72.1%

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

      13. *-commutative 72.1%

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

      14. associate-*l* 72.0%

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

   6. Applied egg-rr 72.0%

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

   if -1.7499999999999999e36 < z < -7.49999999999999981e-20 or 1.55e-43 < z

   1. Initial program 96.6%

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

      1. sub-neg 96.6%

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

      2. sub-neg 96.6%

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

      3. associate-*l* 94.3%

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

      4. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in a around 0 75.1%

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

   if -2.8000000000000001e-45 < z < 1.55e-43

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 84.4%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-20}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-45}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-43}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 4: 81.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ t_3 := x \cdot 2 - t_2\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-91}:\\ \;\;\;\;t_1 - t_2\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-44}:\\ \;\;\;\;x \cdot 2 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b)))
        (t_2 (* 9.0 (* t (* y z))))
        (t_3 (- (* x 2.0) t_2)))
   (if (<= z -2.4e+39)
     (+ (* a (* 27.0 b)) (* z (* -9.0 (* y t))))
     (if (<= z -8.6e-50)
       t_3
       (if (<= z -5.8e-91)
         (- t_1 t_2)
         (if (<= z 6.5e-44) (+ (* x 2.0) t_1) t_3))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = 9.0 * (t * (y * z));
	double t_3 = (x * 2.0) - t_2;
	double tmp;
	if (z <= -2.4e+39) {
		tmp = (a * (27.0 * b)) + (z * (-9.0 * (y * t)));
	} else if (z <= -8.6e-50) {
		tmp = t_3;
	} else if (z <= -5.8e-91) {
		tmp = t_1 - t_2;
	} else if (z <= 6.5e-44) {
		tmp = (x * 2.0) + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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) :: t_3
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = 9.0d0 * (t * (y * z))
    t_3 = (x * 2.0d0) - t_2
    if (z <= (-2.4d+39)) then
        tmp = (a * (27.0d0 * b)) + (z * ((-9.0d0) * (y * t)))
    else if (z <= (-8.6d-50)) then
        tmp = t_3
    else if (z <= (-5.8d-91)) then
        tmp = t_1 - t_2
    else if (z <= 6.5d-44) then
        tmp = (x * 2.0d0) + t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = 9.0 * (t * (y * z));
	double t_3 = (x * 2.0) - t_2;
	double tmp;
	if (z <= -2.4e+39) {
		tmp = (a * (27.0 * b)) + (z * (-9.0 * (y * t)));
	} else if (z <= -8.6e-50) {
		tmp = t_3;
	} else if (z <= -5.8e-91) {
		tmp = t_1 - t_2;
	} else if (z <= 6.5e-44) {
		tmp = (x * 2.0) + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = 9.0 * (t * (y * z))
	t_3 = (x * 2.0) - t_2
	tmp = 0
	if z <= -2.4e+39:
		tmp = (a * (27.0 * b)) + (z * (-9.0 * (y * t)))
	elif z <= -8.6e-50:
		tmp = t_3
	elif z <= -5.8e-91:
		tmp = t_1 - t_2
	elif z <= 6.5e-44:
		tmp = (x * 2.0) + t_1
	else:
		tmp = t_3
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(9.0 * Float64(t * Float64(y * z)))
	t_3 = Float64(Float64(x * 2.0) - t_2)
	tmp = 0.0
	if (z <= -2.4e+39)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(z * Float64(-9.0 * Float64(y * t))));
	elseif (z <= -8.6e-50)
		tmp = t_3;
	elseif (z <= -5.8e-91)
		tmp = Float64(t_1 - t_2);
	elseif (z <= 6.5e-44)
		tmp = Float64(Float64(x * 2.0) + t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = 9.0 * (t * (y * z));
	t_3 = (x * 2.0) - t_2;
	tmp = 0.0;
	if (z <= -2.4e+39)
		tmp = (a * (27.0 * b)) + (z * (-9.0 * (y * t)));
	elseif (z <= -8.6e-50)
		tmp = t_3;
	elseif (z <= -5.8e-91)
		tmp = t_1 - t_2;
	elseif (z <= 6.5e-44)
		tmp = (x * 2.0) + t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 2.0), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[z, -2.4e+39], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.6e-50], t$95$3, If[LessEqual[z, -5.8e-91], N[(t$95$1 - t$95$2), $MachinePrecision], If[LessEqual[z, 6.5e-44], N[(N[(x * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4000000000000001e39

   1. Initial program 94.1%

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

      1. sub-neg 94.1%

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

      2. sub-neg 94.1%

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

      3. associate-*l* 86.7%

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

      4. associate-*l* 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in x around 0 72.9%

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

      1. associate-*r* 72.9%

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

      2. *-commutative 72.9%

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

      3. *-commutative 72.9%

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

      4. associate-*l* 73.0%

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

      5. sub-neg 73.0%

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

      6. +-commutative 73.0%

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

      7. associate-*l* 72.9%

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

      8. *-commutative 72.9%

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

      9. distribute-lft-neg-in 72.9%

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

      10. associate-*r* 74.6%

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

      11. associate-*r* 74.6%

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

      12. metadata-eval 74.6%

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

      13. *-commutative 74.6%

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

      14. associate-*l* 74.6%

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

   6. Applied egg-rr 74.6%

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

   if -2.4000000000000001e39 < z < -8.59999999999999995e-50 or 6.5e-44 < z

   1. Initial program 96.8%

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

      1. sub-neg 96.8%

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

      2. sub-neg 96.8%

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

      3. associate-*l* 94.7%

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

      4. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in a around 0 75.9%

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

   if -8.59999999999999995e-50 < z < -5.8000000000000001e-91

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 74.2%

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

   if -5.8000000000000001e-91 < z < 6.5e-44

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 83.2%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-50}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-91}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-44}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 5: 95.6% accurate, 1.0× speedup

Math

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

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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) (* (* y 9.0) (* t z))) (* a (* 27.0 b))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. sub-neg 97.6%

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

   2. sub-neg 97.6%

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

   3. associate-*l* 95.4%

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

   4. associate-*l* 95.4%

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

3. Simplified 95.4%

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

4. Final simplification 95.4%

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

Alternative 6: 46.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+99}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.65 \cdot 10^{-225}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 (<= x -2.6e+99)
     (* x 2.0)
     (if (<= x -1.25e-23)
       (* z (* -9.0 (* y t)))
       (if (<= x -3.1e-44)
         t_1
         (if (<= x 3.65e-225)
           (* (* y z) (* t -9.0))
           (if (<= x 3.8e+105) t_1 (* x 2.0))))))))

C

assert(y < z && z < t);
assert(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 (x <= -2.6e+99) {
		tmp = x * 2.0;
	} else if (x <= -1.25e-23) {
		tmp = z * (-9.0 * (y * t));
	} else if (x <= -3.1e-44) {
		tmp = t_1;
	} else if (x <= 3.65e-225) {
		tmp = (y * z) * (t * -9.0);
	} else if (x <= 3.8e+105) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 (x <= (-2.6d+99)) then
        tmp = x * 2.0d0
    else if (x <= (-1.25d-23)) then
        tmp = z * ((-9.0d0) * (y * t))
    else if (x <= (-3.1d-44)) then
        tmp = t_1
    else if (x <= 3.65d-225) then
        tmp = (y * z) * (t * (-9.0d0))
    else if (x <= 3.8d+105) then
        tmp = t_1
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert 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 (x <= -2.6e+99) {
		tmp = x * 2.0;
	} else if (x <= -1.25e-23) {
		tmp = z * (-9.0 * (y * t));
	} else if (x <= -3.1e-44) {
		tmp = t_1;
	} else if (x <= 3.65e-225) {
		tmp = (y * z) * (t * -9.0);
	} else if (x <= 3.8e+105) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if x <= -2.6e+99:
		tmp = x * 2.0
	elif x <= -1.25e-23:
		tmp = z * (-9.0 * (y * t))
	elif x <= -3.1e-44:
		tmp = t_1
	elif x <= 3.65e-225:
		tmp = (y * z) * (t * -9.0)
	elif x <= 3.8e+105:
		tmp = t_1
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (x <= -2.6e+99)
		tmp = Float64(x * 2.0);
	elseif (x <= -1.25e-23)
		tmp = Float64(z * Float64(-9.0 * Float64(y * t)));
	elseif (x <= -3.1e-44)
		tmp = t_1;
	elseif (x <= 3.65e-225)
		tmp = Float64(Float64(y * z) * Float64(t * -9.0));
	elseif (x <= 3.8e+105)
		tmp = t_1;
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (x <= -2.6e+99)
		tmp = x * 2.0;
	elseif (x <= -1.25e-23)
		tmp = z * (-9.0 * (y * t));
	elseif (x <= -3.1e-44)
		tmp = t_1;
	elseif (x <= 3.65e-225)
		tmp = (y * z) * (t * -9.0);
	elseif (x <= 3.8e+105)
		tmp = t_1;
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+99], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -1.25e-23], N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.1e-44], t$95$1, If[LessEqual[x, 3.65e-225], N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+105], t$95$1, N[(x * 2.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.6e99 or 3.8e105 < x

   1. Initial program 99.0%

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

      1. sub-neg 99.0%

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

      2. sub-neg 99.0%

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

      3. associate-*l* 99.0%

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

      4. associate-*l* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around inf 72.8%

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

   if -2.6e99 < x < -1.2500000000000001e-23

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 99.7%

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

   3. Taylor expanded in y around inf 44.2%

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

      1. *-commutative 44.2%

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

      2. associate-*r* 44.2%

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

      3. *-commutative 44.2%

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

      4. associate-*l* 44.3%

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

      5. *-commutative 44.3%

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

   5. Simplified 44.3%

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

   6. Taylor expanded in t around 0 44.2%

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

      1. *-commutative 44.2%

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

      2. associate-*r* 44.2%

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

      3. associate-*r* 44.3%

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

      4. *-commutative 44.3%

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

      5. associate-*r* 44.2%

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

   8. Simplified 44.2%

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

   if -1.2500000000000001e-23 < x < -3.09999999999999984e-44 or 3.64999999999999998e-225 < x < 3.8e105

   1. Initial program 95.9%

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

      1. sub-neg 95.9%

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

      2. sub-neg 95.9%

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

      3. associate-*l* 94.6%

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

      4. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in a around inf 49.7%

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

      1. associate-*r* 49.7%

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

      2. *-commutative 49.7%

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

      3. associate-*r* 49.8%

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

   6. Simplified 49.8%

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

   if -3.09999999999999984e-44 < x < 3.64999999999999998e-225

   1. Initial program 96.7%

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

   2. Taylor expanded in y around 0 96.7%

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

   3. Taylor expanded in y around inf 53.8%

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

      1. *-commutative 53.8%

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

      2. associate-*r* 46.8%

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

      3. *-commutative 46.8%

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

      4. associate-*l* 46.8%

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

      5. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in t around 0 53.8%

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

      1. *-commutative 53.8%

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

      2. associate-*r* 46.8%

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

      3. associate-*r* 46.8%

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

      4. *-commutative 46.8%

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

      5. associate-*r* 46.8%

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

   8. Simplified 46.8%

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

   9. Taylor expanded in z around 0 53.8%

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

       1. associate-*r* 53.8%

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

   11. Simplified 53.8%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+99}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 3.65 \cdot 10^{-225}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 7: 46.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+99}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-28}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-9 \cdot z\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-227}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 (<= x -3.5e+99)
     (* x 2.0)
     (if (<= x -4.4e-28)
       (* (* y t) (* -9.0 z))
       (if (<= x -7e-45)
         t_1
         (if (<= x 1.65e-227)
           (* (* y z) (* t -9.0))
           (if (<= x 7e+101) t_1 (* x 2.0))))))))

C

assert(y < z && z < t);
assert(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 (x <= -3.5e+99) {
		tmp = x * 2.0;
	} else if (x <= -4.4e-28) {
		tmp = (y * t) * (-9.0 * z);
	} else if (x <= -7e-45) {
		tmp = t_1;
	} else if (x <= 1.65e-227) {
		tmp = (y * z) * (t * -9.0);
	} else if (x <= 7e+101) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 (x <= (-3.5d+99)) then
        tmp = x * 2.0d0
    else if (x <= (-4.4d-28)) then
        tmp = (y * t) * ((-9.0d0) * z)
    else if (x <= (-7d-45)) then
        tmp = t_1
    else if (x <= 1.65d-227) then
        tmp = (y * z) * (t * (-9.0d0))
    else if (x <= 7d+101) then
        tmp = t_1
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert 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 (x <= -3.5e+99) {
		tmp = x * 2.0;
	} else if (x <= -4.4e-28) {
		tmp = (y * t) * (-9.0 * z);
	} else if (x <= -7e-45) {
		tmp = t_1;
	} else if (x <= 1.65e-227) {
		tmp = (y * z) * (t * -9.0);
	} else if (x <= 7e+101) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if x <= -3.5e+99:
		tmp = x * 2.0
	elif x <= -4.4e-28:
		tmp = (y * t) * (-9.0 * z)
	elif x <= -7e-45:
		tmp = t_1
	elif x <= 1.65e-227:
		tmp = (y * z) * (t * -9.0)
	elif x <= 7e+101:
		tmp = t_1
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (x <= -3.5e+99)
		tmp = Float64(x * 2.0);
	elseif (x <= -4.4e-28)
		tmp = Float64(Float64(y * t) * Float64(-9.0 * z));
	elseif (x <= -7e-45)
		tmp = t_1;
	elseif (x <= 1.65e-227)
		tmp = Float64(Float64(y * z) * Float64(t * -9.0));
	elseif (x <= 7e+101)
		tmp = t_1;
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (x <= -3.5e+99)
		tmp = x * 2.0;
	elseif (x <= -4.4e-28)
		tmp = (y * t) * (-9.0 * z);
	elseif (x <= -7e-45)
		tmp = t_1;
	elseif (x <= 1.65e-227)
		tmp = (y * z) * (t * -9.0);
	elseif (x <= 7e+101)
		tmp = t_1;
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.5e+99], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -4.4e-28], N[(N[(y * t), $MachinePrecision] * N[(-9.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7e-45], t$95$1, If[LessEqual[x, 1.65e-227], N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e+101], t$95$1, N[(x * 2.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.4999999999999998e99 or 7.00000000000000046e101 < x

   1. Initial program 99.0%

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

      1. sub-neg 99.0%

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

      2. sub-neg 99.0%

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

      3. associate-*l* 99.0%

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

      4. associate-*l* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around inf 72.8%

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

   if -3.4999999999999998e99 < x < -4.39999999999999992e-28

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 99.7%

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

   3. Taylor expanded in y around inf 44.2%

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

      1. *-commutative 44.2%

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

      2. associate-*r* 44.2%

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

      3. *-commutative 44.2%

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

      4. associate-*l* 44.3%

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

      5. *-commutative 44.3%

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

   5. Simplified 44.3%

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

   if -4.39999999999999992e-28 < x < -7e-45 or 1.65e-227 < x < 7.00000000000000046e101

   1. Initial program 95.9%

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

      1. sub-neg 95.9%

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

      2. sub-neg 95.9%

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

      3. associate-*l* 94.6%

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

      4. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in a around inf 49.7%

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

      1. associate-*r* 49.7%

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

      2. *-commutative 49.7%

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

      3. associate-*r* 49.8%

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

   6. Simplified 49.8%

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

   if -7e-45 < x < 1.65e-227

   1. Initial program 96.7%

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

   2. Taylor expanded in y around 0 96.7%

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

   3. Taylor expanded in y around inf 53.8%

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

      1. *-commutative 53.8%

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

      2. associate-*r* 46.8%

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

      3. *-commutative 46.8%

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

      4. associate-*l* 46.8%

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

      5. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in t around 0 53.8%

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

      1. *-commutative 53.8%

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

      2. associate-*r* 46.8%

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

      3. associate-*r* 46.8%

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

      4. *-commutative 46.8%

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

      5. associate-*r* 46.8%

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

   8. Simplified 46.8%

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

   9. Taylor expanded in z around 0 53.8%

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

       1. associate-*r* 53.8%

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

   11. Simplified 53.8%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+99}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-28}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-9 \cdot z\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-45}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-227}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+101}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 8: 77.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.35 \cdot 10^{+82} \lor \neg \left(a \leq 0.0082\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.35e+82) (not (<= a 0.0082)))
   (+ (* x 2.0) (* 27.0 (* a b)))
   (- (* x 2.0) (* 9.0 (* t (* y z))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.35e+82) || !(a <= 0.0082)) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.35d+82)) .or. (.not. (a <= 0.0082d0))) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.35e+82) || !(a <= 0.0082)) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.35e+82) or not (a <= 0.0082):
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.35e+82) || !(a <= 0.0082))
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.35e+82) || ~((a <= 0.0082)))
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.35e+82], N[Not[LessEqual[a, 0.0082]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.35e82 or 0.00820000000000000069 < a

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. sub-neg 96.9%

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

      3. associate-*l* 94.0%

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

      4. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around 0 78.8%

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

   if -2.35e82 < a < 0.00820000000000000069

   1. Initial program 98.0%

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

      1. sub-neg 98.0%

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

      2. sub-neg 98.0%

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

      3. associate-*l* 96.2%

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

      4. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in a around 0 85.0%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.35 \cdot 10^{+82} \lor \neg \left(a \leq 0.0082\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 9: 47.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+126}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-226}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 (<= x -2.1e+126)
     (* x 2.0)
     (if (<= x -2.3e-257)
       t_1
       (if (<= x 2.7e-226)
         (* -9.0 (* t (* y z)))
         (if (<= x 1.75e+103) t_1 (* x 2.0)))))))

C

assert(y < z && z < t);
assert(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 (x <= -2.1e+126) {
		tmp = x * 2.0;
	} else if (x <= -2.3e-257) {
		tmp = t_1;
	} else if (x <= 2.7e-226) {
		tmp = -9.0 * (t * (y * z));
	} else if (x <= 1.75e+103) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 (x <= (-2.1d+126)) then
        tmp = x * 2.0d0
    else if (x <= (-2.3d-257)) then
        tmp = t_1
    else if (x <= 2.7d-226) then
        tmp = (-9.0d0) * (t * (y * z))
    else if (x <= 1.75d+103) then
        tmp = t_1
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert 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 (x <= -2.1e+126) {
		tmp = x * 2.0;
	} else if (x <= -2.3e-257) {
		tmp = t_1;
	} else if (x <= 2.7e-226) {
		tmp = -9.0 * (t * (y * z));
	} else if (x <= 1.75e+103) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if x <= -2.1e+126:
		tmp = x * 2.0
	elif x <= -2.3e-257:
		tmp = t_1
	elif x <= 2.7e-226:
		tmp = -9.0 * (t * (y * z))
	elif x <= 1.75e+103:
		tmp = t_1
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (x <= -2.1e+126)
		tmp = Float64(x * 2.0);
	elseif (x <= -2.3e-257)
		tmp = t_1;
	elseif (x <= 2.7e-226)
		tmp = Float64(-9.0 * Float64(t * Float64(y * z)));
	elseif (x <= 1.75e+103)
		tmp = t_1;
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (x <= -2.1e+126)
		tmp = x * 2.0;
	elseif (x <= -2.3e-257)
		tmp = t_1;
	elseif (x <= 2.7e-226)
		tmp = -9.0 * (t * (y * z));
	elseif (x <= 1.75e+103)
		tmp = t_1;
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+126], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -2.3e-257], t$95$1, If[LessEqual[x, 2.7e-226], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75e+103], t$95$1, N[(x * 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.0999999999999999e126 or 1.75e103 < x

   1. Initial program 98.9%

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

      1. sub-neg 98.9%

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

      2. sub-neg 98.9%

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

      3. associate-*l* 98.9%

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

      4. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in x around inf 75.3%

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

   if -2.0999999999999999e126 < x < -2.3e-257 or 2.70000000000000014e-226 < x < 1.75e103

   1. Initial program 96.3%

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

      1. sub-neg 96.3%

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

      2. sub-neg 96.3%

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

      3. associate-*l* 93.0%

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

      4. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in a around inf 47.3%

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

      1. associate-*r* 47.3%

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

      2. *-commutative 47.3%

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

      3. associate-*r* 47.4%

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

   6. Simplified 47.4%

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

   if -2.3e-257 < x < 2.70000000000000014e-226

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. associate-*l* 96.0%

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

      4. associate-*l* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in y around inf 68.6%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+126}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-226}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+103}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 10: 70.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+185}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-131}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-9 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.4e+185)
   (* -9.0 (* t (* y z)))
   (if (<= y 2.1e-131) (+ (* x 2.0) (* 27.0 (* a b))) (* (* y t) (* -9.0 z)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.4e+185) {
		tmp = -9.0 * (t * (y * z));
	} else if (y <= 2.1e-131) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (y * t) * (-9.0 * z);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 <= (-3.4d+185)) then
        tmp = (-9.0d0) * (t * (y * z))
    else if (y <= 2.1d-131) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (y * t) * ((-9.0d0) * z)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.4e+185) {
		tmp = -9.0 * (t * (y * z));
	} else if (y <= 2.1e-131) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (y * t) * (-9.0 * z);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.4e+185:
		tmp = -9.0 * (t * (y * z))
	elif y <= 2.1e-131:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (y * t) * (-9.0 * z)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.4e+185)
		tmp = Float64(-9.0 * Float64(t * Float64(y * z)));
	elseif (y <= 2.1e-131)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(y * t) * Float64(-9.0 * z));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.4e+185)
		tmp = -9.0 * (t * (y * z));
	elseif (y <= 2.1e-131)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (y * t) * (-9.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.4e+185], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-131], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * t), $MachinePrecision] * N[(-9.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.40000000000000017e185

   1. Initial program 79.7%

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

      1. sub-neg 79.7%

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

      2. sub-neg 79.7%

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

      3. associate-*l* 94.4%

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

      4. associate-*l* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around inf 54.0%

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

   if -3.40000000000000017e185 < y < 2.09999999999999997e-131

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 94.8%

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

      4. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in y around 0 81.4%

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

   if 2.09999999999999997e-131 < y

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 97.6%

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

   3. Taylor expanded in y around inf 48.9%

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

      1. *-commutative 48.9%

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

      2. associate-*r* 43.5%

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

      3. *-commutative 43.5%

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

      4. associate-*l* 43.5%

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

      5. *-commutative 43.5%

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

   5. Simplified 43.5%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+185}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-131}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-9 \cdot z\right)\\ \end{array} \]

Alternative 11: 47.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+128} \lor \neg \left(x \leq 5.5 \cdot 10^{+102}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -5.2e+128) (not (<= x 5.5e+102))) (* x 2.0) (* 27.0 (* a b))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -5.2e+128) || !(x <= 5.5e+102)) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 ((x <= (-5.2d+128)) .or. (.not. (x <= 5.5d+102))) then
        tmp = x * 2.0d0
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -5.2e+128) || !(x <= 5.5e+102)) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -5.2e+128) or not (x <= 5.5e+102):
		tmp = x * 2.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -5.2e+128) || !(x <= 5.5e+102))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -5.2e+128) || ~((x <= 5.5e+102)))
		tmp = x * 2.0;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -5.2e+128], N[Not[LessEqual[x, 5.5e+102]], $MachinePrecision]], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.2e128 or 5.49999999999999981e102 < x

   1. Initial program 98.9%

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

      1. sub-neg 98.9%

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

      2. sub-neg 98.9%

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

      3. associate-*l* 98.9%

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

      4. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in x around inf 75.3%

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

   if -5.2e128 < x < 5.49999999999999981e102

   1. Initial program 96.8%

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

      1. sub-neg 96.8%

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

      2. sub-neg 96.8%

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

      3. associate-*l* 93.5%

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

      4. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in a around inf 45.1%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+128} \lor \neg \left(x \leq 5.5 \cdot 10^{+102}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 12: 47.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+127} \lor \neg \left(x \leq 9 \cdot 10^{+108}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -3.3e+127) (not (<= x 9e+108))) (* x 2.0) (* a (* 27.0 b))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -3.3e+127) || !(x <= 9e+108)) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 ((x <= (-3.3d+127)) .or. (.not. (x <= 9d+108))) then
        tmp = x * 2.0d0
    else
        tmp = a * (27.0d0 * b)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -3.3e+127) || !(x <= 9e+108)) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -3.3e+127) or not (x <= 9e+108):
		tmp = x * 2.0
	else:
		tmp = a * (27.0 * b)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -3.3e+127) || !(x <= 9e+108))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(a * Float64(27.0 * b));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -3.3e+127) || ~((x <= 9e+108)))
		tmp = x * 2.0;
	else
		tmp = a * (27.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -3.3e+127], N[Not[LessEqual[x, 9e+108]], $MachinePrecision]], N[(x * 2.0), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.29999999999999977e127 or 9e108 < x

   1. Initial program 98.9%

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

      1. sub-neg 98.9%

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

      2. sub-neg 98.9%

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

      3. associate-*l* 98.9%

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

      4. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in x around inf 75.3%

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

   if -3.29999999999999977e127 < x < 9e108

   1. Initial program 96.8%

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

      1. sub-neg 96.8%

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

      2. sub-neg 96.8%

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

      3. associate-*l* 93.5%

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

      4. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in a around inf 45.1%

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

      1. associate-*r* 45.1%

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

      2. *-commutative 45.1%

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

      3. associate-*r* 45.1%

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

   6. Simplified 45.1%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+127} \lor \neg \left(x \leq 9 \cdot 10^{+108}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]

Alternative 13: 30.3% accurate, 5.7× speedup

Math

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

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. sub-neg 97.6%

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

   2. sub-neg 97.6%

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

   3. associate-*l* 95.4%

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

   4. associate-*l* 95.4%

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

3. Simplified 95.4%

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

4. Taylor expanded in x around inf 36.4%

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

5. Final simplification 36.4%

   \[\leadsto x \cdot 2 \]

Developer target: 95.1% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023320 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

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

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