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

Percentage Accurate: 95.4% → 98.9%

Time: 13.3s

Alternatives: 16

Speedup: 0.9×

• 26.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(z \cdot y\right) \cdot \left(9 \cdot t\right)\right)\\ \end{array} \end{array} \]

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 (<= z 4e-31)
   (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t)))))
   (fma a (* 27.0 b) (- (* x 2.0) (* (* z y) (* 9.0 t))))))

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 <= 4e-31) {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	} else {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - ((z * y) * (9.0 * t))));
	}
	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 <= 4e-31)
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	else
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(Float64(z * y) * Float64(9.0 * t))));
	end
	return 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, 4e-31], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4e-31

   1. Initial program 95.8%

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

      1. +-commutative 95.8%

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

      2. associate-*l* 95.2%

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

      3. fma-def 95.8%

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

      4. associate-*l* 95.9%

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

      5. *-commutative 95.9%

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

      6. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

   if 4e-31 < z

   1. Initial program 89.9%

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

      1. +-commutative 89.9%

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

      2. associate-*l* 89.9%

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

      3. fma-def 91.4%

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

      4. associate-*l* 95.7%

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

      5. *-commutative 95.7%

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

      6. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around 0 95.6%

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

      1. *-commutative 95.6%

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

      2. *-commutative 95.6%

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

      3. *-commutative 95.6%

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

      4. associate-*r* 91.4%

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

      5. associate-*r* 91.4%

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

      6. *-commutative 91.4%

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

      7. associate-*l* 91.5%

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

   6. Simplified 91.5%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(z \cdot y\right) \cdot \left(9 \cdot t\right)\right)\\ \end{array} \]

Alternative 2: 98.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 8.8 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

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 8.8e+58)
   (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t)))))
   (+ (- (* x 2.0) (* t (* z (* 9.0 y)))) (* 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 <= 8.8e+58) {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	} else {
		tmp = ((x * 2.0) - (t * (z * (9.0 * y)))) + (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 <= 8.8e+58)
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(9.0 * y)))) + Float64(b * Float64(a * 27.0)));
	end
	return 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, 8.8e+58], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.8000000000000003e58

   1. Initial program 96.1%

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

      1. +-commutative 96.1%

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

      2. associate-*l* 95.6%

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

      3. fma-def 96.1%

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

      4. associate-*l* 96.3%

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

      5. *-commutative 96.3%

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

      6. associate-*l* 96.8%

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

   3. Simplified 96.8%

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

   if 8.8000000000000003e58 < z

   1. Initial program 86.0%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8.8 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 3: 97.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(9 \cdot y\right)\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+261}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot t_1\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* z (* 9.0 y))))
   (if (<= t_1 2e+261)
     (+ (- (* x 2.0) (* t t_1)) (* b (* a 27.0)))
     (- (* 27.0 (* a b)) (* 9.0 (* y (* z t)))))))

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 = z * (9.0 * y);
	double tmp;
	if (t_1 <= 2e+261) {
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	} else {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	}
	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 = z * (9.0d0 * y)
    if (t_1 <= 2d+261) then
        tmp = ((x * 2.0d0) - (t * t_1)) + (b * (a * 27.0d0))
    else
        tmp = (27.0d0 * (a * b)) - (9.0d0 * (y * (z * t)))
    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 = z * (9.0 * y);
	double tmp;
	if (t_1 <= 2e+261) {
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	} else {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	}
	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 = z * (9.0 * y)
	tmp = 0
	if t_1 <= 2e+261:
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0))
	else:
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)))
	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(z * Float64(9.0 * y))
	tmp = 0.0
	if (t_1 <= 2e+261)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * t_1)) + Float64(b * Float64(a * 27.0)));
	else
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * Float64(y * Float64(z * t))));
	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 = z * (9.0 * y);
	tmp = 0.0;
	if (t_1 <= 2e+261)
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	else
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	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[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+261], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 1.9999999999999999e261

   1. Initial program 96.6%

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

   if 1.9999999999999999e261 < (*.f64 (*.f64 y 9) z)

   1. Initial program 72.9%

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

      1. +-commutative 72.9%

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

      2. associate-*l* 72.9%

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

      3. fma-def 80.9%

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

      4. associate-*l* 96.2%

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

      5. *-commutative 96.2%

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

      6. associate-*l* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in x around 0 91.2%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(9 \cdot y\right) \leq 2 \cdot 10^{+261}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 4: 79.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -5 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{elif}\;x \cdot 2 \leq 9.8 \cdot 10^{-36}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

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 (<= (* x 2.0) -5e+24)
   (- (* x 2.0) (* a (* b -27.0)))
   (if (<= (* x 2.0) 9.8e-36)
     (- (* 27.0 (* a b)) (* 9.0 (* y (* z t))))
     (+ (* x 2.0) (* 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 ((x * 2.0) <= -5e+24) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else if ((x * 2.0) <= 9.8e-36) {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	} else {
		tmp = (x * 2.0) + (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 ((x * 2.0d0) <= (-5d+24)) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else if ((x * 2.0d0) <= 9.8d-36) then
        tmp = (27.0d0 * (a * b)) - (9.0d0 * (y * (z * t)))
    else
        tmp = (x * 2.0d0) + (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 ((x * 2.0) <= -5e+24) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else if ((x * 2.0) <= 9.8e-36) {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	} else {
		tmp = (x * 2.0) + (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 (x * 2.0) <= -5e+24:
		tmp = (x * 2.0) - (a * (b * -27.0))
	elif (x * 2.0) <= 9.8e-36:
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)))
	else:
		tmp = (x * 2.0) + (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 (Float64(x * 2.0) <= -5e+24)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	elseif (Float64(x * 2.0) <= 9.8e-36)
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * Float64(y * Float64(z * t))));
	else
		tmp = Float64(Float64(x * 2.0) + 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 ((x * 2.0) <= -5e+24)
		tmp = (x * 2.0) - (a * (b * -27.0));
	elseif ((x * 2.0) <= 9.8e-36)
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	else
		tmp = (x * 2.0) + (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[N[(x * 2.0), $MachinePrecision], -5e+24], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * 2.0), $MachinePrecision], 9.8e-36], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x 2) < -5.00000000000000045e24

   1. Initial program 91.8%

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

      1. associate-+l- 91.8%

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

      2. sub-neg 91.8%

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

      3. neg-mul-1 91.8%

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

      4. metadata-eval 91.8%

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

      5. metadata-eval 91.8%

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

      6. cancel-sign-sub-inv 91.8%

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

      7. metadata-eval 91.8%

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

      8. *-lft-identity 91.8%

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

      9. associate-*l* 96.6%

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

      10. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in y around 0 83.6%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 83.6%

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

      2. associate-*l* 80.3%

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

   6. Simplified 80.3%

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

   if -5.00000000000000045e24 < (*.f64 x 2) < 9.7999999999999994e-36

   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. +-commutative 94.7%

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

      2. associate-*l* 94.6%

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

      3. fma-def 95.4%

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

      4. associate-*l* 95.0%

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

      5. *-commutative 95.0%

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

      6. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in x around 0 84.1%

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

   if 9.7999999999999994e-36 < (*.f64 x 2)

   1. Initial program 95.6%

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

      1. +-commutative 95.6%

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

      2. associate-*l* 95.6%

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

      3. fma-def 95.6%

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

      4. associate-*l* 98.5%

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

      5. *-commutative 98.5%

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

      6. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 85.7%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 85.7%

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

      2. *-commutative 85.7%

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

      3. fma-def 85.7%

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

      4. *-commutative 85.7%

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

   6. Simplified 85.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]
   7. Step-by-step derivation

      1. fma-udef 85.7%

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

      2. associate-*r* 85.7%

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

      3. *-commutative 85.7%

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

   8. Applied egg-rr 85.7%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -5 \cdot 10^{+24}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{elif}\;x \cdot 2 \leq 9.8 \cdot 10^{-36}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 5: 46.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := \left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+18}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+105}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* 27.0 (* a b))) (t_2 (* (* y (* z t)) -9.0)))
   (if (<= t -3.3e-49)
     t_2
     (if (<= t 6.6e-193)
       t_1
       (if (<= t 2.6e+18)
         (* x 2.0)
         (if (<= t 1.1e+82)
           t_1
           (if (<= t 5.2e+105) (* x 2.0) (if (<= t 4.5e+121) t_1 t_2))))))))

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 = (y * (z * t)) * -9.0;
	double tmp;
	if (t <= -3.3e-49) {
		tmp = t_2;
	} else if (t <= 6.6e-193) {
		tmp = t_1;
	} else if (t <= 2.6e+18) {
		tmp = x * 2.0;
	} else if (t <= 1.1e+82) {
		tmp = t_1;
	} else if (t <= 5.2e+105) {
		tmp = x * 2.0;
	} else if (t <= 4.5e+121) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = 27.0d0 * (a * b)
    t_2 = (y * (z * t)) * (-9.0d0)
    if (t <= (-3.3d-49)) then
        tmp = t_2
    else if (t <= 6.6d-193) then
        tmp = t_1
    else if (t <= 2.6d+18) then
        tmp = x * 2.0d0
    else if (t <= 1.1d+82) then
        tmp = t_1
    else if (t <= 5.2d+105) then
        tmp = x * 2.0d0
    else if (t <= 4.5d+121) then
        tmp = t_1
    else
        tmp = t_2
    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 = (y * (z * t)) * -9.0;
	double tmp;
	if (t <= -3.3e-49) {
		tmp = t_2;
	} else if (t <= 6.6e-193) {
		tmp = t_1;
	} else if (t <= 2.6e+18) {
		tmp = x * 2.0;
	} else if (t <= 1.1e+82) {
		tmp = t_1;
	} else if (t <= 5.2e+105) {
		tmp = x * 2.0;
	} else if (t <= 4.5e+121) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = (y * (z * t)) * -9.0
	tmp = 0
	if t <= -3.3e-49:
		tmp = t_2
	elif t <= 6.6e-193:
		tmp = t_1
	elif t <= 2.6e+18:
		tmp = x * 2.0
	elif t <= 1.1e+82:
		tmp = t_1
	elif t <= 5.2e+105:
		tmp = x * 2.0
	elif t <= 4.5e+121:
		tmp = t_1
	else:
		tmp = t_2
	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(Float64(y * Float64(z * t)) * -9.0)
	tmp = 0.0
	if (t <= -3.3e-49)
		tmp = t_2;
	elseif (t <= 6.6e-193)
		tmp = t_1;
	elseif (t <= 2.6e+18)
		tmp = Float64(x * 2.0);
	elseif (t <= 1.1e+82)
		tmp = t_1;
	elseif (t <= 5.2e+105)
		tmp = Float64(x * 2.0);
	elseif (t <= 4.5e+121)
		tmp = t_1;
	else
		tmp = t_2;
	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 = (y * (z * t)) * -9.0;
	tmp = 0.0;
	if (t <= -3.3e-49)
		tmp = t_2;
	elseif (t <= 6.6e-193)
		tmp = t_1;
	elseif (t <= 2.6e+18)
		tmp = x * 2.0;
	elseif (t <= 1.1e+82)
		tmp = t_1;
	elseif (t <= 5.2e+105)
		tmp = x * 2.0;
	elseif (t <= 4.5e+121)
		tmp = t_1;
	else
		tmp = t_2;
	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[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision]}, If[LessEqual[t, -3.3e-49], t$95$2, If[LessEqual[t, 6.6e-193], t$95$1, If[LessEqual[t, 2.6e+18], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 1.1e+82], t$95$1, If[LessEqual[t, 5.2e+105], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 4.5e+121], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3e-49 or 4.5000000000000003e121 < t

   1. Initial program 96.1%

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

      1. +-commutative 96.1%

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

      2. associate-*l* 96.1%

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

      3. fma-def 97.9%

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

      4. associate-*l* 93.7%

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

      5. *-commutative 93.7%

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

      6. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around inf 48.1%

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

   if -3.3e-49 < t < 6.5999999999999998e-193 or 2.6e18 < t < 1.1000000000000001e82 or 5.2000000000000004e105 < t < 4.5000000000000003e121

   1. Initial program 91.5%

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

      1. +-commutative 91.5%

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

      2. associate-*l* 90.5%

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

      3. fma-def 90.5%

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

      4. associate-*l* 96.4%

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

      5. *-commutative 96.4%

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

      6. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in a around inf 45.5%

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

   if 6.5999999999999998e-193 < t < 2.6e18 or 1.1000000000000001e82 < t < 5.2000000000000004e105

   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. +-commutative 95.9%

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

      2. associate-*l* 95.9%

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

      3. fma-def 95.9%

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

      4. associate-*l* 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 54.4%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-49}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-193}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+18}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+82}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+105}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+121}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \end{array} \]

Alternative 6: 46.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-53}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+19}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+105}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= t -2.2e-53)
     (* (* y (* z t)) -9.0)
     (if (<= t 2.7e-192)
       t_1
       (if (<= t 1.02e+19)
         (* x 2.0)
         (if (<= t 4.3e+77)
           t_1
           (if (<= t 5.5e+105)
             (* x 2.0)
             (if (<= t 1.2e+121) t_1 (* y (* t (* z -9.0)))))))))))

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 = 27.0 * (a * b);
	double tmp;
	if (t <= -2.2e-53) {
		tmp = (y * (z * t)) * -9.0;
	} else if (t <= 2.7e-192) {
		tmp = t_1;
	} else if (t <= 1.02e+19) {
		tmp = x * 2.0;
	} else if (t <= 4.3e+77) {
		tmp = t_1;
	} else if (t <= 5.5e+105) {
		tmp = x * 2.0;
	} else if (t <= 1.2e+121) {
		tmp = t_1;
	} else {
		tmp = y * (t * (z * -9.0));
	}
	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 = 27.0d0 * (a * b)
    if (t <= (-2.2d-53)) then
        tmp = (y * (z * t)) * (-9.0d0)
    else if (t <= 2.7d-192) then
        tmp = t_1
    else if (t <= 1.02d+19) then
        tmp = x * 2.0d0
    else if (t <= 4.3d+77) then
        tmp = t_1
    else if (t <= 5.5d+105) then
        tmp = x * 2.0d0
    else if (t <= 1.2d+121) then
        tmp = t_1
    else
        tmp = y * (t * (z * (-9.0d0)))
    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 = 27.0 * (a * b);
	double tmp;
	if (t <= -2.2e-53) {
		tmp = (y * (z * t)) * -9.0;
	} else if (t <= 2.7e-192) {
		tmp = t_1;
	} else if (t <= 1.02e+19) {
		tmp = x * 2.0;
	} else if (t <= 4.3e+77) {
		tmp = t_1;
	} else if (t <= 5.5e+105) {
		tmp = x * 2.0;
	} else if (t <= 1.2e+121) {
		tmp = t_1;
	} else {
		tmp = y * (t * (z * -9.0));
	}
	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 = 27.0 * (a * b)
	tmp = 0
	if t <= -2.2e-53:
		tmp = (y * (z * t)) * -9.0
	elif t <= 2.7e-192:
		tmp = t_1
	elif t <= 1.02e+19:
		tmp = x * 2.0
	elif t <= 4.3e+77:
		tmp = t_1
	elif t <= 5.5e+105:
		tmp = x * 2.0
	elif t <= 1.2e+121:
		tmp = t_1
	else:
		tmp = y * (t * (z * -9.0))
	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(27.0 * Float64(a * b))
	tmp = 0.0
	if (t <= -2.2e-53)
		tmp = Float64(Float64(y * Float64(z * t)) * -9.0);
	elseif (t <= 2.7e-192)
		tmp = t_1;
	elseif (t <= 1.02e+19)
		tmp = Float64(x * 2.0);
	elseif (t <= 4.3e+77)
		tmp = t_1;
	elseif (t <= 5.5e+105)
		tmp = Float64(x * 2.0);
	elseif (t <= 1.2e+121)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(t * Float64(z * -9.0)));
	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 = 27.0 * (a * b);
	tmp = 0.0;
	if (t <= -2.2e-53)
		tmp = (y * (z * t)) * -9.0;
	elseif (t <= 2.7e-192)
		tmp = t_1;
	elseif (t <= 1.02e+19)
		tmp = x * 2.0;
	elseif (t <= 4.3e+77)
		tmp = t_1;
	elseif (t <= 5.5e+105)
		tmp = x * 2.0;
	elseif (t <= 1.2e+121)
		tmp = t_1;
	else
		tmp = y * (t * (z * -9.0));
	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[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e-53], N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision], If[LessEqual[t, 2.7e-192], t$95$1, If[LessEqual[t, 1.02e+19], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 4.3e+77], t$95$1, If[LessEqual[t, 5.5e+105], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 1.2e+121], t$95$1, N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.20000000000000018e-53

   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. +-commutative 95.9%

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

      2. associate-*l* 95.8%

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

      3. fma-def 97.2%

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

      4. associate-*l* 96.0%

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

      5. *-commutative 96.0%

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

      6. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in y around inf 42.0%

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

   if -2.20000000000000018e-53 < t < 2.69999999999999991e-192 or 1.02e19 < t < 4.29999999999999991e77 or 5.49999999999999979e105 < t < 1.2e121

   1. Initial program 91.5%

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

      1. +-commutative 91.5%

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

      2. associate-*l* 90.5%

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

      3. fma-def 90.5%

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

      4. associate-*l* 96.4%

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

      5. *-commutative 96.4%

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

      6. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in a around inf 45.5%

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

   if 2.69999999999999991e-192 < t < 1.02e19 or 4.29999999999999991e77 < t < 5.49999999999999979e105

   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. +-commutative 95.9%

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

      2. associate-*l* 95.9%

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

      3. fma-def 95.9%

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

      4. associate-*l* 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 54.4%

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

   if 1.2e121 < t

   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. +-commutative 96.6%

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

      2. associate-*l* 96.6%

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

      3. fma-def 99.6%

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

      4. associate-*l* 88.3%

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

      5. *-commutative 88.3%

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

      6. associate-*l* 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in y around 0 88.3%

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

      1. *-commutative 88.3%

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

      2. *-commutative 88.3%

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

      3. *-commutative 88.3%

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

      4. associate-*r* 99.4%

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

      5. associate-*r* 99.6%

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

      6. *-commutative 99.6%

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

      7. associate-*l* 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in y around inf 61.9%

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

      1. *-commutative 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*l* 61.9%

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

      4. *-commutative 61.9%

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

   9. Simplified 61.9%

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

   10. Taylor expanded in t around 0 61.9%

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

       1. *-commutative 61.9%

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

       2. associate-*l* 61.8%

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

   12. Simplified 61.8%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-53}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-192}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+19}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+77}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+105}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+121}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]

Alternative 7: 96.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+122}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(z \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= z -4.2e+122)
   (- (* 27.0 (* a b)) (* 9.0 (* y (* z t))))
   (+ (* b (* a 27.0)) (- (* x 2.0) (* t (* 9.0 (* z y)))))))

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 <= -4.2e+122) {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (z * y))));
	}
	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 <= (-4.2d+122)) then
        tmp = (27.0d0 * (a * b)) - (9.0d0 * (y * (z * t)))
    else
        tmp = (b * (a * 27.0d0)) + ((x * 2.0d0) - (t * (9.0d0 * (z * y))))
    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 <= -4.2e+122) {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (z * y))));
	}
	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 <= -4.2e+122:
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)))
	else:
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (z * y))))
	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 <= -4.2e+122)
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * Float64(y * Float64(z * t))));
	else
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(t * Float64(9.0 * Float64(z * y)))));
	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 <= -4.2e+122)
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	else
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (z * y))));
	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, -4.2e+122], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.20000000000000032e122

   1. Initial program 80.8%

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

      1. +-commutative 80.8%

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

      2. associate-*l* 80.8%

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

      3. fma-def 84.8%

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

      4. associate-*l* 92.4%

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

      5. *-commutative 92.4%

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

      6. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 68.4%

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

   if -4.20000000000000032e122 < z

   1. Initial program 95.7%

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

   2. Taylor expanded in y around 0 96.1%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+122}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(z \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 8: 96.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+122}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= z -5.6e+122)
   (- (* 27.0 (* a b)) (* 9.0 (* y (* z t))))
   (+ (* b (* a 27.0)) (- (* x 2.0) (* t (* y (* z 9.0)))))))

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 <= -5.6e+122) {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (y * (z * 9.0))));
	}
	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 <= (-5.6d+122)) then
        tmp = (27.0d0 * (a * b)) - (9.0d0 * (y * (z * t)))
    else
        tmp = (b * (a * 27.0d0)) + ((x * 2.0d0) - (t * (y * (z * 9.0d0))))
    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 <= -5.6e+122) {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (y * (z * 9.0))));
	}
	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 <= -5.6e+122:
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)))
	else:
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (y * (z * 9.0))))
	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 <= -5.6e+122)
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * Float64(y * Float64(z * t))));
	else
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(z * 9.0)))));
	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 <= -5.6e+122)
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	else
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (y * (z * 9.0))));
	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, -5.6e+122], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5999999999999999e122

   1. Initial program 80.8%

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

      1. +-commutative 80.8%

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

      2. associate-*l* 80.8%

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

      3. fma-def 84.8%

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

      4. associate-*l* 92.4%

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

      5. *-commutative 92.4%

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

      6. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 68.4%

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

   if -5.5999999999999999e122 < z

   1. Initial program 95.7%

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

   2. Taylor expanded in y around 0 96.1%

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

      1. *-commutative 96.1%

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

      2. associate-*r* 96.1%

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

   4. Simplified 96.1%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+122}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \]

Alternative 9: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.5 \cdot 10^{+34}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \left(z \cdot t\right) \cdot \left(9 \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= z 1.5e+34)
   (+ (* x 2.0) (- (* a (* 27.0 b)) (* (* z t) (* 9.0 y))))
   (+ (* b (* a 27.0)) (- (* x 2.0) (* t (* y (* z 9.0)))))))

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 <= 1.5e+34) {
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((z * t) * (9.0 * y)));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (y * (z * 9.0))));
	}
	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 <= 1.5d+34) then
        tmp = (x * 2.0d0) + ((a * (27.0d0 * b)) - ((z * t) * (9.0d0 * y)))
    else
        tmp = (b * (a * 27.0d0)) + ((x * 2.0d0) - (t * (y * (z * 9.0d0))))
    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 <= 1.5e+34) {
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((z * t) * (9.0 * y)));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (y * (z * 9.0))));
	}
	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 <= 1.5e+34:
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((z * t) * (9.0 * y)))
	else:
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (y * (z * 9.0))))
	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 <= 1.5e+34)
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(a * Float64(27.0 * b)) - Float64(Float64(z * t) * Float64(9.0 * y))));
	else
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(z * 9.0)))));
	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 <= 1.5e+34)
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((z * t) * (9.0 * y)));
	else
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (y * (z * 9.0))));
	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, 1.5e+34], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] - N[(N[(z * t), $MachinePrecision] * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.50000000000000009e34

   1. Initial program 96.1%

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

      1. associate-+l- 96.1%

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

      2. sub-neg 96.1%

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

      3. neg-mul-1 96.1%

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

      4. metadata-eval 96.1%

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

      5. metadata-eval 96.1%

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

      6. cancel-sign-sub-inv 96.1%

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

      7. metadata-eval 96.1%

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

      8. *-lft-identity 96.1%

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

      9. associate-*l* 96.2%

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

      10. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   if 1.50000000000000009e34 < z

   1. Initial program 87.3%

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

   2. Taylor expanded in y around 0 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-*r* 87.2%

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

   4. Simplified 87.2%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.5 \cdot 10^{+34}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \left(z \cdot t\right) \cdot \left(9 \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \]

Alternative 10: 48.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+19}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-303}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-33}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= z -3.5e+19)
     (* (* y (* z t)) -9.0)
     (if (<= z -1.55e-221)
       t_1
       (if (<= z 1.05e-303)
         (* x 2.0)
         (if (<= z 2.1e-271)
           t_1
           (if (<= z 3.4e-33) (* x 2.0) (* z (* -9.0 (* y t))))))))))

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 tmp;
	if (z <= -3.5e+19) {
		tmp = (y * (z * t)) * -9.0;
	} else if (z <= -1.55e-221) {
		tmp = t_1;
	} else if (z <= 1.05e-303) {
		tmp = x * 2.0;
	} else if (z <= 2.1e-271) {
		tmp = t_1;
	} else if (z <= 3.4e-33) {
		tmp = x * 2.0;
	} else {
		tmp = z * (-9.0 * (y * t));
	}
	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 = 27.0d0 * (a * b)
    if (z <= (-3.5d+19)) then
        tmp = (y * (z * t)) * (-9.0d0)
    else if (z <= (-1.55d-221)) then
        tmp = t_1
    else if (z <= 1.05d-303) then
        tmp = x * 2.0d0
    else if (z <= 2.1d-271) then
        tmp = t_1
    else if (z <= 3.4d-33) then
        tmp = x * 2.0d0
    else
        tmp = z * ((-9.0d0) * (y * t))
    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 tmp;
	if (z <= -3.5e+19) {
		tmp = (y * (z * t)) * -9.0;
	} else if (z <= -1.55e-221) {
		tmp = t_1;
	} else if (z <= 1.05e-303) {
		tmp = x * 2.0;
	} else if (z <= 2.1e-271) {
		tmp = t_1;
	} else if (z <= 3.4e-33) {
		tmp = x * 2.0;
	} else {
		tmp = z * (-9.0 * (y * t));
	}
	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)
	tmp = 0
	if z <= -3.5e+19:
		tmp = (y * (z * t)) * -9.0
	elif z <= -1.55e-221:
		tmp = t_1
	elif z <= 1.05e-303:
		tmp = x * 2.0
	elif z <= 2.1e-271:
		tmp = t_1
	elif z <= 3.4e-33:
		tmp = x * 2.0
	else:
		tmp = z * (-9.0 * (y * t))
	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))
	tmp = 0.0
	if (z <= -3.5e+19)
		tmp = Float64(Float64(y * Float64(z * t)) * -9.0);
	elseif (z <= -1.55e-221)
		tmp = t_1;
	elseif (z <= 1.05e-303)
		tmp = Float64(x * 2.0);
	elseif (z <= 2.1e-271)
		tmp = t_1;
	elseif (z <= 3.4e-33)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(z * Float64(-9.0 * Float64(y * t)));
	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);
	tmp = 0.0;
	if (z <= -3.5e+19)
		tmp = (y * (z * t)) * -9.0;
	elseif (z <= -1.55e-221)
		tmp = t_1;
	elseif (z <= 1.05e-303)
		tmp = x * 2.0;
	elseif (z <= 2.1e-271)
		tmp = t_1;
	elseif (z <= 3.4e-33)
		tmp = x * 2.0;
	else
		tmp = z * (-9.0 * (y * t));
	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]}, If[LessEqual[z, -3.5e+19], N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision], If[LessEqual[z, -1.55e-221], t$95$1, If[LessEqual[z, 1.05e-303], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 2.1e-271], t$95$1, If[LessEqual[z, 3.4e-33], N[(x * 2.0), $MachinePrecision], N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.5e19

   1. Initial program 87.1%

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

      1. +-commutative 87.1%

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

      2. associate-*l* 87.1%

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

      3. fma-def 89.3%

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

      4. associate-*l* 91.5%

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

      5. *-commutative 91.5%

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

      6. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in y around inf 48.4%

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

   if -3.5e19 < z < -1.55e-221 or 1.05e-303 < z < 2.1000000000000001e-271

   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. +-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. associate-*l* 98.2%

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

      5. *-commutative 98.2%

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

      6. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in a around inf 49.0%

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

   if -1.55e-221 < z < 1.05e-303 or 2.1000000000000001e-271 < z < 3.4000000000000001e-33

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. associate-*l* 96.0%

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

      3. fma-def 96.0%

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

      4. associate-*l* 96.4%

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

      5. *-commutative 96.4%

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

      6. associate-*l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in x around inf 50.1%

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

   if 3.4000000000000001e-33 < z

   1. Initial program 89.9%

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

      1. +-commutative 89.9%

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

      2. associate-*l* 89.9%

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

      3. fma-def 91.4%

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

      4. associate-*l* 95.7%

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

      5. *-commutative 95.7%

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

      6. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around inf 57.7%

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

      1. *-commutative 57.7%

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

      2. *-commutative 57.7%

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

      3. associate-*r* 57.9%

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

      4. associate-*r* 57.9%

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

      5. *-commutative 57.9%

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

      6. associate-*l* 60.5%

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

   6. Simplified 60.5%

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

   7. Taylor expanded in y around 0 60.5%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+19}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-221}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-303}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-271}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-33}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \]

Alternative 11: 48.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+19}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-303}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= z -2.7e+19)
     (* (* y (* z t)) -9.0)
     (if (<= z -2e-219)
       t_1
       (if (<= z 1.1e-303)
         (* x 2.0)
         (if (<= z 1.16e-271)
           t_1
           (if (<= z 9.2e-33) (* x 2.0) (* z (* y (* t -9.0))))))))))

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 = 27.0 * (a * b);
	double tmp;
	if (z <= -2.7e+19) {
		tmp = (y * (z * t)) * -9.0;
	} else if (z <= -2e-219) {
		tmp = t_1;
	} else if (z <= 1.1e-303) {
		tmp = x * 2.0;
	} else if (z <= 1.16e-271) {
		tmp = t_1;
	} else if (z <= 9.2e-33) {
		tmp = x * 2.0;
	} else {
		tmp = z * (y * (t * -9.0));
	}
	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 = 27.0d0 * (a * b)
    if (z <= (-2.7d+19)) then
        tmp = (y * (z * t)) * (-9.0d0)
    else if (z <= (-2d-219)) then
        tmp = t_1
    else if (z <= 1.1d-303) then
        tmp = x * 2.0d0
    else if (z <= 1.16d-271) then
        tmp = t_1
    else if (z <= 9.2d-33) then
        tmp = x * 2.0d0
    else
        tmp = z * (y * (t * (-9.0d0)))
    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 = 27.0 * (a * b);
	double tmp;
	if (z <= -2.7e+19) {
		tmp = (y * (z * t)) * -9.0;
	} else if (z <= -2e-219) {
		tmp = t_1;
	} else if (z <= 1.1e-303) {
		tmp = x * 2.0;
	} else if (z <= 1.16e-271) {
		tmp = t_1;
	} else if (z <= 9.2e-33) {
		tmp = x * 2.0;
	} else {
		tmp = z * (y * (t * -9.0));
	}
	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 = 27.0 * (a * b)
	tmp = 0
	if z <= -2.7e+19:
		tmp = (y * (z * t)) * -9.0
	elif z <= -2e-219:
		tmp = t_1
	elif z <= 1.1e-303:
		tmp = x * 2.0
	elif z <= 1.16e-271:
		tmp = t_1
	elif z <= 9.2e-33:
		tmp = x * 2.0
	else:
		tmp = z * (y * (t * -9.0))
	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(27.0 * Float64(a * b))
	tmp = 0.0
	if (z <= -2.7e+19)
		tmp = Float64(Float64(y * Float64(z * t)) * -9.0);
	elseif (z <= -2e-219)
		tmp = t_1;
	elseif (z <= 1.1e-303)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.16e-271)
		tmp = t_1;
	elseif (z <= 9.2e-33)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(z * Float64(y * Float64(t * -9.0)));
	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 = 27.0 * (a * b);
	tmp = 0.0;
	if (z <= -2.7e+19)
		tmp = (y * (z * t)) * -9.0;
	elseif (z <= -2e-219)
		tmp = t_1;
	elseif (z <= 1.1e-303)
		tmp = x * 2.0;
	elseif (z <= 1.16e-271)
		tmp = t_1;
	elseif (z <= 9.2e-33)
		tmp = x * 2.0;
	else
		tmp = z * (y * (t * -9.0));
	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[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+19], N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision], If[LessEqual[z, -2e-219], t$95$1, If[LessEqual[z, 1.1e-303], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.16e-271], t$95$1, If[LessEqual[z, 9.2e-33], N[(x * 2.0), $MachinePrecision], N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7e19

   1. Initial program 87.1%

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

      1. +-commutative 87.1%

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

      2. associate-*l* 87.1%

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

      3. fma-def 89.3%

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

      4. associate-*l* 91.5%

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

      5. *-commutative 91.5%

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

      6. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in y around inf 48.4%

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

   if -2.7e19 < z < -2.0000000000000001e-219 or 1.10000000000000007e-303 < z < 1.15999999999999998e-271

   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. +-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. associate-*l* 98.2%

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

      5. *-commutative 98.2%

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

      6. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in a around inf 48.3%

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

   if -2.0000000000000001e-219 < z < 1.10000000000000007e-303 or 1.15999999999999998e-271 < z < 9.19999999999999942e-33

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. associate-*l* 96.0%

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

      3. fma-def 96.0%

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

      4. associate-*l* 96.5%

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

      5. *-commutative 96.5%

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

      6. associate-*l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in x around inf 49.5%

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

   if 9.19999999999999942e-33 < z

   1. Initial program 89.9%

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

      1. +-commutative 89.9%

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

      2. associate-*l* 89.9%

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

      3. fma-def 91.4%

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

      4. associate-*l* 95.7%

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

      5. *-commutative 95.7%

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

      6. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around inf 57.7%

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

      1. *-commutative 57.7%

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

      2. *-commutative 57.7%

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

      3. associate-*r* 57.9%

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

      4. associate-*r* 57.9%

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

      5. *-commutative 57.9%

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

      6. associate-*l* 60.5%

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

   6. Simplified 60.5%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+19}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-219}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-303}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-271}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \end{array} \]

Alternative 12: 77.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{-64}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+20}:\\ \;\;\;\;x \cdot 2 + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

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 (<= b -2.9e-64)
   (- (* x 2.0) (* a (* b -27.0)))
   (if (<= b 7.8e+20)
     (+ (* x 2.0) (* y (* z (* t -9.0))))
     (+ (* x 2.0) (* 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 (b <= -2.9e-64) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else if (b <= 7.8e+20) {
		tmp = (x * 2.0) + (y * (z * (t * -9.0)));
	} else {
		tmp = (x * 2.0) + (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 (b <= (-2.9d-64)) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else if (b <= 7.8d+20) then
        tmp = (x * 2.0d0) + (y * (z * (t * (-9.0d0))))
    else
        tmp = (x * 2.0d0) + (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 (b <= -2.9e-64) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else if (b <= 7.8e+20) {
		tmp = (x * 2.0) + (y * (z * (t * -9.0)));
	} else {
		tmp = (x * 2.0) + (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 b <= -2.9e-64:
		tmp = (x * 2.0) - (a * (b * -27.0))
	elif b <= 7.8e+20:
		tmp = (x * 2.0) + (y * (z * (t * -9.0)))
	else:
		tmp = (x * 2.0) + (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 (b <= -2.9e-64)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	elseif (b <= 7.8e+20)
		tmp = Float64(Float64(x * 2.0) + Float64(y * Float64(z * Float64(t * -9.0))));
	else
		tmp = Float64(Float64(x * 2.0) + 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 (b <= -2.9e-64)
		tmp = (x * 2.0) - (a * (b * -27.0));
	elseif (b <= 7.8e+20)
		tmp = (x * 2.0) + (y * (z * (t * -9.0)));
	else
		tmp = (x * 2.0) + (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[b, -2.9e-64], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.8e+20], N[(N[(x * 2.0), $MachinePrecision] + N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.8999999999999999e-64

   1. Initial program 90.2%

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

      1. associate-+l- 90.2%

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

      2. sub-neg 90.2%

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

      3. neg-mul-1 90.2%

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

      4. metadata-eval 90.2%

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

      5. metadata-eval 90.2%

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

      6. cancel-sign-sub-inv 90.2%

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

      7. metadata-eval 90.2%

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

      8. *-lft-identity 90.2%

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

      9. associate-*l* 97.2%

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

      10. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in y around 0 74.6%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 74.6%

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

      2. associate-*l* 72.2%

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

   6. Simplified 72.2%

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

   if -2.8999999999999999e-64 < b < 7.8e20

   1. Initial program 96.0%

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

   2. Taylor expanded in y around 0 96.0%

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

      1. *-commutative 96.0%

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

      2. associate-*r* 96.0%

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

   4. Simplified 96.0%

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

   5. Taylor expanded in a around 0 82.7%

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

      1. cancel-sign-sub-inv 82.7%

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

      2. metadata-eval 82.7%

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

      3. *-commutative 82.7%

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

      4. *-commutative 82.7%

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

      5. associate-*r* 82.7%

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

      6. *-commutative 82.7%

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

      7. *-commutative 82.7%

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

      8. associate-*r* 82.8%

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

   7. Simplified 82.8%

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

   if 7.8e20 < b

   1. Initial program 96.3%

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

      1. +-commutative 96.3%

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

      2. associate-*l* 96.3%

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

      3. fma-def 96.3%

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

      4. associate-*l* 98.1%

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

      5. *-commutative 98.1%

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

      6. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 79.4%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 79.4%

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

      2. *-commutative 79.4%

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

      3. fma-def 79.4%

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

      4. *-commutative 79.4%

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

   6. Simplified 79.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]
   7. Step-by-step derivation

      1. fma-udef 79.4%

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

      2. associate-*r* 79.4%

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

      3. *-commutative 79.4%

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

   8. Applied egg-rr 79.4%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{-64}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+20}:\\ \;\;\;\;x \cdot 2 + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 13: 76.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+46}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+25}:\\ \;\;\;\;x \cdot 2 + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \end{array} \end{array} \]

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 (<= z -2e+46)
   (* (* y (* z t)) -9.0)
   (if (<= z 1.66e+25) (+ (* x 2.0) (* b (* a 27.0))) (* z (* y (* t -9.0))))))

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 <= -2e+46) {
		tmp = (y * (z * t)) * -9.0;
	} else if (z <= 1.66e+25) {
		tmp = (x * 2.0) + (b * (a * 27.0));
	} else {
		tmp = z * (y * (t * -9.0));
	}
	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 <= (-2d+46)) then
        tmp = (y * (z * t)) * (-9.0d0)
    else if (z <= 1.66d+25) then
        tmp = (x * 2.0d0) + (b * (a * 27.0d0))
    else
        tmp = z * (y * (t * (-9.0d0)))
    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 <= -2e+46) {
		tmp = (y * (z * t)) * -9.0;
	} else if (z <= 1.66e+25) {
		tmp = (x * 2.0) + (b * (a * 27.0));
	} else {
		tmp = z * (y * (t * -9.0));
	}
	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 <= -2e+46:
		tmp = (y * (z * t)) * -9.0
	elif z <= 1.66e+25:
		tmp = (x * 2.0) + (b * (a * 27.0))
	else:
		tmp = z * (y * (t * -9.0))
	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 <= -2e+46)
		tmp = Float64(Float64(y * Float64(z * t)) * -9.0);
	elseif (z <= 1.66e+25)
		tmp = Float64(Float64(x * 2.0) + Float64(b * Float64(a * 27.0)));
	else
		tmp = Float64(z * Float64(y * Float64(t * -9.0)));
	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 <= -2e+46)
		tmp = (y * (z * t)) * -9.0;
	elseif (z <= 1.66e+25)
		tmp = (x * 2.0) + (b * (a * 27.0));
	else
		tmp = z * (y * (t * -9.0));
	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, -2e+46], N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision], If[LessEqual[z, 1.66e+25], N[(N[(x * 2.0), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e46

   1. Initial program 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-*l* 85.1%

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

      3. fma-def 87.7%

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

      4. associate-*l* 90.3%

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

      5. *-commutative 90.3%

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

      6. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around inf 47.7%

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

   if -2e46 < z < 1.6600000000000001e25

   1. Initial program 98.7%

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

      1. +-commutative 98.7%

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

      2. associate-*l* 98.0%

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

      3. fma-def 98.0%

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

      4. associate-*l* 97.6%

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

      5. *-commutative 97.6%

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

      6. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around 0 77.7%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 77.7%

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

      2. *-commutative 77.7%

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

      3. fma-def 77.7%

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

      4. *-commutative 77.7%

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

   6. Simplified 77.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]
   7. Step-by-step derivation

      1. fma-udef 77.7%

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

      2. associate-*r* 77.7%

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

      3. *-commutative 77.7%

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

   8. Applied egg-rr 77.7%

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

   if 1.6600000000000001e25 < z

   1. Initial program 87.7%

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

      1. +-commutative 87.7%

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

      2. associate-*l* 87.7%

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

      3. fma-def 89.6%

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

      4. associate-*l* 94.8%

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

      5. *-commutative 94.8%

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

      6. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. *-commutative 57.2%

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

      3. associate-*r* 57.5%

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

      4. associate-*r* 57.5%

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

      5. *-commutative 57.5%

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

      6. associate-*l* 60.7%

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

   6. Simplified 60.7%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+46}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+25}:\\ \;\;\;\;x \cdot 2 + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \end{array} \]

Alternative 14: 76.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+47}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+27}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \end{array} \end{array} \]

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 (<= z -4.8e+47)
   (* (* y (* z t)) -9.0)
   (if (<= z 1.2e+27) (- (* x 2.0) (* a (* b -27.0))) (* z (* y (* t -9.0))))))

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 <= -4.8e+47) {
		tmp = (y * (z * t)) * -9.0;
	} else if (z <= 1.2e+27) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = z * (y * (t * -9.0));
	}
	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 <= (-4.8d+47)) then
        tmp = (y * (z * t)) * (-9.0d0)
    else if (z <= 1.2d+27) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else
        tmp = z * (y * (t * (-9.0d0)))
    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 <= -4.8e+47) {
		tmp = (y * (z * t)) * -9.0;
	} else if (z <= 1.2e+27) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = z * (y * (t * -9.0));
	}
	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 <= -4.8e+47:
		tmp = (y * (z * t)) * -9.0
	elif z <= 1.2e+27:
		tmp = (x * 2.0) - (a * (b * -27.0))
	else:
		tmp = z * (y * (t * -9.0))
	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 <= -4.8e+47)
		tmp = Float64(Float64(y * Float64(z * t)) * -9.0);
	elseif (z <= 1.2e+27)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	else
		tmp = Float64(z * Float64(y * Float64(t * -9.0)));
	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 <= -4.8e+47)
		tmp = (y * (z * t)) * -9.0;
	elseif (z <= 1.2e+27)
		tmp = (x * 2.0) - (a * (b * -27.0));
	else
		tmp = z * (y * (t * -9.0));
	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, -4.8e+47], N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision], If[LessEqual[z, 1.2e+27], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.80000000000000037e47

   1. Initial program 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-*l* 85.1%

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

      3. fma-def 87.7%

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

      4. associate-*l* 90.3%

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

      5. *-commutative 90.3%

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

      6. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around inf 47.7%

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

   if -4.80000000000000037e47 < z < 1.19999999999999999e27

   1. Initial program 98.7%

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

      1. associate-+l- 98.7%

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

      2. sub-neg 98.7%

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

      3. neg-mul-1 98.7%

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

      4. metadata-eval 98.7%

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

      5. metadata-eval 98.7%

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

      6. cancel-sign-sub-inv 98.7%

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

      7. metadata-eval 98.7%

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

      8. *-lft-identity 98.7%

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

      9. associate-*l* 98.2%

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

      10. associate-*l* 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in y around 0 77.7%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 77.7%

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

      2. associate-*l* 77.1%

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

   6. Simplified 77.1%

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

   if 1.19999999999999999e27 < z

   1. Initial program 87.7%

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

      1. +-commutative 87.7%

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

      2. associate-*l* 87.7%

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

      3. fma-def 89.6%

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

      4. associate-*l* 94.8%

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

      5. *-commutative 94.8%

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

      6. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. *-commutative 57.2%

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

      3. associate-*r* 57.5%

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

      4. associate-*r* 57.5%

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

      5. *-commutative 57.5%

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

      6. associate-*l* 60.7%

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

   6. Simplified 60.7%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+47}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+27}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \end{array} \]

Alternative 15: 48.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-11}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+28}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

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
 (if (<= x -2.9e-11) (* x 2.0) (if (<= x 4.6e+28) (* 27.0 (* a b)) (* 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 tmp;
	if (x <= -2.9e-11) {
		tmp = x * 2.0;
	} else if (x <= 4.6e+28) {
		tmp = 27.0 * (a * b);
	} 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) :: tmp
    if (x <= (-2.9d-11)) then
        tmp = x * 2.0d0
    else if (x <= 4.6d+28) then
        tmp = 27.0d0 * (a * b)
    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 tmp;
	if (x <= -2.9e-11) {
		tmp = x * 2.0;
	} else if (x <= 4.6e+28) {
		tmp = 27.0 * (a * b);
	} 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):
	tmp = 0
	if x <= -2.9e-11:
		tmp = x * 2.0
	elif x <= 4.6e+28:
		tmp = 27.0 * (a * b)
	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)
	tmp = 0.0
	if (x <= -2.9e-11)
		tmp = Float64(x * 2.0);
	elseif (x <= 4.6e+28)
		tmp = Float64(27.0 * Float64(a * b));
	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)
	tmp = 0.0;
	if (x <= -2.9e-11)
		tmp = x * 2.0;
	elseif (x <= 4.6e+28)
		tmp = 27.0 * (a * b);
	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_] := If[LessEqual[x, -2.9e-11], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, 4.6e+28], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9e-11 or 4.59999999999999968e28 < x

   1. Initial program 94.5%

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

      1. +-commutative 94.5%

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

      2. associate-*l* 93.8%

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

      3. fma-def 94.6%

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

      4. associate-*l* 96.1%

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

      5. *-commutative 96.1%

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

      6. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 55.2%

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

   if -2.9e-11 < x < 4.59999999999999968e28

   1. Initial program 94.0%

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

      1. +-commutative 94.0%

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

      2. associate-*l* 93.9%

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

      3. fma-def 94.7%

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

      4. associate-*l* 95.6%

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

      5. *-commutative 95.6%

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

      6. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in a around inf 43.6%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-11}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+28}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 16: 31.4% 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 94.2%

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

   1. +-commutative 94.2%

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

   2. associate-*l* 93.8%

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

   3. fma-def 94.6%

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

   4. associate-*l* 95.9%

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

   5. *-commutative 95.9%

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

   6. associate-*l* 96.2%

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

3. Simplified 96.2%

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

4. Taylor expanded in x around inf 32.7%

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

5. Final simplification 32.7%

   \[\leadsto x \cdot 2 \]

Developer target: 94.9% 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 2023215 
(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)))