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

Percentage Accurate: 95.2% → 98.7%

Time: 16.0s

Alternatives: 14

Speedup: 0.9×

• 27.4% 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: 95.2% 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: 98.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 10^{+141}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \left(a \cdot 27\right) \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= (* (* y 9.0) z) 1e+141)
   (fma x 2.0 (fma t (* (* y z) -9.0) (* (* a 27.0) b)))
   (fma a (* 27.0 b) (- (* x 2.0) (* 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 tmp;
	if (((y * 9.0) * z) <= 1e+141) {
		tmp = fma(x, 2.0, fma(t, ((y * z) * -9.0), ((a * 27.0) * b)));
	} else {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (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)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 1e+141)
		tmp = fma(x, 2.0, fma(t, Float64(Float64(y * z) * -9.0), Float64(Float64(a * 27.0) * b)));
	else
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * 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[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 1e+141], N[(x * 2.0 + N[(t * N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 1.00000000000000002e141

   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. associate-+l- 95.9%

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

      2. fma-neg 95.9%

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

      3. neg-sub0 95.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. associate-+l- 95.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]

      5. neg-sub0 95.9%

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

      6. *-commutative 95.9%

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

      7. distribute-rgt-neg-in 95.9%

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

      8. fma-def 95.9%

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

      9. *-commutative 95.9%

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

      10. associate-*r* 95.9%

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

      11. distribute-rgt-neg-in 95.9%

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

      12. *-commutative 95.9%

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

      13. metadata-eval 95.9%

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

   3. Simplified 95.9%

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

   if 1.00000000000000002e141 < (*.f64 (*.f64 y 9) z)

   1. Initial program 86.9%

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

      1. +-commutative 86.9%

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

      2. associate-*l* 86.9%

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

      3. fma-def 92.2%

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

      4. associate-*l* 97.2%

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

      5. *-commutative 97.2%

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

      6. associate-*l* 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%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 10^{+141}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \left(a \cdot 27\right) \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 2: 96.1% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

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* 94.5%

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

   3. fma-def 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* 94.7%

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

   5. *-commutative 94.7%

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

   6. associate-*l* 94.7%

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

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. Final simplification 94.7%

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

Alternative 3: 47.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -1.22 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.76 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-186}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-222}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+203}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

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 (* -9.0 (* y (* z t)))) (t_2 (* 27.0 (* a b))))
   (if (<= b -1.22e-53)
     t_2
     (if (<= b -1.76e-141)
       t_1
       (if (<= b -1.15e-186)
         (* x 2.0)
         (if (<= b -3.2e-270)
           t_1
           (if (<= b 8.5e-222)
             (* x 2.0)
             (if (<= b 4.5e+60)
               t_1
               (if (<= b 8.8e+183)
                 t_2
                 (if (<= b 9.5e+203) (* x 2.0) (* (* a 27.0) b)))))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (b <= -1.22e-53) {
		tmp = t_2;
	} else if (b <= -1.76e-141) {
		tmp = t_1;
	} else if (b <= -1.15e-186) {
		tmp = x * 2.0;
	} else if (b <= -3.2e-270) {
		tmp = t_1;
	} else if (b <= 8.5e-222) {
		tmp = x * 2.0;
	} else if (b <= 4.5e+60) {
		tmp = t_1;
	} else if (b <= 8.8e+183) {
		tmp = t_2;
	} else if (b <= 9.5e+203) {
		tmp = x * 2.0;
	} else {
		tmp = (a * 27.0) * b;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-9.0d0) * (y * (z * t))
    t_2 = 27.0d0 * (a * b)
    if (b <= (-1.22d-53)) then
        tmp = t_2
    else if (b <= (-1.76d-141)) then
        tmp = t_1
    else if (b <= (-1.15d-186)) then
        tmp = x * 2.0d0
    else if (b <= (-3.2d-270)) then
        tmp = t_1
    else if (b <= 8.5d-222) then
        tmp = x * 2.0d0
    else if (b <= 4.5d+60) then
        tmp = t_1
    else if (b <= 8.8d+183) then
        tmp = t_2
    else if (b <= 9.5d+203) then
        tmp = x * 2.0d0
    else
        tmp = (a * 27.0d0) * b
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (b <= -1.22e-53) {
		tmp = t_2;
	} else if (b <= -1.76e-141) {
		tmp = t_1;
	} else if (b <= -1.15e-186) {
		tmp = x * 2.0;
	} else if (b <= -3.2e-270) {
		tmp = t_1;
	} else if (b <= 8.5e-222) {
		tmp = x * 2.0;
	} else if (b <= 4.5e+60) {
		tmp = t_1;
	} else if (b <= 8.8e+183) {
		tmp = t_2;
	} else if (b <= 9.5e+203) {
		tmp = x * 2.0;
	} else {
		tmp = (a * 27.0) * b;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (y * (z * t))
	t_2 = 27.0 * (a * b)
	tmp = 0
	if b <= -1.22e-53:
		tmp = t_2
	elif b <= -1.76e-141:
		tmp = t_1
	elif b <= -1.15e-186:
		tmp = x * 2.0
	elif b <= -3.2e-270:
		tmp = t_1
	elif b <= 8.5e-222:
		tmp = x * 2.0
	elif b <= 4.5e+60:
		tmp = t_1
	elif b <= 8.8e+183:
		tmp = t_2
	elif b <= 9.5e+203:
		tmp = x * 2.0
	else:
		tmp = (a * 27.0) * b
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(y * Float64(z * t)))
	t_2 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (b <= -1.22e-53)
		tmp = t_2;
	elseif (b <= -1.76e-141)
		tmp = t_1;
	elseif (b <= -1.15e-186)
		tmp = Float64(x * 2.0);
	elseif (b <= -3.2e-270)
		tmp = t_1;
	elseif (b <= 8.5e-222)
		tmp = Float64(x * 2.0);
	elseif (b <= 4.5e+60)
		tmp = t_1;
	elseif (b <= 8.8e+183)
		tmp = t_2;
	elseif (b <= 9.5e+203)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(Float64(a * 27.0) * b);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (y * (z * t));
	t_2 = 27.0 * (a * b);
	tmp = 0.0;
	if (b <= -1.22e-53)
		tmp = t_2;
	elseif (b <= -1.76e-141)
		tmp = t_1;
	elseif (b <= -1.15e-186)
		tmp = x * 2.0;
	elseif (b <= -3.2e-270)
		tmp = t_1;
	elseif (b <= 8.5e-222)
		tmp = x * 2.0;
	elseif (b <= 4.5e+60)
		tmp = t_1;
	elseif (b <= 8.8e+183)
		tmp = t_2;
	elseif (b <= 9.5e+203)
		tmp = x * 2.0;
	else
		tmp = (a * 27.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.22e-53], t$95$2, If[LessEqual[b, -1.76e-141], t$95$1, If[LessEqual[b, -1.15e-186], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, -3.2e-270], t$95$1, If[LessEqual[b, 8.5e-222], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 4.5e+60], t$95$1, If[LessEqual[b, 8.8e+183], t$95$2, If[LessEqual[b, 9.5e+203], N[(x * 2.0), $MachinePrecision], N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.22000000000000003e-53 or 4.50000000000000013e60 < b < 8.79999999999999962e183

   1. Initial program 95.0%

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

      1. +-commutative 95.0%

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

      2. associate-*l* 95.0%

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

      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* 97.0%

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

      5. *-commutative 97.0%

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

      6. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in a around inf 55.0%

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

   if -1.22000000000000003e-53 < b < -1.76000000000000013e-141 or -1.15e-186 < b < -3.19999999999999988e-270 or 8.5000000000000003e-222 < b < 4.50000000000000013e60

   1. Initial program 95.2%

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

      1. +-commutative 95.2%

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

      2. associate-*l* 95.3%

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

      3. fma-def 95.3%

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

      4. associate-*l* 94.2%

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

      5. *-commutative 94.2%

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

      6. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around inf 45.0%

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

   if -1.76000000000000013e-141 < b < -1.15e-186 or -3.19999999999999988e-270 < b < 8.5000000000000003e-222 or 8.79999999999999962e183 < b < 9.4999999999999995e203

   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* 95.5%

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

      3. fma-def 95.5%

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

      4. associate-*l* 91.3%

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

      5. *-commutative 91.3%

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

      6. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in x around inf 60.4%

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

   if 9.4999999999999995e203 < b

   1. Initial program 89.2%

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

      1. +-commutative 89.2%

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

      2. associate-*l* 89.2%

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

      3. fma-def 92.7%

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

      4. associate-*l* 92.9%

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

      5. *-commutative 92.9%

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

      6. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around 0 69.2%

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

      1. cancel-sign-sub-inv 69.2%

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

      2. associate-*r* 69.3%

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

      3. metadata-eval 69.3%

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

      4. add-sqr-sqrt 69.3%

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

      5. associate-*r* 69.3%

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

      6. fma-def 69.3%

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

      7. add-sqr-sqrt 47.3%

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

      8. sqrt-unprod 47.9%

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

      9. swap-sqr 47.9%

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

      10. metadata-eval 47.9%

          \[\leadsto \mathsf{fma}\left(\left(27 \cdot a\right) \cdot \sqrt{b}, \sqrt{b}, \sqrt{\color{blue}{81} \cdot \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}\right) \]

      11. metadata-eval 47.9%

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

      12. swap-sqr 47.9%

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

      13. sqrt-unprod 39.9%

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

      14. add-sqr-sqrt 61.9%

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

      15. *-commutative 61.9%

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

      16. associate-*l* 61.9%

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

   6. Applied egg-rr 61.9%

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

   7. Taylor expanded in a around inf 66.1%

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

      1. *-commutative 66.1%

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

      2. *-commutative 66.1%

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

      3. associate-*l* 66.3%

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

   9. Simplified 66.3%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.22 \cdot 10^{-53}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -1.76 \cdot 10^{-141}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-186}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-270}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-222}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+60}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+183}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+203}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b\\ \end{array} \]

Alternative 4: 47.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -2.65 \cdot 10^{-54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-180}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-270}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-204}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+203}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

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 (* t (* (* y z) -9.0))) (t_2 (* 27.0 (* a b))))
   (if (<= b -2.65e-54)
     t_2
     (if (<= b -1.75e-140)
       t_1
       (if (<= b -1.5e-180)
         (* x 2.0)
         (if (<= b -5.4e-270)
           (* -9.0 (* y (* z t)))
           (if (<= b 1.7e-204)
             (* x 2.0)
             (if (<= b 8.5e+59)
               t_1
               (if (<= b 8.8e+183)
                 t_2
                 (if (<= b 9.5e+203) (* x 2.0) (* (* a 27.0) b)))))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * ((y * z) * -9.0);
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (b <= -2.65e-54) {
		tmp = t_2;
	} else if (b <= -1.75e-140) {
		tmp = t_1;
	} else if (b <= -1.5e-180) {
		tmp = x * 2.0;
	} else if (b <= -5.4e-270) {
		tmp = -9.0 * (y * (z * t));
	} else if (b <= 1.7e-204) {
		tmp = x * 2.0;
	} else if (b <= 8.5e+59) {
		tmp = t_1;
	} else if (b <= 8.8e+183) {
		tmp = t_2;
	} else if (b <= 9.5e+203) {
		tmp = x * 2.0;
	} else {
		tmp = (a * 27.0) * b;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y * z) * (-9.0d0))
    t_2 = 27.0d0 * (a * b)
    if (b <= (-2.65d-54)) then
        tmp = t_2
    else if (b <= (-1.75d-140)) then
        tmp = t_1
    else if (b <= (-1.5d-180)) then
        tmp = x * 2.0d0
    else if (b <= (-5.4d-270)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (b <= 1.7d-204) then
        tmp = x * 2.0d0
    else if (b <= 8.5d+59) then
        tmp = t_1
    else if (b <= 8.8d+183) then
        tmp = t_2
    else if (b <= 9.5d+203) then
        tmp = x * 2.0d0
    else
        tmp = (a * 27.0d0) * b
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * ((y * z) * -9.0);
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (b <= -2.65e-54) {
		tmp = t_2;
	} else if (b <= -1.75e-140) {
		tmp = t_1;
	} else if (b <= -1.5e-180) {
		tmp = x * 2.0;
	} else if (b <= -5.4e-270) {
		tmp = -9.0 * (y * (z * t));
	} else if (b <= 1.7e-204) {
		tmp = x * 2.0;
	} else if (b <= 8.5e+59) {
		tmp = t_1;
	} else if (b <= 8.8e+183) {
		tmp = t_2;
	} else if (b <= 9.5e+203) {
		tmp = x * 2.0;
	} else {
		tmp = (a * 27.0) * b;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = t * ((y * z) * -9.0)
	t_2 = 27.0 * (a * b)
	tmp = 0
	if b <= -2.65e-54:
		tmp = t_2
	elif b <= -1.75e-140:
		tmp = t_1
	elif b <= -1.5e-180:
		tmp = x * 2.0
	elif b <= -5.4e-270:
		tmp = -9.0 * (y * (z * t))
	elif b <= 1.7e-204:
		tmp = x * 2.0
	elif b <= 8.5e+59:
		tmp = t_1
	elif b <= 8.8e+183:
		tmp = t_2
	elif b <= 9.5e+203:
		tmp = x * 2.0
	else:
		tmp = (a * 27.0) * b
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(Float64(y * z) * -9.0))
	t_2 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (b <= -2.65e-54)
		tmp = t_2;
	elseif (b <= -1.75e-140)
		tmp = t_1;
	elseif (b <= -1.5e-180)
		tmp = Float64(x * 2.0);
	elseif (b <= -5.4e-270)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (b <= 1.7e-204)
		tmp = Float64(x * 2.0);
	elseif (b <= 8.5e+59)
		tmp = t_1;
	elseif (b <= 8.8e+183)
		tmp = t_2;
	elseif (b <= 9.5e+203)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(Float64(a * 27.0) * b);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * ((y * z) * -9.0);
	t_2 = 27.0 * (a * b);
	tmp = 0.0;
	if (b <= -2.65e-54)
		tmp = t_2;
	elseif (b <= -1.75e-140)
		tmp = t_1;
	elseif (b <= -1.5e-180)
		tmp = x * 2.0;
	elseif (b <= -5.4e-270)
		tmp = -9.0 * (y * (z * t));
	elseif (b <= 1.7e-204)
		tmp = x * 2.0;
	elseif (b <= 8.5e+59)
		tmp = t_1;
	elseif (b <= 8.8e+183)
		tmp = t_2;
	elseif (b <= 9.5e+203)
		tmp = x * 2.0;
	else
		tmp = (a * 27.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.65e-54], t$95$2, If[LessEqual[b, -1.75e-140], t$95$1, If[LessEqual[b, -1.5e-180], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, -5.4e-270], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-204], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 8.5e+59], t$95$1, If[LessEqual[b, 8.8e+183], t$95$2, If[LessEqual[b, 9.5e+203], N[(x * 2.0), $MachinePrecision], N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.65000000000000028e-54 or 8.4999999999999999e59 < b < 8.79999999999999962e183

   1. Initial program 95.0%

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

      1. +-commutative 95.0%

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

      2. associate-*l* 95.0%

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

      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* 97.0%

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

      5. *-commutative 97.0%

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

      6. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in a around inf 55.0%

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

   if -2.65000000000000028e-54 < b < -1.7499999999999999e-140 or 1.7000000000000001e-204 < b < 8.4999999999999999e59

   1. Initial program 93.4%

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

      1. +-commutative 93.4%

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

      2. associate-*l* 93.4%

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

      3. fma-def 93.4%

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

      4. associate-*l* 96.7%

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

      5. *-commutative 96.7%

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

      6. associate-*l* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around 0 67.6%

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

   5. Taylor expanded in a around 0 47.1%

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

      1. associate-*r* 47.2%

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

      2. *-commutative 47.2%

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

      3. *-commutative 47.2%

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

      4. associate-*r* 45.5%

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

      5. *-commutative 45.5%

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

      6. *-commutative 45.5%

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

      7. associate-*l* 45.5%

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

   7. Simplified 45.5%

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

   if -1.7499999999999999e-140 < b < -1.5e-180 or -5.40000000000000014e-270 < b < 1.7000000000000001e-204 or 8.79999999999999962e183 < b < 9.4999999999999995e203

   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. Step-by-step derivation

      1. +-commutative 96.0%

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

      2. associate-*l* 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* 90.1%

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

      5. *-commutative 90.1%

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

      6. associate-*l* 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in x around inf 59.8%

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

   if -1.5e-180 < b < -5.40000000000000014e-270

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. associate-*l* 90.4%

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

      5. *-commutative 90.4%

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

      6. associate-*l* 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 37.3%

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

   if 9.4999999999999995e203 < b

   1. Initial program 89.2%

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

      1. +-commutative 89.2%

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

      2. associate-*l* 89.2%

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

      3. fma-def 92.7%

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

      4. associate-*l* 92.9%

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

      5. *-commutative 92.9%

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

      6. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around 0 69.2%

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

      1. cancel-sign-sub-inv 69.2%

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

      2. associate-*r* 69.3%

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

      3. metadata-eval 69.3%

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

      4. add-sqr-sqrt 69.3%

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

      5. associate-*r* 69.3%

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

      6. fma-def 69.3%

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

      7. add-sqr-sqrt 47.3%

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

      8. sqrt-unprod 47.9%

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

      9. swap-sqr 47.9%

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

      10. metadata-eval 47.9%

          \[\leadsto \mathsf{fma}\left(\left(27 \cdot a\right) \cdot \sqrt{b}, \sqrt{b}, \sqrt{\color{blue}{81} \cdot \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}\right) \]

      11. metadata-eval 47.9%

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

      12. swap-sqr 47.9%

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

      13. sqrt-unprod 39.9%

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

      14. add-sqr-sqrt 61.9%

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

      15. *-commutative 61.9%

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

      16. associate-*l* 61.9%

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

   6. Applied egg-rr 61.9%

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

   7. Taylor expanded in a around inf 66.1%

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

      1. *-commutative 66.1%

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

      2. *-commutative 66.1%

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

      3. associate-*l* 66.3%

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

   9. Simplified 66.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot 27\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.65 \cdot 10^{-54}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-180}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-270}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-204}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+183}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+203}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b\\ \end{array} \]

Alternative 5: 47.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -8.6 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-189}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-270}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-204}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+203}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

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 (* t (* (* y z) -9.0))) (t_2 (* 27.0 (* a b))))
   (if (<= b -8.6e-52)
     t_2
     (if (<= b -9.5e-139)
       t_1
       (if (<= b -6.8e-189)
         (* x 2.0)
         (if (<= b -8e-270)
           (* z (* y (* t -9.0)))
           (if (<= b 7.5e-204)
             (* x 2.0)
             (if (<= b 1.12e+60)
               t_1
               (if (<= b 8.8e+183)
                 t_2
                 (if (<= b 9.5e+203) (* x 2.0) (* (* a 27.0) b)))))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * ((y * z) * -9.0);
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (b <= -8.6e-52) {
		tmp = t_2;
	} else if (b <= -9.5e-139) {
		tmp = t_1;
	} else if (b <= -6.8e-189) {
		tmp = x * 2.0;
	} else if (b <= -8e-270) {
		tmp = z * (y * (t * -9.0));
	} else if (b <= 7.5e-204) {
		tmp = x * 2.0;
	} else if (b <= 1.12e+60) {
		tmp = t_1;
	} else if (b <= 8.8e+183) {
		tmp = t_2;
	} else if (b <= 9.5e+203) {
		tmp = x * 2.0;
	} else {
		tmp = (a * 27.0) * b;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y * z) * (-9.0d0))
    t_2 = 27.0d0 * (a * b)
    if (b <= (-8.6d-52)) then
        tmp = t_2
    else if (b <= (-9.5d-139)) then
        tmp = t_1
    else if (b <= (-6.8d-189)) then
        tmp = x * 2.0d0
    else if (b <= (-8d-270)) then
        tmp = z * (y * (t * (-9.0d0)))
    else if (b <= 7.5d-204) then
        tmp = x * 2.0d0
    else if (b <= 1.12d+60) then
        tmp = t_1
    else if (b <= 8.8d+183) then
        tmp = t_2
    else if (b <= 9.5d+203) then
        tmp = x * 2.0d0
    else
        tmp = (a * 27.0d0) * b
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * ((y * z) * -9.0);
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (b <= -8.6e-52) {
		tmp = t_2;
	} else if (b <= -9.5e-139) {
		tmp = t_1;
	} else if (b <= -6.8e-189) {
		tmp = x * 2.0;
	} else if (b <= -8e-270) {
		tmp = z * (y * (t * -9.0));
	} else if (b <= 7.5e-204) {
		tmp = x * 2.0;
	} else if (b <= 1.12e+60) {
		tmp = t_1;
	} else if (b <= 8.8e+183) {
		tmp = t_2;
	} else if (b <= 9.5e+203) {
		tmp = x * 2.0;
	} else {
		tmp = (a * 27.0) * b;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = t * ((y * z) * -9.0)
	t_2 = 27.0 * (a * b)
	tmp = 0
	if b <= -8.6e-52:
		tmp = t_2
	elif b <= -9.5e-139:
		tmp = t_1
	elif b <= -6.8e-189:
		tmp = x * 2.0
	elif b <= -8e-270:
		tmp = z * (y * (t * -9.0))
	elif b <= 7.5e-204:
		tmp = x * 2.0
	elif b <= 1.12e+60:
		tmp = t_1
	elif b <= 8.8e+183:
		tmp = t_2
	elif b <= 9.5e+203:
		tmp = x * 2.0
	else:
		tmp = (a * 27.0) * b
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(Float64(y * z) * -9.0))
	t_2 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (b <= -8.6e-52)
		tmp = t_2;
	elseif (b <= -9.5e-139)
		tmp = t_1;
	elseif (b <= -6.8e-189)
		tmp = Float64(x * 2.0);
	elseif (b <= -8e-270)
		tmp = Float64(z * Float64(y * Float64(t * -9.0)));
	elseif (b <= 7.5e-204)
		tmp = Float64(x * 2.0);
	elseif (b <= 1.12e+60)
		tmp = t_1;
	elseif (b <= 8.8e+183)
		tmp = t_2;
	elseif (b <= 9.5e+203)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(Float64(a * 27.0) * b);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * ((y * z) * -9.0);
	t_2 = 27.0 * (a * b);
	tmp = 0.0;
	if (b <= -8.6e-52)
		tmp = t_2;
	elseif (b <= -9.5e-139)
		tmp = t_1;
	elseif (b <= -6.8e-189)
		tmp = x * 2.0;
	elseif (b <= -8e-270)
		tmp = z * (y * (t * -9.0));
	elseif (b <= 7.5e-204)
		tmp = x * 2.0;
	elseif (b <= 1.12e+60)
		tmp = t_1;
	elseif (b <= 8.8e+183)
		tmp = t_2;
	elseif (b <= 9.5e+203)
		tmp = x * 2.0;
	else
		tmp = (a * 27.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.6e-52], t$95$2, If[LessEqual[b, -9.5e-139], t$95$1, If[LessEqual[b, -6.8e-189], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, -8e-270], N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e-204], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 1.12e+60], t$95$1, If[LessEqual[b, 8.8e+183], t$95$2, If[LessEqual[b, 9.5e+203], N[(x * 2.0), $MachinePrecision], N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -8.6000000000000007e-52 or 1.1199999999999999e60 < b < 8.79999999999999962e183

   1. Initial program 94.9%

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

      1. +-commutative 94.9%

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

      2. associate-*l* 94.9%

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

      3. fma-def 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* 97.0%

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

      5. *-commutative 97.0%

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

      6. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in a around inf 54.5%

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

   if -8.6000000000000007e-52 < b < -9.5000000000000006e-139 or 7.5000000000000003e-204 < b < 1.1199999999999999e60

   1. Initial program 93.4%

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

      1. +-commutative 93.4%

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

      2. associate-*l* 93.5%

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

      3. fma-def 93.5%

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

      4. associate-*l* 96.8%

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

      5. *-commutative 96.8%

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

      6. associate-*l* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around 0 68.1%

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

   5. Taylor expanded in a around 0 46.3%

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

      1. associate-*r* 46.4%

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

      2. *-commutative 46.4%

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

      3. *-commutative 46.4%

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

      4. associate-*r* 44.7%

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

      5. *-commutative 44.7%

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

      6. *-commutative 44.7%

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

      7. associate-*l* 44.8%

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

   7. Simplified 44.8%

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

   if -9.5000000000000006e-139 < b < -6.8000000000000002e-189 or -8.0000000000000003e-270 < b < 7.5000000000000003e-204 or 8.79999999999999962e183 < b < 9.4999999999999995e203

   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 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* 90.5%

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

      5. *-commutative 90.5%

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

      6. associate-*l* 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in x around inf 57.4%

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

   if -6.8000000000000002e-189 < b < -8.0000000000000003e-270

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. associate-*l* 89.4%

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

      5. *-commutative 89.4%

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

      6. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in y around inf 35.7%

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

      1. *-commutative 35.7%

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

      2. *-commutative 35.7%

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

      3. associate-*r* 46.2%

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

      4. associate-*r* 46.4%

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

      5. *-commutative 46.4%

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

      6. associate-*l* 46.0%

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

   6. Simplified 46.0%

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

   if 9.4999999999999995e203 < b

   1. Initial program 89.2%

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

      1. +-commutative 89.2%

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

      2. associate-*l* 89.2%

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

      3. fma-def 92.7%

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

      4. associate-*l* 92.9%

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

      5. *-commutative 92.9%

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

      6. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around 0 69.2%

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

      1. cancel-sign-sub-inv 69.2%

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

      2. associate-*r* 69.3%

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

      3. metadata-eval 69.3%

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

      4. add-sqr-sqrt 69.3%

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

      5. associate-*r* 69.3%

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

      6. fma-def 69.3%

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

      7. add-sqr-sqrt 47.3%

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

      8. sqrt-unprod 47.9%

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

      9. swap-sqr 47.9%

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

      10. metadata-eval 47.9%

          \[\leadsto \mathsf{fma}\left(\left(27 \cdot a\right) \cdot \sqrt{b}, \sqrt{b}, \sqrt{\color{blue}{81} \cdot \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}\right) \]

      11. metadata-eval 47.9%

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

      12. swap-sqr 47.9%

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

      13. sqrt-unprod 39.9%

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

      14. add-sqr-sqrt 61.9%

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

      15. *-commutative 61.9%

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

      16. associate-*l* 61.9%

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

   6. Applied egg-rr 61.9%

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

   7. Taylor expanded in a around inf 66.1%

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

      1. *-commutative 66.1%

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

      2. *-commutative 66.1%

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

      3. associate-*l* 66.3%

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

   9. Simplified 66.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot 27\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.6 \cdot 10^{-52}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-189}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-270}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-204}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+183}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+203}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b\\ \end{array} \]

Alternative 6: 77.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{-20}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (- (* 27.0 (* a b)) (* 9.0 (* y (* z t))))))
   (if (<= b -6.8e-91)
     t_1
     (if (<= b 2.65e-20)
       (+ (* x 2.0) (* (* y z) (* t -9.0)))
       (if (<= b 1.6e+165) t_1 (- (* x 2.0) (* a (* b -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 t_1 = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	double tmp;
	if (b <= -6.8e-91) {
		tmp = t_1;
	} else if (b <= 2.65e-20) {
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	} else if (b <= 1.6e+165) {
		tmp = t_1;
	} else {
		tmp = (x * 2.0) - (a * (b * -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) :: t_1
    real(8) :: tmp
    t_1 = (27.0d0 * (a * b)) - (9.0d0 * (y * (z * t)))
    if (b <= (-6.8d-91)) then
        tmp = t_1
    else if (b <= 2.65d-20) then
        tmp = (x * 2.0d0) + ((y * z) * (t * (-9.0d0)))
    else if (b <= 1.6d+165) then
        tmp = t_1
    else
        tmp = (x * 2.0d0) - (a * (b * (-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 t_1 = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	double tmp;
	if (b <= -6.8e-91) {
		tmp = t_1;
	} else if (b <= 2.65e-20) {
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	} else if (b <= 1.6e+165) {
		tmp = t_1;
	} else {
		tmp = (x * 2.0) - (a * (b * -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):
	t_1 = (27.0 * (a * b)) - (9.0 * (y * (z * t)))
	tmp = 0
	if b <= -6.8e-91:
		tmp = t_1
	elif b <= 2.65e-20:
		tmp = (x * 2.0) + ((y * z) * (t * -9.0))
	elif b <= 1.6e+165:
		tmp = t_1
	else:
		tmp = (x * 2.0) - (a * (b * -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)
	t_1 = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * Float64(y * Float64(z * t))))
	tmp = 0.0
	if (b <= -6.8e-91)
		tmp = t_1;
	elseif (b <= 2.65e-20)
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(y * z) * Float64(t * -9.0)));
	elseif (b <= 1.6e+165)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -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)
	t_1 = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	tmp = 0.0;
	if (b <= -6.8e-91)
		tmp = t_1;
	elseif (b <= 2.65e-20)
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	elseif (b <= 1.6e+165)
		tmp = t_1;
	else
		tmp = (x * 2.0) - (a * (b * -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_] := Block[{t$95$1 = N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e-91], t$95$1, If[LessEqual[b, 2.65e-20], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e+165], t$95$1, N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.80000000000000053e-91 or 2.6500000000000001e-20 < b < 1.6e165

   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 98.9%

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

      4. associate-*l* 97.3%

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

      5. *-commutative 97.3%

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

      6. associate-*l* 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 x around 0 79.9%

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

   if -6.80000000000000053e-91 < b < 2.6500000000000001e-20

   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* 94.5%

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

      3. fma-def 94.5%

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

      4. associate-*l* 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* 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in a around 0 83.8%

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

      1. sub-neg 83.8%

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

      2. *-commutative 83.8%

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

      3. *-commutative 83.8%

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

      4. *-commutative 83.8%

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

      5. associate-*l* 83.8%

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

      6. *-commutative 83.8%

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

      7. +-commutative 83.8%

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

      8. distribute-rgt-neg-in 83.8%

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

      9. *-commutative 83.8%

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

      10. distribute-rgt-neg-in 83.8%

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

      11. metadata-eval 83.8%

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

      12. associate-*r* 83.8%

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

      13. associate-*r* 84.7%

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

      14. fma-def 84.7%

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

      15. *-commutative 84.7%

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

   6. Simplified 84.7%

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

      1. fma-udef 84.7%

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

   8. Applied egg-rr 84.7%

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

   if 1.6e165 < b

   1. Initial program 89.3%

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

      1. associate-+l- 89.3%

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

      2. sub-neg 89.3%

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

      3. neg-mul-1 89.3%

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

      4. metadata-eval 89.3%

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

      5. metadata-eval 89.3%

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

      6. cancel-sign-sub-inv 89.3%

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

      7. metadata-eval 89.3%

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

      8. *-lft-identity 89.3%

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

      9. associate-*l* 86.9%

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

      10. associate-*l* 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in y around 0 82.0%

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

      1. *-commutative 82.0%

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

      2. associate-*l* 82.1%

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

   6. Simplified 82.1%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-91}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{-20}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+165}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \end{array} \]

Alternative 7: 96.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+106}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \end{array} \end{array} \]

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+106)
   (- (* x 2.0) (* 9.0 (* y (* z t))))
   (+ (* (* a 27.0) b) (- (* x 2.0) (* (* (* y 9.0) 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 tmp;
	if (z <= -5.6e+106) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (((y * 9.0) * 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) :: tmp
    if (z <= (-5.6d+106)) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else
        tmp = ((a * 27.0d0) * b) + ((x * 2.0d0) - (((y * 9.0d0) * 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 tmp;
	if (z <= -5.6e+106) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (((y * 9.0) * 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):
	tmp = 0
	if z <= -5.6e+106:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	else:
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (((y * 9.0) * 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)
	tmp = 0.0
	if (z <= -5.6e+106)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	else
		tmp = Float64(Float64(Float64(a * 27.0) * b) + Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * 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)
	tmp = 0.0;
	if (z <= -5.6e+106)
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	else
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (((y * 9.0) * 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_] := If[LessEqual[z, -5.6e+106], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.59999999999999986e106

   1. Initial program 85.9%

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

      1. +-commutative 85.9%

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

      2. associate-*l* 85.9%

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

      3. fma-def 85.9%

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

      4. associate-*l* 86.0%

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

      5. *-commutative 86.0%

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

      6. associate-*l* 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in a around 0 68.9%

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

   if -5.59999999999999986e106 < z

   1. Initial program 95.9%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+106}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \end{array} \]

Alternative 8: 97.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-211}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \end{array} \end{array} \]

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 -5e-211)
   (+ (* x 2.0) (- (* a (* 27.0 b)) (* (* y 9.0) (* z t))))
   (+ (* (* a 27.0) b) (- (* x 2.0) (* (* (* y 9.0) 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 tmp;
	if (z <= -5e-211) {
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((y * 9.0) * (z * t)));
	} else {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (((y * 9.0) * 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) :: tmp
    if (z <= (-5d-211)) then
        tmp = (x * 2.0d0) + ((a * (27.0d0 * b)) - ((y * 9.0d0) * (z * t)))
    else
        tmp = ((a * 27.0d0) * b) + ((x * 2.0d0) - (((y * 9.0d0) * 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 tmp;
	if (z <= -5e-211) {
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((y * 9.0) * (z * t)));
	} else {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (((y * 9.0) * 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):
	tmp = 0
	if z <= -5e-211:
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((y * 9.0) * (z * t)))
	else:
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (((y * 9.0) * 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)
	tmp = 0.0
	if (z <= -5e-211)
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(a * Float64(27.0 * b)) - Float64(Float64(y * 9.0) * Float64(z * t))));
	else
		tmp = Float64(Float64(Float64(a * 27.0) * b) + Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * 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)
	tmp = 0.0;
	if (z <= -5e-211)
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((y * 9.0) * (z * t)));
	else
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (((y * 9.0) * 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_] := If[LessEqual[z, -5e-211], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000002e-211

   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. associate-+l- 94.7%

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

      2. sub-neg 94.7%

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

      3. neg-mul-1 94.7%

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

      4. metadata-eval 94.7%

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

      5. metadata-eval 94.7%

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

      6. cancel-sign-sub-inv 94.7%

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

      7. metadata-eval 94.7%

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

      8. *-lft-identity 94.7%

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

      9. associate-*l* 92.8%

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

      10. associate-*l* 92.8%

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

   3. Simplified 92.8%

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

   if -5.0000000000000002e-211 < z

   1. Initial program 94.4%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-211}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \end{array} \]

Alternative 9: 73.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{-53}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{-23}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \end{array} \end{array} \]

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 (- (* x 2.0) (* a (* b -27.0)))))
   (if (<= z -9e-53)
     (* -9.0 (* y (* z t)))
     (if (<= z 2.25e-63)
       t_1
       (if (<= z 3.95e-23)
         (* t (* (* y z) -9.0))
         (if (<= z 1.6e+35) t_1 (* 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 = (x * 2.0) - (a * (b * -27.0));
	double tmp;
	if (z <= -9e-53) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 2.25e-63) {
		tmp = t_1;
	} else if (z <= 3.95e-23) {
		tmp = t * ((y * z) * -9.0);
	} else if (z <= 1.6e+35) {
		tmp = t_1;
	} 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 = (x * 2.0d0) - (a * (b * (-27.0d0)))
    if (z <= (-9d-53)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= 2.25d-63) then
        tmp = t_1
    else if (z <= 3.95d-23) then
        tmp = t * ((y * z) * (-9.0d0))
    else if (z <= 1.6d+35) then
        tmp = t_1
    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 = (x * 2.0) - (a * (b * -27.0));
	double tmp;
	if (z <= -9e-53) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 2.25e-63) {
		tmp = t_1;
	} else if (z <= 3.95e-23) {
		tmp = t * ((y * z) * -9.0);
	} else if (z <= 1.6e+35) {
		tmp = t_1;
	} 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 = (x * 2.0) - (a * (b * -27.0))
	tmp = 0
	if z <= -9e-53:
		tmp = -9.0 * (y * (z * t))
	elif z <= 2.25e-63:
		tmp = t_1
	elif z <= 3.95e-23:
		tmp = t * ((y * z) * -9.0)
	elif z <= 1.6e+35:
		tmp = t_1
	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(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)))
	tmp = 0.0
	if (z <= -9e-53)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= 2.25e-63)
		tmp = t_1;
	elseif (z <= 3.95e-23)
		tmp = Float64(t * Float64(Float64(y * z) * -9.0));
	elseif (z <= 1.6e+35)
		tmp = t_1;
	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 = (x * 2.0) - (a * (b * -27.0));
	tmp = 0.0;
	if (z <= -9e-53)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= 2.25e-63)
		tmp = t_1;
	elseif (z <= 3.95e-23)
		tmp = t * ((y * z) * -9.0);
	elseif (z <= 1.6e+35)
		tmp = t_1;
	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[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e-53], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e-63], t$95$1, If[LessEqual[z, 3.95e-23], N[(t * N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+35], t$95$1, N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.9999999999999997e-53

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. associate-*l* 91.6%

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

      3. fma-def 91.6%

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

      4. associate-*l* 88.5%

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

      5. *-commutative 88.5%

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

      6. associate-*l* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around inf 41.8%

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

   if -8.9999999999999997e-53 < z < 2.25e-63 or 3.9500000000000002e-23 < z < 1.59999999999999991e35

   1. Initial program 98.3%

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

      1. associate-+l- 98.3%

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

      2. sub-neg 98.3%

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

      3. neg-mul-1 98.3%

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

      4. metadata-eval 98.3%

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

      5. metadata-eval 98.3%

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

      6. cancel-sign-sub-inv 98.3%

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

      7. metadata-eval 98.3%

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

      8. *-lft-identity 98.3%

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

      9. associate-*l* 96.8%

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

      10. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in y around 0 79.9%

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

      1. *-commutative 79.9%

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

      2. associate-*l* 80.0%

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

   6. Simplified 80.0%

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

   if 2.25e-63 < z < 3.9500000000000002e-23

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l* 100.0%

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

      3. fma-def 100.0%

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

      4. associate-*l* 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 71.0%

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

   5. Taylor expanded in a around 0 41.8%

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

      1. associate-*r* 41.8%

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

      2. *-commutative 41.8%

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

      3. *-commutative 41.8%

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

      4. associate-*r* 41.7%

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

      5. *-commutative 41.7%

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

      6. *-commutative 41.7%

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

      7. associate-*l* 41.7%

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

   7. Simplified 41.7%

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

   if 1.59999999999999991e35 < 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 93.1%

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

      4. associate-*l* 93.3%

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

      5. *-commutative 93.3%

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

      6. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around inf 55.0%

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

      1. *-commutative 55.0%

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

      2. *-commutative 55.0%

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

      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 4 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-53}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-63}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{-23}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+35}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \end{array} \]

Alternative 10: 76.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -8.6 \cdot 10^{-52}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+57}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \end{array} \end{array} \]

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 -8.6e-52)
   (* 27.0 (* a b))
   (if (<= b 1.9e+57)
     (+ (* x 2.0) (* (* y z) (* t -9.0)))
     (- (* x 2.0) (* a (* b -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 <= -8.6e-52) {
		tmp = 27.0 * (a * b);
	} else if (b <= 1.9e+57) {
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	} else {
		tmp = (x * 2.0) - (a * (b * -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 <= (-8.6d-52)) then
        tmp = 27.0d0 * (a * b)
    else if (b <= 1.9d+57) then
        tmp = (x * 2.0d0) + ((y * z) * (t * (-9.0d0)))
    else
        tmp = (x * 2.0d0) - (a * (b * (-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 <= -8.6e-52) {
		tmp = 27.0 * (a * b);
	} else if (b <= 1.9e+57) {
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	} else {
		tmp = (x * 2.0) - (a * (b * -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 <= -8.6e-52:
		tmp = 27.0 * (a * b)
	elif b <= 1.9e+57:
		tmp = (x * 2.0) + ((y * z) * (t * -9.0))
	else:
		tmp = (x * 2.0) - (a * (b * -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 <= -8.6e-52)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (b <= 1.9e+57)
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(y * z) * Float64(t * -9.0)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -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 <= -8.6e-52)
		tmp = 27.0 * (a * b);
	elseif (b <= 1.9e+57)
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	else
		tmp = (x * 2.0) - (a * (b * -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, -8.6e-52], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e+57], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.6000000000000007e-52

   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. Step-by-step derivation

      1. +-commutative 95.7%

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

      2. associate-*l* 95.7%

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

      3. fma-def 98.5%

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

      4. associate-*l* 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* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in a around inf 50.3%

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

   if -8.6000000000000007e-52 < b < 1.8999999999999999e57

   1. Initial program 95.2%

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

      1. +-commutative 95.2%

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

      2. associate-*l* 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 95.2%

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

      4. associate-*l* 94.5%

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

      5. *-commutative 94.5%

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

      6. associate-*l* 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 a around 0 79.7%

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

      1. sub-neg 79.7%

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

      2. *-commutative 79.7%

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

      3. *-commutative 79.7%

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

      4. *-commutative 79.7%

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

      5. associate-*l* 79.7%

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

      6. *-commutative 79.7%

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

      7. +-commutative 79.7%

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

      8. distribute-rgt-neg-in 79.7%

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

      9. *-commutative 79.7%

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

      10. distribute-rgt-neg-in 79.7%

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

      11. metadata-eval 79.7%

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

      12. associate-*r* 79.7%

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

      13. associate-*r* 81.2%

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

      14. fma-def 81.2%

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

      15. *-commutative 81.2%

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

   6. Simplified 81.2%

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

      1. fma-udef 81.2%

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

   8. Applied egg-rr 81.2%

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

   if 1.8999999999999999e57 < b

   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* 90.4%

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

      10. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around 0 79.5%

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

      1. *-commutative 79.5%

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

      2. associate-*l* 79.5%

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

   6. Simplified 79.5%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.6 \cdot 10^{-52}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+57}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \end{array} \]

Alternative 11: 46.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{-103} \lor \neg \left(b \leq 1.52 \cdot 10^{-21}\right) \land \left(b \leq 8.8 \cdot 10^{+183} \lor \neg \left(b \leq 9.5 \cdot 10^{+203}\right)\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

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 (or (<= b -3.1e-103)
         (and (not (<= b 1.52e-21))
              (or (<= b 8.8e+183) (not (<= b 9.5e+203)))))
   (* 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 ((b <= -3.1e-103) || (!(b <= 1.52e-21) && ((b <= 8.8e+183) || !(b <= 9.5e+203)))) {
		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 ((b <= (-3.1d-103)) .or. (.not. (b <= 1.52d-21)) .and. (b <= 8.8d+183) .or. (.not. (b <= 9.5d+203))) 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 ((b <= -3.1e-103) || (!(b <= 1.52e-21) && ((b <= 8.8e+183) || !(b <= 9.5e+203)))) {
		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 (b <= -3.1e-103) or (not (b <= 1.52e-21) and ((b <= 8.8e+183) or not (b <= 9.5e+203))):
		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 ((b <= -3.1e-103) || (!(b <= 1.52e-21) && ((b <= 8.8e+183) || !(b <= 9.5e+203))))
		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 ((b <= -3.1e-103) || (~((b <= 1.52e-21)) && ((b <= 8.8e+183) || ~((b <= 9.5e+203)))))
		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[Or[LessEqual[b, -3.1e-103], And[N[Not[LessEqual[b, 1.52e-21]], $MachinePrecision], Or[LessEqual[b, 8.8e+183], N[Not[LessEqual[b, 9.5e+203]], $MachinePrecision]]]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.1000000000000001e-103 or 1.52000000000000009e-21 < b < 8.79999999999999962e183 or 9.4999999999999995e203 < b

   1. Initial program 93.8%

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

      1. +-commutative 93.8%

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

      2. associate-*l* 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 96.6%

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

      4. associate-*l* 96.6%

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

      5. *-commutative 96.6%

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

      6. associate-*l* 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in a around inf 56.3%

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

   if -3.1000000000000001e-103 < b < 1.52000000000000009e-21 or 8.79999999999999962e183 < b < 9.4999999999999995e203

   1. Initial program 95.5%

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

      1. +-commutative 95.5%

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

      2. associate-*l* 95.5%

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

      3. fma-def 95.5%

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

      4. associate-*l* 92.1%

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

      5. *-commutative 92.1%

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

      6. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in x around inf 46.6%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{-103} \lor \neg \left(b \leq 1.52 \cdot 10^{-21}\right) \land \left(b \leq 8.8 \cdot 10^{+183} \lor \neg \left(b \leq 9.5 \cdot 10^{+203}\right)\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 12: 46.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -2.75 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-21}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+203}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= b -2.75e-84)
     t_1
     (if (<= b 1.06e-21)
       (* x 2.0)
       (if (<= b 6e+183)
         t_1
         (if (<= b 9.5e+203) (* x 2.0) (* a (* 27.0 b))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (b <= -2.75e-84) {
		tmp = t_1;
	} else if (b <= 1.06e-21) {
		tmp = x * 2.0;
	} else if (b <= 6e+183) {
		tmp = t_1;
	} else if (b <= 9.5e+203) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (b <= (-2.75d-84)) then
        tmp = t_1
    else if (b <= 1.06d-21) then
        tmp = x * 2.0d0
    else if (b <= 6d+183) then
        tmp = t_1
    else if (b <= 9.5d+203) then
        tmp = x * 2.0d0
    else
        tmp = a * (27.0d0 * b)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (b <= -2.75e-84) {
		tmp = t_1;
	} else if (b <= 1.06e-21) {
		tmp = x * 2.0;
	} else if (b <= 6e+183) {
		tmp = t_1;
	} else if (b <= 9.5e+203) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if b <= -2.75e-84:
		tmp = t_1
	elif b <= 1.06e-21:
		tmp = x * 2.0
	elif b <= 6e+183:
		tmp = t_1
	elif b <= 9.5e+203:
		tmp = x * 2.0
	else:
		tmp = a * (27.0 * b)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (b <= -2.75e-84)
		tmp = t_1;
	elseif (b <= 1.06e-21)
		tmp = Float64(x * 2.0);
	elseif (b <= 6e+183)
		tmp = t_1;
	elseif (b <= 9.5e+203)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(a * Float64(27.0 * b));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (b <= -2.75e-84)
		tmp = t_1;
	elseif (b <= 1.06e-21)
		tmp = x * 2.0;
	elseif (b <= 6e+183)
		tmp = t_1;
	elseif (b <= 9.5e+203)
		tmp = x * 2.0;
	else
		tmp = a * (27.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.75e-84], t$95$1, If[LessEqual[b, 1.06e-21], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 6e+183], t$95$1, If[LessEqual[b, 9.5e+203], N[(x * 2.0), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.7500000000000001e-84 or 1.05999999999999994e-21 < b < 5.99999999999999992e183

   1. Initial program 94.9%

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

      1. +-commutative 94.9%

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

      2. associate-*l* 95.0%

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

      3. fma-def 97.5%

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

      4. associate-*l* 97.5%

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

      5. *-commutative 97.5%

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

      6. associate-*l* 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in a around inf 54.0%

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

   if -2.7500000000000001e-84 < b < 1.05999999999999994e-21 or 5.99999999999999992e183 < b < 9.4999999999999995e203

   1. Initial program 95.5%

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

      1. +-commutative 95.5%

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

      2. associate-*l* 95.5%

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

      3. fma-def 95.5%

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

      4. associate-*l* 92.1%

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

      5. *-commutative 92.1%

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

      6. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in x around inf 46.6%

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

   if 9.4999999999999995e203 < b

   1. Initial program 89.2%

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

      1. +-commutative 89.2%

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

      2. associate-*l* 89.2%

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

      3. fma-def 92.7%

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

      4. associate-*l* 92.9%

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

      5. *-commutative 92.9%

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

      6. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around 0 69.2%

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

      1. cancel-sign-sub-inv 69.2%

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

      2. associate-*r* 69.3%

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

      3. metadata-eval 69.3%

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

      4. add-sqr-sqrt 69.3%

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

      5. associate-*r* 69.3%

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

      6. fma-def 69.3%

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

      7. add-sqr-sqrt 47.3%

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

      8. sqrt-unprod 47.9%

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

      9. swap-sqr 47.9%

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

      10. metadata-eval 47.9%

          \[\leadsto \mathsf{fma}\left(\left(27 \cdot a\right) \cdot \sqrt{b}, \sqrt{b}, \sqrt{\color{blue}{81} \cdot \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}\right) \]

      11. metadata-eval 47.9%

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

      12. swap-sqr 47.9%

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

      13. sqrt-unprod 39.9%

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

      14. add-sqr-sqrt 61.9%

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

      15. *-commutative 61.9%

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

      16. associate-*l* 61.9%

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

   6. Applied egg-rr 61.9%

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

   7. Taylor expanded in a around inf 66.1%

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

      1. associate-*r* 66.3%

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

      2. *-commutative 66.3%

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

      3. associate-*l* 66.2%

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

   9. Simplified 66.2%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.75 \cdot 10^{-84}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-21}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+183}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+203}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]

Alternative 13: 46.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -7.9 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-22}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+203}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

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 (<= b -7.9e-87)
     t_1
     (if (<= b 5.2e-22)
       (* x 2.0)
       (if (<= b 8.8e+183)
         t_1
         (if (<= b 9.5e+203) (* x 2.0) (* (* a 27.0) b)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (b <= -7.9e-87) {
		tmp = t_1;
	} else if (b <= 5.2e-22) {
		tmp = x * 2.0;
	} else if (b <= 8.8e+183) {
		tmp = t_1;
	} else if (b <= 9.5e+203) {
		tmp = x * 2.0;
	} else {
		tmp = (a * 27.0) * b;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (b <= (-7.9d-87)) then
        tmp = t_1
    else if (b <= 5.2d-22) then
        tmp = x * 2.0d0
    else if (b <= 8.8d+183) then
        tmp = t_1
    else if (b <= 9.5d+203) then
        tmp = x * 2.0d0
    else
        tmp = (a * 27.0d0) * b
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (b <= -7.9e-87) {
		tmp = t_1;
	} else if (b <= 5.2e-22) {
		tmp = x * 2.0;
	} else if (b <= 8.8e+183) {
		tmp = t_1;
	} else if (b <= 9.5e+203) {
		tmp = x * 2.0;
	} else {
		tmp = (a * 27.0) * b;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if b <= -7.9e-87:
		tmp = t_1
	elif b <= 5.2e-22:
		tmp = x * 2.0
	elif b <= 8.8e+183:
		tmp = t_1
	elif b <= 9.5e+203:
		tmp = x * 2.0
	else:
		tmp = (a * 27.0) * b
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (b <= -7.9e-87)
		tmp = t_1;
	elseif (b <= 5.2e-22)
		tmp = Float64(x * 2.0);
	elseif (b <= 8.8e+183)
		tmp = t_1;
	elseif (b <= 9.5e+203)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(Float64(a * 27.0) * b);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (b <= -7.9e-87)
		tmp = t_1;
	elseif (b <= 5.2e-22)
		tmp = x * 2.0;
	elseif (b <= 8.8e+183)
		tmp = t_1;
	elseif (b <= 9.5e+203)
		tmp = x * 2.0;
	else
		tmp = (a * 27.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.9e-87], t$95$1, If[LessEqual[b, 5.2e-22], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 8.8e+183], t$95$1, If[LessEqual[b, 9.5e+203], N[(x * 2.0), $MachinePrecision], N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.90000000000000033e-87 or 5.2e-22 < b < 8.79999999999999962e183

   1. Initial program 94.9%

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

      1. +-commutative 94.9%

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

      2. associate-*l* 95.0%

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

      3. fma-def 97.5%

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

      4. associate-*l* 97.5%

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

      5. *-commutative 97.5%

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

      6. associate-*l* 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in a around inf 54.0%

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

   if -7.90000000000000033e-87 < b < 5.2e-22 or 8.79999999999999962e183 < b < 9.4999999999999995e203

   1. Initial program 95.5%

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

      1. +-commutative 95.5%

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

      2. associate-*l* 95.5%

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

      3. fma-def 95.5%

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

      4. associate-*l* 92.1%

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

      5. *-commutative 92.1%

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

      6. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in x around inf 46.6%

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

   if 9.4999999999999995e203 < b

   1. Initial program 89.2%

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

      1. +-commutative 89.2%

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

      2. associate-*l* 89.2%

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

      3. fma-def 92.7%

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

      4. associate-*l* 92.9%

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

      5. *-commutative 92.9%

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

      6. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around 0 69.2%

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

      1. cancel-sign-sub-inv 69.2%

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

      2. associate-*r* 69.3%

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

      3. metadata-eval 69.3%

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

      4. add-sqr-sqrt 69.3%

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

      5. associate-*r* 69.3%

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

      6. fma-def 69.3%

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

      7. add-sqr-sqrt 47.3%

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

      8. sqrt-unprod 47.9%

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

      9. swap-sqr 47.9%

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

      10. metadata-eval 47.9%

          \[\leadsto \mathsf{fma}\left(\left(27 \cdot a\right) \cdot \sqrt{b}, \sqrt{b}, \sqrt{\color{blue}{81} \cdot \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}\right) \]

      11. metadata-eval 47.9%

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

      12. swap-sqr 47.9%

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

      13. sqrt-unprod 39.9%

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

      14. add-sqr-sqrt 61.9%

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

      15. *-commutative 61.9%

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

      16. associate-*l* 61.9%

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

   6. Applied egg-rr 61.9%

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

   7. Taylor expanded in a around inf 66.1%

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

      1. *-commutative 66.1%

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

      2. *-commutative 66.1%

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

      3. associate-*l* 66.3%

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

   9. Simplified 66.3%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.9 \cdot 10^{-87}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-22}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+183}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+203}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b\\ \end{array} \]

Alternative 14: 31.6% 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 94.5%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
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* 94.5%

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

   3. fma-def 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* 94.7%

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

   5. *-commutative 94.7%

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

   6. associate-*l* 94.7%

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

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 x around inf 30.2%

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

5. Final simplification 30.2%

   \[\leadsto x \cdot 2 \]

Developer target: 94.7% 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 2023257 
(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)))