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

Percentage Accurate: 95.6% → 98.4%

Time: 10.4s

Alternatives: 12

Speedup: 0.9×

• 27.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+34}:\\ \;\;\;\;\left(x \cdot 2 - \left(9 \cdot \left(y \cdot z\right)\right) \cdot t\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, -9 \cdot \left(z \cdot t\right), t_1\right)\right)\\ \end{array} \end{array} \]

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 (* (* a 27.0) b)))
   (if (<= (* (* y 9.0) z) 5e+34)
     (+ (- (* x 2.0) (* (* 9.0 (* y z)) t)) t_1)
     (fma x 2.0 (fma y (* -9.0 (* z t)) t_1)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (((y * 9.0) * z) <= 5e+34) {
		tmp = ((x * 2.0) - ((9.0 * (y * z)) * t)) + t_1;
	} else {
		tmp = fma(x, 2.0, fma(y, (-9.0 * (z * t)), t_1));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 5e+34)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(9.0 * Float64(y * z)) * t)) + t_1);
	else
		tmp = fma(x, 2.0, fma(y, Float64(-9.0 * Float64(z * t)), t_1));
	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_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 5e+34], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x * 2.0 + N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 4.9999999999999998e34

   1. Initial program 97.9%

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

   2. Taylor expanded in y around 0 97.9%

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

      1. *-commutative 97.9%

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

   4. Simplified 97.9%

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

   if 4.9999999999999998e34 < (*.f64 (*.f64 y 9) z)

   1. Initial program 90.3%

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

      1. associate-+l- 90.3%

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

      2. fma-neg 90.3%

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

      3. neg-sub0 90.3%

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

      4. associate-+l- 90.3%

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

      5. neg-sub0 90.3%

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

      6. associate-*l* 98.3%

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

      7. associate-*l* 98.3%

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

      8. distribute-rgt-neg-in 98.3%

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

      9. fma-def 98.3%

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

      10. *-commutative 98.3%

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

      11. distribute-rgt-neg-in 98.3%

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

      12. metadata-eval 98.3%

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

   3. Simplified 98.3%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+34}:\\ \;\;\;\;\left(x \cdot 2 - \left(9 \cdot \left(y \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, -9 \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b\right)\right)\\ \end{array} \]

Alternative 2: 97.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+226}:\\ \;\;\;\;\left(x \cdot 2 - \left(9 \cdot \left(y \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (* y 9.0) z) 5e+226)
   (+ (- (* x 2.0) (* (* 9.0 (* y z)) t)) (* (* a 27.0) b))
   (- (* 27.0 (* a b)) (* 9.0 (* y (* z t))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * 9.0) * z) <= 5e+226) {
		tmp = ((x * 2.0) - ((9.0 * (y * z)) * t)) + ((a * 27.0) * b);
	} else {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((y * 9.0d0) * z) <= 5d+226) then
        tmp = ((x * 2.0d0) - ((9.0d0 * (y * z)) * t)) + ((a * 27.0d0) * b)
    else
        tmp = (27.0d0 * (a * b)) - (9.0d0 * (y * (z * t)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * 9.0) * z) <= 5e+226) {
		tmp = ((x * 2.0) - ((9.0 * (y * z)) * t)) + ((a * 27.0) * b);
	} else {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if ((y * 9.0) * z) <= 5e+226:
		tmp = ((x * 2.0) - ((9.0 * (y * z)) * t)) + ((a * 27.0) * b)
	else:
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 5e+226)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(9.0 * Float64(y * z)) * t)) + Float64(Float64(a * 27.0) * b));
	else
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * Float64(y * Float64(z * t))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((y * 9.0) * z) <= 5e+226)
		tmp = ((x * 2.0) - ((9.0 * (y * z)) * t)) + ((a * 27.0) * b);
	else
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 5e+226], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 5.0000000000000005e226

   1. Initial program 98.1%

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

   2. Taylor expanded in y around 0 98.2%

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

      1. *-commutative 98.2%

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

   4. Simplified 98.2%

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

   if 5.0000000000000005e226 < (*.f64 (*.f64 y 9) z)

   1. Initial program 79.8%

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

      1. associate-+l- 79.8%

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

      2. sub-neg 79.8%

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

      3. neg-mul-1 79.8%

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

      4. metadata-eval 79.8%

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

      5. metadata-eval 79.8%

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

      6. cancel-sign-sub-inv 79.8%

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

      7. metadata-eval 79.8%

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

      8. *-lft-identity 79.8%

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

      9. associate-*l* 99.8%

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

      10. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 96.5%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+226}:\\ \;\;\;\;\left(x \cdot 2 - \left(9 \cdot \left(y \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 3: 96.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 8.2 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + \left(x \cdot 2 + 27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 8.2e+27)
   (+ (* y (* t (* z -9.0))) (+ (* x 2.0) (* 27.0 (* a b))))
   (+ (* x 2.0) (* t (* (* y z) -9.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 8.2e+27) {
		tmp = (y * (t * (z * -9.0))) + ((x * 2.0) + (27.0 * (a * b)));
	} else {
		tmp = (x * 2.0) + (t * ((y * z) * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 8.2d+27) then
        tmp = (y * (t * (z * (-9.0d0)))) + ((x * 2.0d0) + (27.0d0 * (a * b)))
    else
        tmp = (x * 2.0d0) + (t * ((y * z) * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 8.2e+27) {
		tmp = (y * (t * (z * -9.0))) + ((x * 2.0) + (27.0 * (a * b)));
	} else {
		tmp = (x * 2.0) + (t * ((y * z) * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 8.2e+27:
		tmp = (y * (t * (z * -9.0))) + ((x * 2.0) + (27.0 * (a * b)))
	else:
		tmp = (x * 2.0) + (t * ((y * z) * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 8.2e+27)
		tmp = Float64(Float64(y * Float64(t * Float64(z * -9.0))) + Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b))));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(t * Float64(Float64(y * z) * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 8.2e+27)
		tmp = (y * (t * (z * -9.0))) + ((x * 2.0) + (27.0 * (a * b)));
	else
		tmp = (x * 2.0) + (t * ((y * z) * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 8.2e+27], N[(N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(t * N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.2000000000000005e27

   1. Initial program 97.6%

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

      1. associate-+l- 97.6%

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

      2. fma-neg 97.6%

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

      3. neg-sub0 97.6%

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

      4. associate-+l- 97.6%

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

      5. neg-sub0 97.6%

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

      6. *-commutative 97.6%

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

      7. distribute-rgt-neg-in 97.6%

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

      8. fma-def 97.6%

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

      9. *-commutative 97.6%

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

      10. associate-*r* 97.6%

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

      11. distribute-rgt-neg-in 97.6%

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

      12. *-commutative 97.6%

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

      13. metadata-eval 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in t around 0 96.7%

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

      1. +-commutative 96.7%

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

      2. fma-def 96.7%

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

      3. *-commutative 96.7%

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

      4. associate-*r* 97.7%

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

      5. associate-*l* 97.7%

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

      6. *-commutative 97.7%

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

      7. associate-*r* 97.7%

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

   6. Simplified 97.7%

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

      1. fma-udef 97.7%

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

      2. fma-udef 97.7%

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

      3. associate-*r* 97.7%

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

      4. *-commutative 97.7%

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

      5. associate-+r+ 97.7%

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

      6. *-commutative 97.7%

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

      7. associate-*l* 97.7%

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

      8. associate-*l* 96.6%

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

   8. Applied egg-rr 96.6%

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

   if 8.2000000000000005e27 < z

   1. Initial program 92.5%

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

      1. associate-+l- 92.5%

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

      2. sub-neg 92.5%

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

      3. neg-mul-1 92.5%

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

      4. metadata-eval 92.5%

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

      5. metadata-eval 92.5%

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

      6. cancel-sign-sub-inv 92.5%

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

      7. metadata-eval 92.5%

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

      8. *-lft-identity 92.5%

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

      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* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in a around 0 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-*r* 76.0%

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

      3. associate-*l* 76.1%

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

      4. *-commutative 76.1%

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

      5. sub-neg 76.1%

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

      6. *-commutative 76.1%

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

      7. *-commutative 76.1%

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

      8. distribute-rgt-neg-in 76.1%

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

      9. distribute-rgt-neg-in 76.1%

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

      10. metadata-eval 76.1%

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

   6. Applied egg-rr 76.1%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8.2 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + \left(x \cdot 2 + 27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \end{array} \]

Alternative 4: 98.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right) + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x 2.0) (* 27.0 (* a b)))))
   (if (<= y -5e+31)
     (+ (* y (* t (* z -9.0))) t_1)
     (+ (* z (* y (* t -9.0))) t_1))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) + (27.0 * (a * b));
	double tmp;
	if (y <= -5e+31) {
		tmp = (y * (t * (z * -9.0))) + t_1;
	} else {
		tmp = (z * (y * (t * -9.0))) + t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) + (27.0d0 * (a * b))
    if (y <= (-5d+31)) then
        tmp = (y * (t * (z * (-9.0d0)))) + t_1
    else
        tmp = (z * (y * (t * (-9.0d0)))) + t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) + (27.0 * (a * b));
	double tmp;
	if (y <= -5e+31) {
		tmp = (y * (t * (z * -9.0))) + t_1;
	} else {
		tmp = (z * (y * (t * -9.0))) + t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) + (27.0 * (a * b))
	tmp = 0
	if y <= -5e+31:
		tmp = (y * (t * (z * -9.0))) + t_1
	else:
		tmp = (z * (y * (t * -9.0))) + t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)))
	tmp = 0.0
	if (y <= -5e+31)
		tmp = Float64(Float64(y * Float64(t * Float64(z * -9.0))) + t_1);
	else
		tmp = Float64(Float64(z * Float64(y * Float64(t * -9.0))) + t_1);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) + (27.0 * (a * b));
	tmp = 0.0;
	if (y <= -5e+31)
		tmp = (y * (t * (z * -9.0))) + t_1;
	else
		tmp = (z * (y * (t * -9.0))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+31], N[(N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000000027e31

   1. Initial program 91.4%

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

      1. associate-+l- 91.4%

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

      2. fma-neg 91.4%

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

      3. neg-sub0 91.4%

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

      4. associate-+l- 91.4%

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

      5. neg-sub0 91.4%

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

      6. *-commutative 91.4%

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

      7. distribute-rgt-neg-in 91.4%

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

      8. fma-def 91.4%

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

      9. *-commutative 91.4%

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

      10. associate-*r* 91.4%

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

      11. distribute-rgt-neg-in 91.4%

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

      12. *-commutative 91.4%

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

      13. metadata-eval 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in t around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-*r* 91.4%

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

      5. associate-*l* 91.5%

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

      6. *-commutative 91.5%

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

      7. associate-*r* 91.4%

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

   6. Simplified 91.4%

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

      1. fma-udef 91.4%

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

      2. fma-udef 91.4%

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

      3. associate-*r* 91.5%

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

      4. *-commutative 91.5%

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

      5. associate-+r+ 91.5%

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

      6. *-commutative 91.5%

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

      7. associate-*l* 91.4%

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

      8. associate-*l* 99.9%

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

   8. Applied egg-rr 99.9%

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

   if -5.00000000000000027e31 < y

   1. Initial program 97.7%

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

      1. associate-+l- 97.7%

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

      2. fma-neg 97.7%

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

      3. neg-sub0 97.7%

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

      4. associate-+l- 97.7%

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

      5. neg-sub0 97.7%

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

      6. *-commutative 97.7%

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

      7. distribute-rgt-neg-in 97.7%

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

      8. fma-def 97.7%

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

      9. *-commutative 97.7%

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

      10. associate-*r* 97.7%

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

      11. distribute-rgt-neg-in 97.7%

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

      12. *-commutative 97.7%

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

      13. metadata-eval 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in t around 0 92.9%

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

      1. +-commutative 92.9%

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

      2. fma-def 92.9%

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

      3. *-commutative 92.9%

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

      4. associate-*r* 97.7%

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

      5. associate-*l* 97.8%

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

      6. *-commutative 97.8%

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

      7. associate-*r* 97.7%

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

   6. Simplified 97.7%

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

      1. fma-udef 97.7%

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

      2. fma-udef 97.7%

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

      3. associate-*r* 97.8%

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

      4. *-commutative 97.8%

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

      5. associate-+r+ 97.8%

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

      6. *-commutative 97.8%

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

      7. associate-*l* 97.8%

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

      8. associate-*l* 92.9%

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

   8. Applied egg-rr 92.9%

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

   9. Taylor expanded in y around 0 92.9%

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

       1. associate-*r* 97.3%

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

       2. *-commutative 97.3%

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

       3. associate-*r* 96.8%

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

       4. associate-*l* 96.8%

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

       5. *-commutative 96.8%

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

       6. *-commutative 96.8%

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

   11. Simplified 96.8%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right) + \left(x \cdot 2 + 27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right) + \left(x \cdot 2 + 27 \cdot \left(a \cdot b\right)\right)\\ \end{array} \]

Alternative 5: 98.1% accurate, 0.9× speedup

Math

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

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 (<= t 1e+64)
   (+ (* y (* t (* z -9.0))) (+ (* x 2.0) (* 27.0 (* a b))))
   (+ (* (* 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 (t <= 1e+64) {
		tmp = (y * (t * (z * -9.0))) + ((x * 2.0) + (27.0 * (a * b)));
	} 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 (t <= 1d+64) then
        tmp = (y * (t * (z * (-9.0d0)))) + ((x * 2.0d0) + (27.0d0 * (a * b)))
    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 (t <= 1e+64) {
		tmp = (y * (t * (z * -9.0))) + ((x * 2.0) + (27.0 * (a * b)));
	} 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 t <= 1e+64:
		tmp = (y * (t * (z * -9.0))) + ((x * 2.0) + (27.0 * (a * b)))
	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 (t <= 1e+64)
		tmp = Float64(Float64(y * Float64(t * Float64(z * -9.0))) + Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b))));
	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 (t <= 1e+64)
		tmp = (y * (t * (z * -9.0))) + ((x * 2.0) + (27.0 * (a * b)));
	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[t, 1e+64], N[(N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $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 t < 1.00000000000000002e64

   1. Initial program 95.1%

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

      1. associate-+l- 95.1%

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

      2. fma-neg 95.1%

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

      3. neg-sub0 95.1%

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

      4. associate-+l- 95.1%

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

      5. neg-sub0 95.1%

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

      6. *-commutative 95.1%

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

      7. distribute-rgt-neg-in 95.1%

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

      8. fma-def 95.1%

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

      9. *-commutative 95.1%

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

      10. associate-*r* 95.1%

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

      11. distribute-rgt-neg-in 95.1%

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

      12. *-commutative 95.1%

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

      13. metadata-eval 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in t around 0 97.6%

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

      1. +-commutative 97.6%

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

      2. fma-def 97.6%

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

      3. *-commutative 97.6%

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

      4. associate-*r* 95.1%

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

      5. associate-*l* 95.2%

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

      6. *-commutative 95.2%

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

      7. associate-*r* 95.1%

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

   6. Simplified 95.1%

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

      1. fma-udef 95.1%

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

      2. fma-udef 95.1%

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

      3. associate-*r* 95.2%

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

      4. *-commutative 95.2%

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

      5. associate-+r+ 95.2%

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

      6. *-commutative 95.2%

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

      7. associate-*l* 95.2%

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

      8. associate-*l* 97.6%

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

   8. Applied egg-rr 97.6%

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

   if 1.00000000000000002e64 < t

   1. Initial program 99.8%

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

4. Final simplification 98.0%

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

Alternative 6: 46.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-199}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+38} \lor \neg \left(t \leq 1.06 \cdot 10^{+67}\right) \land t \leq 1.2 \cdot 10^{+119}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* y (* z t)))))
   (if (<= t -1.15e-95)
     t_1
     (if (<= t 5.8e-199)
       (* x 2.0)
       (if (or (<= t 2.2e+38) (and (not (<= t 1.06e+67)) (<= t 1.2e+119)))
         (* 27.0 (* a b))
         t_1)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double tmp;
	if (t <= -1.15e-95) {
		tmp = t_1;
	} else if (t <= 5.8e-199) {
		tmp = x * 2.0;
	} else if ((t <= 2.2e+38) || (!(t <= 1.06e+67) && (t <= 1.2e+119))) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-9.0d0) * (y * (z * t))
    if (t <= (-1.15d-95)) then
        tmp = t_1
    else if (t <= 5.8d-199) then
        tmp = x * 2.0d0
    else if ((t <= 2.2d+38) .or. (.not. (t <= 1.06d+67)) .and. (t <= 1.2d+119)) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double tmp;
	if (t <= -1.15e-95) {
		tmp = t_1;
	} else if (t <= 5.8e-199) {
		tmp = x * 2.0;
	} else if ((t <= 2.2e+38) || (!(t <= 1.06e+67) && (t <= 1.2e+119))) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (y * (z * t))
	tmp = 0
	if t <= -1.15e-95:
		tmp = t_1
	elif t <= 5.8e-199:
		tmp = x * 2.0
	elif (t <= 2.2e+38) or (not (t <= 1.06e+67) and (t <= 1.2e+119)):
		tmp = 27.0 * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(y * Float64(z * t)))
	tmp = 0.0
	if (t <= -1.15e-95)
		tmp = t_1;
	elseif (t <= 5.8e-199)
		tmp = Float64(x * 2.0);
	elseif ((t <= 2.2e+38) || (!(t <= 1.06e+67) && (t <= 1.2e+119)))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (y * (z * t));
	tmp = 0.0;
	if (t <= -1.15e-95)
		tmp = t_1;
	elseif (t <= 5.8e-199)
		tmp = x * 2.0;
	elseif ((t <= 2.2e+38) || (~((t <= 1.06e+67)) && (t <= 1.2e+119)))
		tmp = 27.0 * (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e-95], t$95$1, If[LessEqual[t, 5.8e-199], N[(x * 2.0), $MachinePrecision], If[Or[LessEqual[t, 2.2e+38], And[N[Not[LessEqual[t, 1.06e+67]], $MachinePrecision], LessEqual[t, 1.2e+119]]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15e-95 or 2.20000000000000006e38 < t < 1.0599999999999999e67 or 1.2e119 < t

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 99.1%

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

      1. *-commutative 99.1%

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

   4. Simplified 99.1%

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

   5. Taylor expanded in y around inf 54.0%

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

   if -1.15e-95 < t < 5.8e-199

   1. Initial program 89.8%

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

      1. associate-+l- 89.8%

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

      2. fma-neg 89.8%

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

      3. neg-sub0 89.8%

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

      4. associate-+l- 89.8%

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

      5. neg-sub0 89.8%

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

      6. *-commutative 89.8%

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

      7. distribute-rgt-neg-in 89.8%

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

      8. fma-def 89.8%

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

      9. *-commutative 89.8%

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

      10. associate-*r* 89.9%

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

      11. distribute-rgt-neg-in 89.9%

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

      12. *-commutative 89.9%

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

      13. metadata-eval 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in x around inf 55.7%

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

   if 5.8e-199 < t < 2.20000000000000006e38 or 1.0599999999999999e67 < t < 1.2e119

   1. Initial program 96.6%

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

   2. Taylor expanded in y around 0 96.7%

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

      1. *-commutative 96.7%

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

   4. Simplified 96.7%

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

   5. Taylor expanded in a around inf 44.0%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-95}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-199}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+38} \lor \neg \left(t \leq 1.06 \cdot 10^{+67}\right) \land t \leq 1.2 \cdot 10^{+119}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 7: 46.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{-91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{-205}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \end{array} \end{array} \]

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))) (t_2 (* -9.0 (* y (* z t)))))
   (if (<= t -2.6e-91)
     t_2
     (if (<= t 3.45e-205)
       (* x 2.0)
       (if (<= t 2.8e+38)
         t_1
         (if (<= t 3.6e+65)
           t_2
           (if (<= t 2e+116) t_1 (* (* z t) (* y -9.0)))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (y * (z * t));
	double tmp;
	if (t <= -2.6e-91) {
		tmp = t_2;
	} else if (t <= 3.45e-205) {
		tmp = x * 2.0;
	} else if (t <= 2.8e+38) {
		tmp = t_1;
	} else if (t <= 3.6e+65) {
		tmp = t_2;
	} else if (t <= 2e+116) {
		tmp = t_1;
	} else {
		tmp = (z * t) * (y * -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) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = (-9.0d0) * (y * (z * t))
    if (t <= (-2.6d-91)) then
        tmp = t_2
    else if (t <= 3.45d-205) then
        tmp = x * 2.0d0
    else if (t <= 2.8d+38) then
        tmp = t_1
    else if (t <= 3.6d+65) then
        tmp = t_2
    else if (t <= 2d+116) then
        tmp = t_1
    else
        tmp = (z * t) * (y * (-9.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (y * (z * t));
	double tmp;
	if (t <= -2.6e-91) {
		tmp = t_2;
	} else if (t <= 3.45e-205) {
		tmp = x * 2.0;
	} else if (t <= 2.8e+38) {
		tmp = t_1;
	} else if (t <= 3.6e+65) {
		tmp = t_2;
	} else if (t <= 2e+116) {
		tmp = t_1;
	} else {
		tmp = (z * t) * (y * -9.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = -9.0 * (y * (z * t))
	tmp = 0
	if t <= -2.6e-91:
		tmp = t_2
	elif t <= 3.45e-205:
		tmp = x * 2.0
	elif t <= 2.8e+38:
		tmp = t_1
	elif t <= 3.6e+65:
		tmp = t_2
	elif t <= 2e+116:
		tmp = t_1
	else:
		tmp = (z * t) * (y * -9.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(-9.0 * Float64(y * Float64(z * t)))
	tmp = 0.0
	if (t <= -2.6e-91)
		tmp = t_2;
	elseif (t <= 3.45e-205)
		tmp = Float64(x * 2.0);
	elseif (t <= 2.8e+38)
		tmp = t_1;
	elseif (t <= 3.6e+65)
		tmp = t_2;
	elseif (t <= 2e+116)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * t) * Float64(y * -9.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = -9.0 * (y * (z * t));
	tmp = 0.0;
	if (t <= -2.6e-91)
		tmp = t_2;
	elseif (t <= 3.45e-205)
		tmp = x * 2.0;
	elseif (t <= 2.8e+38)
		tmp = t_1;
	elseif (t <= 3.6e+65)
		tmp = t_2;
	elseif (t <= 2e+116)
		tmp = t_1;
	else
		tmp = (z * t) * (y * -9.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e-91], t$95$2, If[LessEqual[t, 3.45e-205], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 2.8e+38], t$95$1, If[LessEqual[t, 3.6e+65], t$95$2, If[LessEqual[t, 2e+116], t$95$1, N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.60000000000000014e-91 or 2.8e38 < t < 3.59999999999999978e65

   1. Initial program 98.7%

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

   2. Taylor expanded in y around 0 98.7%

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

      1. *-commutative 98.7%

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

   4. Simplified 98.7%

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

   5. Taylor expanded in y around inf 48.9%

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

   if -2.60000000000000014e-91 < t < 3.4499999999999999e-205

   1. Initial program 91.2%

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

      1. associate-+l- 91.2%

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

      2. fma-neg 91.2%

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

      3. neg-sub0 91.2%

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

      4. associate-+l- 91.2%

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

      5. neg-sub0 91.2%

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

      6. *-commutative 91.2%

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

      7. distribute-rgt-neg-in 91.2%

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

      8. fma-def 91.2%

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

      9. *-commutative 91.2%

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

      10. associate-*r* 91.2%

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

      11. distribute-rgt-neg-in 91.2%

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

      12. *-commutative 91.2%

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

      13. metadata-eval 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in x around inf 53.6%

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

   if 3.4499999999999999e-205 < t < 2.8e38 or 3.59999999999999978e65 < t < 2.00000000000000003e116

   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. Taylor expanded in y around 0 95.2%

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

      1. *-commutative 95.2%

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

   4. Simplified 95.2%

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

   5. Taylor expanded in a around inf 42.0%

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

   if 2.00000000000000003e116 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. *-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around inf 65.8%

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

      1. associate-*r* 65.8%

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

   7. Simplified 65.8%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-91}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{-205}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+38}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+65}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+116}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \end{array} \]

Alternative 8: 77.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-97} \lor \neg \left(z \leq 1.5 \cdot 10^{-78}\right):\\ \;\;\;\;x \cdot 2 + t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.2e-97) (not (<= z 1.5e-78)))
   (+ (* x 2.0) (* t (* (* y z) -9.0)))
   (+ (* x 2.0) (* 27.0 (* a b)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.2e-97) || !(z <= 1.5e-78)) {
		tmp = (x * 2.0) + (t * ((y * z) * -9.0));
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-5.2d-97)) .or. (.not. (z <= 1.5d-78))) then
        tmp = (x * 2.0d0) + (t * ((y * z) * (-9.0d0)))
    else
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.2e-97) || !(z <= 1.5e-78)) {
		tmp = (x * 2.0) + (t * ((y * z) * -9.0));
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.2e-97) or not (z <= 1.5e-78):
		tmp = (x * 2.0) + (t * ((y * z) * -9.0))
	else:
		tmp = (x * 2.0) + (27.0 * (a * b))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.2e-97) || !(z <= 1.5e-78))
		tmp = Float64(Float64(x * 2.0) + Float64(t * Float64(Float64(y * z) * -9.0)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.2e-97) || ~((z <= 1.5e-78)))
		tmp = (x * 2.0) + (t * ((y * z) * -9.0));
	else
		tmp = (x * 2.0) + (27.0 * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.2e-97], N[Not[LessEqual[z, 1.5e-78]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(t * N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000014e-97 or 1.49999999999999994e-78 < z

   1. Initial program 94.1%

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

      1. associate-+l- 94.1%

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

      2. sub-neg 94.1%

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

      3. neg-mul-1 94.1%

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

      4. metadata-eval 94.1%

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

      5. metadata-eval 94.1%

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

      6. cancel-sign-sub-inv 94.1%

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

      7. metadata-eval 94.1%

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

      8. *-lft-identity 94.1%

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

      9. associate-*l* 92.0%

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

      10. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in a around 0 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-*r* 73.9%

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

      3. associate-*l* 74.0%

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

      4. *-commutative 74.0%

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

      5. sub-neg 74.0%

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

      6. *-commutative 74.0%

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

      7. *-commutative 74.0%

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

      8. distribute-rgt-neg-in 74.0%

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

      9. distribute-rgt-neg-in 74.0%

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

      10. metadata-eval 74.0%

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

   6. Applied egg-rr 74.0%

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

   if -5.20000000000000014e-97 < z < 1.49999999999999994e-78

   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. associate-+l- 99.8%

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

      2. fma-neg 99.8%

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

      3. neg-sub0 99.8%

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

      4. associate-+l- 99.8%

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

      5. neg-sub0 99.8%

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

      6. *-commutative 99.8%

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

      7. distribute-rgt-neg-in 99.8%

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

      8. fma-def 99.8%

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

      9. *-commutative 99.8%

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

      10. associate-*r* 99.8%

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

      11. distribute-rgt-neg-in 99.8%

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

      12. *-commutative 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 92.1%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-97} \lor \neg \left(z \leq 1.5 \cdot 10^{-78}\right):\\ \;\;\;\;x \cdot 2 + t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 9: 79.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-97}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-82}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \end{array} \end{array} \]

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-97)
   (- (* x 2.0) (* 9.0 (* y (* z t))))
   (if (<= z 8e-82)
     (+ (* x 2.0) (* 27.0 (* a b)))
     (+ (* x 2.0) (* t (* (* y z) -9.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5e-97) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (z <= 8e-82) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) + (t * ((y * z) * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-5d-97)) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else if (z <= 8d-82) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) + (t * ((y * z) * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5e-97) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (z <= 8e-82) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) + (t * ((y * z) * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5e-97:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	elif z <= 8e-82:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) + (t * ((y * z) * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5e-97)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	elseif (z <= 8e-82)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(t * Float64(Float64(y * z) * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5e-97)
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	elseif (z <= 8e-82)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) + (t * ((y * z) * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5e-97], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-82], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(t * N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.9999999999999995e-97

   1. Initial program 94.8%

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

      1. associate-+l- 94.8%

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

      2. sub-neg 94.8%

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

      3. neg-mul-1 94.8%

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

      4. metadata-eval 94.8%

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

      5. metadata-eval 94.8%

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

      6. cancel-sign-sub-inv 94.8%

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

      7. metadata-eval 94.8%

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

      8. *-lft-identity 94.8%

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

      9. associate-*l* 92.4%

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

      10. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in a around 0 71.5%

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

   if -4.9999999999999995e-97 < z < 8e-82

   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. associate-+l- 99.8%

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

      2. fma-neg 99.8%

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

      3. neg-sub0 99.8%

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

      4. associate-+l- 99.8%

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

      5. neg-sub0 99.8%

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

      6. *-commutative 99.8%

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

      7. distribute-rgt-neg-in 99.8%

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

      8. fma-def 99.8%

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

      9. *-commutative 99.8%

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

      10. associate-*r* 99.8%

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

      11. distribute-rgt-neg-in 99.8%

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

      12. *-commutative 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 92.1%

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

   if 8e-82 < z

   1. Initial program 93.5%

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

      1. associate-+l- 93.5%

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

      2. sub-neg 93.5%

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

      3. neg-mul-1 93.5%

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

      4. metadata-eval 93.5%

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

      5. metadata-eval 93.5%

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

      6. cancel-sign-sub-inv 93.5%

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

      7. metadata-eval 93.5%

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

      8. *-lft-identity 93.5%

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

      9. associate-*l* 91.8%

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

      10. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in a around 0 70.9%

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

      1. *-commutative 70.9%

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

      2. associate-*r* 75.1%

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

      3. associate-*l* 75.2%

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

      4. *-commutative 75.2%

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

      5. sub-neg 75.2%

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

      6. *-commutative 75.2%

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

      7. *-commutative 75.2%

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

      8. distribute-rgt-neg-in 75.2%

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

      9. distribute-rgt-neg-in 75.2%

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

      10. metadata-eval 75.2%

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

   6. Applied egg-rr 75.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-97}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-82}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \end{array} \]

Alternative 10: 47.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+162} \lor \neg \left(a \leq -7.6 \cdot 10^{+142} \lor \neg \left(a \leq -3 \cdot 10^{+44}\right) \land a \leq 1.5 \cdot 10^{-127}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

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 (<= a -6e+162)
         (not (or (<= a -7.6e+142) (and (not (<= a -3e+44)) (<= a 1.5e-127)))))
   (* 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 ((a <= -6e+162) || !((a <= -7.6e+142) || (!(a <= -3e+44) && (a <= 1.5e-127)))) {
		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 ((a <= (-6d+162)) .or. (.not. (a <= (-7.6d+142)) .or. (.not. (a <= (-3d+44))) .and. (a <= 1.5d-127))) 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 ((a <= -6e+162) || !((a <= -7.6e+142) || (!(a <= -3e+44) && (a <= 1.5e-127)))) {
		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 (a <= -6e+162) or not ((a <= -7.6e+142) or (not (a <= -3e+44) and (a <= 1.5e-127))):
		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 ((a <= -6e+162) || !((a <= -7.6e+142) || (!(a <= -3e+44) && (a <= 1.5e-127))))
		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 ((a <= -6e+162) || ~(((a <= -7.6e+142) || (~((a <= -3e+44)) && (a <= 1.5e-127)))))
		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[a, -6e+162], N[Not[Or[LessEqual[a, -7.6e+142], And[N[Not[LessEqual[a, -3e+44]], $MachinePrecision], LessEqual[a, 1.5e-127]]]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.9999999999999996e162 or -7.59999999999999979e142 < a < -2.99999999999999987e44 or 1.50000000000000004e-127 < a

   1. Initial program 94.2%

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

   2. Taylor expanded in y around 0 94.1%

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

      1. *-commutative 94.1%

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

   4. Simplified 94.1%

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

   5. Taylor expanded in a around inf 49.7%

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

   if -5.9999999999999996e162 < a < -7.59999999999999979e142 or -2.99999999999999987e44 < a < 1.50000000000000004e-127

   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. fma-neg 98.3%

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

      3. neg-sub0 98.3%

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

      4. associate-+l- 98.3%

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

      5. neg-sub0 98.3%

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

      6. *-commutative 98.3%

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

      7. distribute-rgt-neg-in 98.3%

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

      8. fma-def 98.3%

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

      9. *-commutative 98.3%

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

      10. associate-*r* 98.3%

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

      11. distribute-rgt-neg-in 98.3%

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

      12. *-commutative 98.3%

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

      13. metadata-eval 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in x around inf 44.8%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+162} \lor \neg \left(a \leq -7.6 \cdot 10^{+142} \lor \neg \left(a \leq -3 \cdot 10^{+44}\right) \land a \leq 1.5 \cdot 10^{-127}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 11: 71.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+196} \lor \neg \left(y \leq 2.4 \cdot 10^{-111}\right):\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.4e+196) (not (<= y 2.4e-111)))
   (* -9.0 (* y (* z t)))
   (+ (* x 2.0) (* 27.0 (* a b)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.4e+196) || !(y <= 2.4e-111)) {
		tmp = -9.0 * (y * (z * t));
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.4d+196)) .or. (.not. (y <= 2.4d-111))) then
        tmp = (-9.0d0) * (y * (z * t))
    else
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.4e+196) || !(y <= 2.4e-111)) {
		tmp = -9.0 * (y * (z * t));
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.4e+196) or not (y <= 2.4e-111):
		tmp = -9.0 * (y * (z * t))
	else:
		tmp = (x * 2.0) + (27.0 * (a * b))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.4e+196) || !(y <= 2.4e-111))
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.4e+196) || ~((y <= 2.4e-111)))
		tmp = -9.0 * (y * (z * t));
	else
		tmp = (x * 2.0) + (27.0 * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.4e+196], N[Not[LessEqual[y, 2.4e-111]], $MachinePrecision]], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4e196 or 2.4000000000000001e-111 < y

   1. Initial program 95.1%

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

   2. Taylor expanded in y around 0 95.2%

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

      1. *-commutative 95.2%

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

   4. Simplified 95.2%

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

   5. Taylor expanded in y around inf 52.5%

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

   if -3.4e196 < y < 2.4000000000000001e-111

   1. Initial program 96.7%

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

      1. associate-+l- 96.7%

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

      2. fma-neg 96.7%

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

      3. neg-sub0 96.7%

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

      4. associate-+l- 96.7%

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

      5. neg-sub0 96.7%

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

      6. *-commutative 96.7%

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

      7. distribute-rgt-neg-in 96.7%

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

      8. fma-def 96.7%

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

      9. *-commutative 96.7%

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

      10. associate-*r* 96.7%

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

      11. distribute-rgt-neg-in 96.7%

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

      12. *-commutative 96.7%

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

      13. metadata-eval 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in t around 0 72.8%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+196} \lor \neg \left(y \leq 2.4 \cdot 10^{-111}\right):\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 12: 31.5% 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 96.1%

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

   1. associate-+l- 96.1%

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

   2. fma-neg 96.1%

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

   3. neg-sub0 96.1%

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

   4. associate-+l- 96.1%

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

   5. neg-sub0 96.1%

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

   6. *-commutative 96.1%

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

   7. distribute-rgt-neg-in 96.1%

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

   8. fma-def 96.1%

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

   9. *-commutative 96.1%

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

   10. associate-*r* 96.1%

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

   11. distribute-rgt-neg-in 96.1%

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

   12. *-commutative 96.1%

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

   13. metadata-eval 96.1%

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

3. Simplified 96.1%

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

4. Taylor expanded in x around inf 33.5%

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

5. Final simplification 33.5%

   \[\leadsto x \cdot 2 \]

Developer target: 95.1% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023228 
(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)))