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

Percentage Accurate: 95.9% → 98.5%

Time: 16.5s

Alternatives: 16

Speedup: 0.9×

• 28.1% 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: 95.9% 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: 98.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 5.6 \cdot 10^{-155}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(z \cdot y\right) \cdot -9, b \cdot \left(a \cdot 27\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 5.6e-155)
   (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t)))))
   (fma x 2.0 (fma t (* (* z y) -9.0) (* b (* a 27.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 5.6e-155) {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	} else {
		tmp = fma(x, 2.0, fma(t, ((z * y) * -9.0), (b * (a * 27.0))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 5.6e-155)
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	else
		tmp = fma(x, 2.0, fma(t, Float64(Float64(z * y) * -9.0), Float64(b * Float64(a * 27.0))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 5.6e-155], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 2.0 + N[(t * N[(N[(z * y), $MachinePrecision] * -9.0), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.5999999999999999e-155

   1. Initial program 93.1%

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

      1. +-commutative 93.1%

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

      2. associate-*l* 93.1%

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

      3. fma-def 94.3%

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

      4. associate-*l* 96.9%

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

      5. *-commutative 96.9%

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

      6. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   if 5.5999999999999999e-155 < z

   1. Initial program 88.5%

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

      1. associate-+l- 88.5%

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

      2. fma-neg 88.5%

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

      3. neg-sub0 88.5%

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

      4. associate-+l- 88.5%

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

      5. neg-sub0 88.5%

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

      6. *-commutative 88.5%

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

      7. distribute-rgt-neg-in 88.5%

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

      8. fma-def 88.5%

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

      9. *-commutative 88.5%

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

      10. associate-*r* 88.5%

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

      11. distribute-rgt-neg-in 88.5%

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

      12. *-commutative 88.5%

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

      13. metadata-eval 88.5%

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

   3. Simplified 88.5%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5.6 \cdot 10^{-155}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(z \cdot y\right) \cdot -9, b \cdot \left(a \cdot 27\right)\right)\right)\\ \end{array} \]

Alternative 2: 98.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 5.6 \cdot 10^{-155}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 5.6e-155)
   (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t)))))
   (+ (* b (* a 27.0)) (- (* x 2.0) (* t (* z (* 9.0 y)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 5.6e-155) {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (z * (9.0 * y))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 5.6e-155)
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	else
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(9.0 * y)))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 5.6e-155], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.5999999999999999e-155

   1. Initial program 93.1%

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

      1. +-commutative 93.1%

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

      2. associate-*l* 93.1%

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

      3. fma-def 94.3%

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

      4. associate-*l* 96.9%

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

      5. *-commutative 96.9%

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

      6. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   if 5.5999999999999999e-155 < z

   1. Initial program 88.5%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5.6 \cdot 10^{-155}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 3: 82.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(9 \cdot y\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-127}:\\ \;\;\;\;x \cdot 2 - t \cdot t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+44}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* 9.0 y))))
   (if (<= t_1 -5e-127)
     (- (* x 2.0) (* t t_1))
     (if (<= t_1 2e+44)
       (- (* x 2.0) (* (* a b) -27.0))
       (- (* x 2.0) (* 9.0 (* y (* z t))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (9.0 * y);
	double tmp;
	if (t_1 <= -5e-127) {
		tmp = (x * 2.0) - (t * t_1);
	} else if (t_1 <= 2e+44) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (9.0d0 * y)
    if (t_1 <= (-5d-127)) then
        tmp = (x * 2.0d0) - (t * t_1)
    else if (t_1 <= 2d+44) then
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (9.0 * y);
	double tmp;
	if (t_1 <= -5e-127) {
		tmp = (x * 2.0) - (t * t_1);
	} else if (t_1 <= 2e+44) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = z * (9.0 * y)
	tmp = 0
	if t_1 <= -5e-127:
		tmp = (x * 2.0) - (t * t_1)
	elif t_1 <= 2e+44:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	else:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(9.0 * y))
	tmp = 0.0
	if (t_1 <= -5e-127)
		tmp = Float64(Float64(x * 2.0) - Float64(t * t_1));
	elseif (t_1 <= 2e+44)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (9.0 * y);
	tmp = 0.0;
	if (t_1 <= -5e-127)
		tmp = (x * 2.0) - (t * t_1);
	elseif (t_1 <= 2e+44)
		tmp = (x * 2.0) - ((a * b) * -27.0);
	else
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-127], N[(N[(x * 2.0), $MachinePrecision] - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+44], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 y 9) z) < -4.9999999999999997e-127

   1. Initial program 84.4%

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

   2. Taylor expanded in a around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-*l* 68.8%

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

      4. *-commutative 68.8%

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

      5. *-commutative 68.8%

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

      6. associate-*r* 68.9%

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

      7. cancel-sign-sub-inv 68.9%

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

   4. Applied egg-rr 68.9%

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

      1. expm1-log1p-u 15.8%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)\right)}\right) \cdot t \]

      2. expm1-udef 8.1%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)} - 1\right)}\right) \cdot t \]

   6. Applied egg-rr 8.1%

      \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)} - 1\right)}\right) \cdot t \]
   7. Step-by-step derivation

      1. expm1-def 15.8%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)\right)}\right) \cdot t \]

      2. expm1-log1p 68.9%

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

      3. associate-*r* 68.8%

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

      4. *-commutative 68.8%

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

      5. associate-*l* 68.8%

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

   8. Simplified 68.8%

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

      1. distribute-lft-neg-out 68.8%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 18.7%

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

      4. sqr-neg 18.7%

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

      5. sqrt-unprod 18.7%

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

      6. add-sqr-sqrt 18.7%

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

      7. sub-neg 18.7%

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

      8. *-commutative 18.7%

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

      9. add-sqr-sqrt 18.7%

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

      10. sqrt-unprod 18.7%

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

      11. sqr-neg 18.7%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 68.8%

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

      14. associate-*r* 68.8%

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

   10. Applied egg-rr 68.8%

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

   if -4.9999999999999997e-127 < (*.f64 (*.f64 y 9) z) < 2.0000000000000002e44

   1. Initial program 98.0%

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

      1. associate-+l- 98.0%

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

      2. sub-neg 98.0%

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

      3. neg-mul-1 98.0%

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

      4. metadata-eval 98.0%

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

      5. metadata-eval 98.0%

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

      6. cancel-sign-sub-inv 98.0%

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

      7. metadata-eval 98.0%

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

      8. *-lft-identity 98.0%

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

      9. associate-*l* 99.0%

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

      10. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 87.3%

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

      1. *-commutative 87.3%

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

   6. Simplified 87.3%

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

   if 2.0000000000000002e44 < (*.f64 (*.f64 y 9) z)

   1. Initial program 86.9%

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

   2. Taylor expanded in a around 0 82.2%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(9 \cdot y\right) \leq -5 \cdot 10^{-127}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\\ \mathbf{elif}\;z \cdot \left(9 \cdot y\right) \leq 2 \cdot 10^{+44}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 4: 82.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(9 \cdot y\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-127}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+44}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* 9.0 y))))
   (if (<= t_1 -5e-127)
     (- (* x 2.0) (* t (* y (* z 9.0))))
     (if (<= t_1 2e+44)
       (- (* x 2.0) (* (* a b) -27.0))
       (- (* x 2.0) (* 9.0 (* y (* z t))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (9.0 * y);
	double tmp;
	if (t_1 <= -5e-127) {
		tmp = (x * 2.0) - (t * (y * (z * 9.0)));
	} else if (t_1 <= 2e+44) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (9.0d0 * y)
    if (t_1 <= (-5d-127)) then
        tmp = (x * 2.0d0) - (t * (y * (z * 9.0d0)))
    else if (t_1 <= 2d+44) then
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (9.0 * y);
	double tmp;
	if (t_1 <= -5e-127) {
		tmp = (x * 2.0) - (t * (y * (z * 9.0)));
	} else if (t_1 <= 2e+44) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = z * (9.0 * y)
	tmp = 0
	if t_1 <= -5e-127:
		tmp = (x * 2.0) - (t * (y * (z * 9.0)))
	elif t_1 <= 2e+44:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	else:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(9.0 * y))
	tmp = 0.0
	if (t_1 <= -5e-127)
		tmp = Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(z * 9.0))));
	elseif (t_1 <= 2e+44)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (9.0 * y);
	tmp = 0.0;
	if (t_1 <= -5e-127)
		tmp = (x * 2.0) - (t * (y * (z * 9.0)));
	elseif (t_1 <= 2e+44)
		tmp = (x * 2.0) - ((a * b) * -27.0);
	else
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-127], N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+44], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 y 9) z) < -4.9999999999999997e-127

   1. Initial program 84.4%

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

   2. Taylor expanded in a around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-*l* 68.8%

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

      4. *-commutative 68.8%

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

      5. *-commutative 68.8%

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

      6. associate-*r* 68.9%

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

      7. cancel-sign-sub-inv 68.9%

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

   4. Applied egg-rr 68.9%

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

      1. expm1-log1p-u 15.8%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)\right)}\right) \cdot t \]

      2. expm1-udef 8.1%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)} - 1\right)}\right) \cdot t \]

   6. Applied egg-rr 8.1%

      \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)} - 1\right)}\right) \cdot t \]
   7. Step-by-step derivation

      1. expm1-def 15.8%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)\right)}\right) \cdot t \]

      2. expm1-log1p 68.9%

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

      3. associate-*r* 68.8%

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

      4. *-commutative 68.8%

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

      5. associate-*l* 68.8%

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

   8. Simplified 68.8%

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

   if -4.9999999999999997e-127 < (*.f64 (*.f64 y 9) z) < 2.0000000000000002e44

   1. Initial program 98.0%

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

      1. associate-+l- 98.0%

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

      2. sub-neg 98.0%

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

      3. neg-mul-1 98.0%

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

      4. metadata-eval 98.0%

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

      5. metadata-eval 98.0%

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

      6. cancel-sign-sub-inv 98.0%

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

      7. metadata-eval 98.0%

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

      8. *-lft-identity 98.0%

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

      9. associate-*l* 99.0%

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

      10. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 87.3%

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

      1. *-commutative 87.3%

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

   6. Simplified 87.3%

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

   if 2.0000000000000002e44 < (*.f64 (*.f64 y 9) z)

   1. Initial program 86.9%

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

   2. Taylor expanded in a around 0 82.2%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(9 \cdot y\right) \leq -5 \cdot 10^{-127}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\\ \mathbf{elif}\;z \cdot \left(9 \cdot y\right) \leq 2 \cdot 10^{+44}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 5: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot \left(9 \cdot y\right) \leq 10^{+308}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

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 (<= (* z (* 9.0 y)) 1e+308)
   (+ (* b (* a 27.0)) (- (* x 2.0) (* t (* 9.0 (* z y)))))
   (- (* x 2.0) (* 9.0 (* y (* z t))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z * (9.0 * y)) <= 1e+308) {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (z * y))));
	} else {
		tmp = (x * 2.0) - (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 ((z * (9.0d0 * y)) <= 1d+308) then
        tmp = (b * (a * 27.0d0)) + ((x * 2.0d0) - (t * (9.0d0 * (z * y))))
    else
        tmp = (x * 2.0d0) - (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 ((z * (9.0 * y)) <= 1e+308) {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (z * y))));
	} else {
		tmp = (x * 2.0) - (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 (z * (9.0 * y)) <= 1e+308:
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (z * y))))
	else:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(z * Float64(9.0 * y)) <= 1e+308)
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(t * Float64(9.0 * Float64(z * y)))));
	else
		tmp = Float64(Float64(x * 2.0) - 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 ((z * (9.0 * y)) <= 1e+308)
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (z * y))));
	else
		tmp = (x * 2.0) - (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[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision], 1e+308], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $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) < 1e308

   1. Initial program 93.2%

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

   2. Taylor expanded in y around 0 93.3%

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

   if 1e308 < (*.f64 (*.f64 y 9) z)

   1. Initial program 61.1%

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

   2. Taylor expanded in a around 0 100.0%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(9 \cdot y\right) \leq 10^{+308}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 6: 47.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{+105}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.26 \cdot 10^{+29}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-287}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* y (* z t)))) (t_2 (* 27.0 (* a b))))
   (if (<= x -8.8e+105)
     (* x 2.0)
     (if (<= x -6.5e+46)
       t_2
       (if (<= x -1.26e+29)
         (* x 2.0)
         (if (<= x -5.5e-56)
           t_1
           (if (<= x 1.15e-287) t_2 (if (<= x 1.4e+80) t_1 (* x 2.0)))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (x <= -8.8e+105) {
		tmp = x * 2.0;
	} else if (x <= -6.5e+46) {
		tmp = t_2;
	} else if (x <= -1.26e+29) {
		tmp = x * 2.0;
	} else if (x <= -5.5e-56) {
		tmp = t_1;
	} else if (x <= 1.15e-287) {
		tmp = t_2;
	} else if (x <= 1.4e+80) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-9.0d0) * (y * (z * t))
    t_2 = 27.0d0 * (a * b)
    if (x <= (-8.8d+105)) then
        tmp = x * 2.0d0
    else if (x <= (-6.5d+46)) then
        tmp = t_2
    else if (x <= (-1.26d+29)) then
        tmp = x * 2.0d0
    else if (x <= (-5.5d-56)) then
        tmp = t_1
    else if (x <= 1.15d-287) then
        tmp = t_2
    else if (x <= 1.4d+80) then
        tmp = t_1
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (x <= -8.8e+105) {
		tmp = x * 2.0;
	} else if (x <= -6.5e+46) {
		tmp = t_2;
	} else if (x <= -1.26e+29) {
		tmp = x * 2.0;
	} else if (x <= -5.5e-56) {
		tmp = t_1;
	} else if (x <= 1.15e-287) {
		tmp = t_2;
	} else if (x <= 1.4e+80) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (y * (z * t))
	t_2 = 27.0 * (a * b)
	tmp = 0
	if x <= -8.8e+105:
		tmp = x * 2.0
	elif x <= -6.5e+46:
		tmp = t_2
	elif x <= -1.26e+29:
		tmp = x * 2.0
	elif x <= -5.5e-56:
		tmp = t_1
	elif x <= 1.15e-287:
		tmp = t_2
	elif x <= 1.4e+80:
		tmp = t_1
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(y * Float64(z * t)))
	t_2 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (x <= -8.8e+105)
		tmp = Float64(x * 2.0);
	elseif (x <= -6.5e+46)
		tmp = t_2;
	elseif (x <= -1.26e+29)
		tmp = Float64(x * 2.0);
	elseif (x <= -5.5e-56)
		tmp = t_1;
	elseif (x <= 1.15e-287)
		tmp = t_2;
	elseif (x <= 1.4e+80)
		tmp = t_1;
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (y * (z * t));
	t_2 = 27.0 * (a * b);
	tmp = 0.0;
	if (x <= -8.8e+105)
		tmp = x * 2.0;
	elseif (x <= -6.5e+46)
		tmp = t_2;
	elseif (x <= -1.26e+29)
		tmp = x * 2.0;
	elseif (x <= -5.5e-56)
		tmp = t_1;
	elseif (x <= 1.15e-287)
		tmp = t_2;
	elseif (x <= 1.4e+80)
		tmp = t_1;
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.8e+105], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -6.5e+46], t$95$2, If[LessEqual[x, -1.26e+29], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -5.5e-56], t$95$1, If[LessEqual[x, 1.15e-287], t$95$2, If[LessEqual[x, 1.4e+80], t$95$1, N[(x * 2.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.80000000000000027e105 or -6.50000000000000008e46 < x < -1.26e29 or 1.39999999999999992e80 < x

   1. Initial program 88.1%

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

   2. Taylor expanded in x around inf 60.7%

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

   if -8.80000000000000027e105 < x < -6.50000000000000008e46 or -5.4999999999999999e-56 < x < 1.14999999999999993e-287

   1. Initial program 90.6%

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

   2. Taylor expanded in a around inf 54.6%

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

   if -1.26e29 < x < -5.4999999999999999e-56 or 1.14999999999999993e-287 < x < 1.39999999999999992e80

   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 inf 53.6%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+105}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+46}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq -1.26 \cdot 10^{+29}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-56}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-287}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+80}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 7: 98.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-257}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \left(z \cdot t\right) \cdot \left(9 \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3e-257)
   (+ (* x 2.0) (- (* a (* 27.0 b)) (* (* z t) (* 9.0 y))))
   (+ (* b (* a 27.0)) (- (* x 2.0) (* t (* z (* 9.0 y)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3e-257) {
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((z * t) * (9.0 * y)));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (z * (9.0 * y))));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3d-257)) then
        tmp = (x * 2.0d0) + ((a * (27.0d0 * b)) - ((z * t) * (9.0d0 * y)))
    else
        tmp = (b * (a * 27.0d0)) + ((x * 2.0d0) - (t * (z * (9.0d0 * y))))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3e-257) {
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((z * t) * (9.0 * y)));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (z * (9.0 * y))));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3e-257:
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((z * t) * (9.0 * y)))
	else:
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (z * (9.0 * y))))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3e-257)
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(a * Float64(27.0 * b)) - Float64(Float64(z * t) * Float64(9.0 * y))));
	else
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(9.0 * y)))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3e-257)
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((z * t) * (9.0 * y)));
	else
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (z * (9.0 * y))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3e-257], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] - N[(N[(z * t), $MachinePrecision] * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9999999999999999e-257

   1. Initial program 92.6%

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

      1. associate-+l- 92.6%

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

      2. sub-neg 92.6%

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

      3. neg-mul-1 92.6%

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

      4. metadata-eval 92.6%

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

      5. metadata-eval 92.6%

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

      6. cancel-sign-sub-inv 92.6%

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

      7. metadata-eval 92.6%

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

      8. *-lft-identity 92.6%

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

      9. associate-*l* 95.2%

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

      10. associate-*l* 95.2%

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

   3. Simplified 95.2%

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

   if -2.9999999999999999e-257 < z

   1. Initial program 90.2%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-257}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \left(z \cdot t\right) \cdot \left(9 \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 8: 49.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{if}\;z \leq -15.2:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-106}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-194}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))) (t_2 (* -9.0 (* z (* y t)))))
   (if (<= z -15.2)
     t_2
     (if (<= z -2e-106)
       (* x 2.0)
       (if (<= z 1.4e-226)
         t_1
         (if (<= z 5.1e-194)
           (* -9.0 (* y (* z t)))
           (if (<= z 2.15e-54) t_1 t_2)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (z * (y * t));
	double tmp;
	if (z <= -15.2) {
		tmp = t_2;
	} else if (z <= -2e-106) {
		tmp = x * 2.0;
	} else if (z <= 1.4e-226) {
		tmp = t_1;
	} else if (z <= 5.1e-194) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 2.15e-54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = (-9.0d0) * (z * (y * t))
    if (z <= (-15.2d0)) then
        tmp = t_2
    else if (z <= (-2d-106)) then
        tmp = x * 2.0d0
    else if (z <= 1.4d-226) then
        tmp = t_1
    else if (z <= 5.1d-194) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= 2.15d-54) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (z * (y * t));
	double tmp;
	if (z <= -15.2) {
		tmp = t_2;
	} else if (z <= -2e-106) {
		tmp = x * 2.0;
	} else if (z <= 1.4e-226) {
		tmp = t_1;
	} else if (z <= 5.1e-194) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 2.15e-54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = -9.0 * (z * (y * t))
	tmp = 0
	if z <= -15.2:
		tmp = t_2
	elif z <= -2e-106:
		tmp = x * 2.0
	elif z <= 1.4e-226:
		tmp = t_1
	elif z <= 5.1e-194:
		tmp = -9.0 * (y * (z * t))
	elif z <= 2.15e-54:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(-9.0 * Float64(z * Float64(y * t)))
	tmp = 0.0
	if (z <= -15.2)
		tmp = t_2;
	elseif (z <= -2e-106)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.4e-226)
		tmp = t_1;
	elseif (z <= 5.1e-194)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= 2.15e-54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = -9.0 * (z * (y * t));
	tmp = 0.0;
	if (z <= -15.2)
		tmp = t_2;
	elseif (z <= -2e-106)
		tmp = x * 2.0;
	elseif (z <= 1.4e-226)
		tmp = t_1;
	elseif (z <= 5.1e-194)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= 2.15e-54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -15.2], t$95$2, If[LessEqual[z, -2e-106], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.4e-226], t$95$1, If[LessEqual[z, 5.1e-194], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e-54], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -15.199999999999999 or 2.15e-54 < z

   1. Initial program 86.5%

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

   2. Taylor expanded in y around 0 86.5%

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

   3. Taylor expanded in y around inf 48.6%

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

      1. associate-*r* 53.7%

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

   5. Simplified 53.7%

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

   if -15.199999999999999 < z < -1.99999999999999988e-106

   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. Taylor expanded in x around inf 38.5%

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

   if -1.99999999999999988e-106 < z < 1.40000000000000004e-226 or 5.0999999999999998e-194 < z < 2.15e-54

   1. Initial program 96.4%

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

   2. Taylor expanded in a around inf 52.6%

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

   if 1.40000000000000004e-226 < z < 5.0999999999999998e-194

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 50.5%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15.2:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-106}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-226}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-194}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-54}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \]

Alternative 9: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{if}\;z \leq -15.2:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-106}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-194}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))) (t_2 (* -9.0 (* z (* y t)))))
   (if (<= z -15.2)
     t_2
     (if (<= z -1.85e-106)
       (* x 2.0)
       (if (<= z 1.4e-226)
         t_1
         (if (<= z 5.5e-194)
           (* y (* t (* z -9.0)))
           (if (<= z 4e-47) t_1 t_2)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (z * (y * t));
	double tmp;
	if (z <= -15.2) {
		tmp = t_2;
	} else if (z <= -1.85e-106) {
		tmp = x * 2.0;
	} else if (z <= 1.4e-226) {
		tmp = t_1;
	} else if (z <= 5.5e-194) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 4e-47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = (-9.0d0) * (z * (y * t))
    if (z <= (-15.2d0)) then
        tmp = t_2
    else if (z <= (-1.85d-106)) then
        tmp = x * 2.0d0
    else if (z <= 1.4d-226) then
        tmp = t_1
    else if (z <= 5.5d-194) then
        tmp = y * (t * (z * (-9.0d0)))
    else if (z <= 4d-47) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (z * (y * t));
	double tmp;
	if (z <= -15.2) {
		tmp = t_2;
	} else if (z <= -1.85e-106) {
		tmp = x * 2.0;
	} else if (z <= 1.4e-226) {
		tmp = t_1;
	} else if (z <= 5.5e-194) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 4e-47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = -9.0 * (z * (y * t))
	tmp = 0
	if z <= -15.2:
		tmp = t_2
	elif z <= -1.85e-106:
		tmp = x * 2.0
	elif z <= 1.4e-226:
		tmp = t_1
	elif z <= 5.5e-194:
		tmp = y * (t * (z * -9.0))
	elif z <= 4e-47:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(-9.0 * Float64(z * Float64(y * t)))
	tmp = 0.0
	if (z <= -15.2)
		tmp = t_2;
	elseif (z <= -1.85e-106)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.4e-226)
		tmp = t_1;
	elseif (z <= 5.5e-194)
		tmp = Float64(y * Float64(t * Float64(z * -9.0)));
	elseif (z <= 4e-47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = -9.0 * (z * (y * t));
	tmp = 0.0;
	if (z <= -15.2)
		tmp = t_2;
	elseif (z <= -1.85e-106)
		tmp = x * 2.0;
	elseif (z <= 1.4e-226)
		tmp = t_1;
	elseif (z <= 5.5e-194)
		tmp = y * (t * (z * -9.0));
	elseif (z <= 4e-47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -15.2], t$95$2, If[LessEqual[z, -1.85e-106], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.4e-226], t$95$1, If[LessEqual[z, 5.5e-194], N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-47], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -15.199999999999999 or 3.9999999999999999e-47 < z

   1. Initial program 86.4%

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

   2. Taylor expanded in y around 0 86.4%

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

   3. Taylor expanded in y around inf 48.9%

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

      1. associate-*r* 54.1%

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

   5. Simplified 54.1%

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

   if -15.199999999999999 < z < -1.8499999999999999e-106

   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. Taylor expanded in x around inf 38.5%

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

   if -1.8499999999999999e-106 < z < 1.40000000000000004e-226 or 5.49999999999999941e-194 < z < 3.9999999999999999e-47

   1. Initial program 96.4%

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

   2. Taylor expanded in a around inf 53.1%

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

   if 1.40000000000000004e-226 < z < 5.49999999999999941e-194

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 99.7%

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

   3. Taylor expanded in y around inf 50.5%

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

      1. *-commutative 50.5%

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

      2. *-commutative 50.5%

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

      3. associate-*r* 50.3%

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

      4. *-commutative 50.3%

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

      5. associate-*l* 50.3%

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

   5. Simplified 50.3%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15.2:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-106}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-226}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-194}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-47}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \]

Alternative 10: 77.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.26 \cdot 10^{+80} \lor \neg \left(y \leq 2.9 \cdot 10^{-149}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \end{array} \end{array} \]

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 -2.26e+80) (not (<= y 2.9e-149)))
   (- (* x 2.0) (* 9.0 (* y (* z t))))
   (- (* x 2.0) (* (* a b) -27.0))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.26e+80) || !(y <= 2.9e-149)) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.26d+80)) .or. (.not. (y <= 2.9d-149))) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.26e+80) || !(y <= 2.9e-149)) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.26e+80) or not (y <= 2.9e-149):
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	else:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.26e+80) || !(y <= 2.9e-149))
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.26e+80) || ~((y <= 2.9e-149)))
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	else
		tmp = (x * 2.0) - ((a * b) * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.26e+80], N[Not[LessEqual[y, 2.9e-149]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.26e80 or 2.9e-149 < y

   1. Initial program 86.5%

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

   2. Taylor expanded in a around 0 74.6%

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

   if -2.26e80 < y < 2.9e-149

   1. Initial program 97.1%

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

      1. associate-+l- 97.1%

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

      2. sub-neg 97.1%

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

      3. neg-mul-1 97.1%

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

      4. metadata-eval 97.1%

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

      5. metadata-eval 97.1%

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

      6. cancel-sign-sub-inv 97.1%

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

      7. metadata-eval 97.1%

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

      8. *-lft-identity 97.1%

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

      9. associate-*l* 94.1%

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

      10. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in y around 0 82.5%

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

      1. *-commutative 82.5%

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

   6. Simplified 82.5%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.26 \cdot 10^{+80} \lor \neg \left(y \leq 2.9 \cdot 10^{-149}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \end{array} \]

Alternative 11: 77.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+78}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-202}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.9e+78)
   (- (* x 2.0) (* 9.0 (* y (* z t))))
   (if (<= y 3.2e-202)
     (- (* x 2.0) (* (* a b) -27.0))
     (- (* x 2.0) (* 9.0 (* z (* y t)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.9e+78) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (y <= 3.2e-202) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (z * (y * t)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.9d+78)) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else if (y <= 3.2d-202) then
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (z * (y * t)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.9e+78) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (y <= 3.2e-202) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (z * (y * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.9e+78:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	elif y <= 3.2e-202:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	else:
		tmp = (x * 2.0) - (9.0 * (z * (y * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.9e+78)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	elseif (y <= 3.2e-202)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(z * Float64(y * t))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.9e+78)
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	elseif (y <= 3.2e-202)
		tmp = (x * 2.0) - ((a * b) * -27.0);
	else
		tmp = (x * 2.0) - (9.0 * (z * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.9e+78], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-202], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.9e78

   1. Initial program 79.7%

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

   2. Taylor expanded in a around 0 87.3%

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

   if -5.9e78 < y < 3.2000000000000001e-202

   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. sub-neg 97.7%

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

      3. neg-mul-1 97.7%

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

      4. metadata-eval 97.7%

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

      5. metadata-eval 97.7%

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

      6. cancel-sign-sub-inv 97.7%

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

      7. metadata-eval 97.7%

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

      8. *-lft-identity 97.7%

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

      9. associate-*l* 96.2%

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

      10. associate-*l* 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in y around 0 84.2%

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

      1. *-commutative 84.2%

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

   6. Simplified 84.2%

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

   if 3.2000000000000001e-202 < y

   1. Initial program 89.5%

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

   2. Taylor expanded in a around 0 67.4%

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

      1. *-commutative 67.4%

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

      2. *-commutative 67.4%

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

      3. associate-*l* 66.2%

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

      4. *-commutative 66.2%

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

      5. *-commutative 66.2%

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

      6. associate-*r* 66.2%

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

      7. cancel-sign-sub-inv 66.2%

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

   4. Applied egg-rr 66.2%

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

      1. distribute-lft-neg-out 66.2%

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

      2. associate-*r* 66.2%

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

      3. unsub-neg 66.2%

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

      4. *-commutative 66.2%

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

      5. associate-*r* 68.9%

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

   6. Applied egg-rr 68.9%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+78}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-202}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \]

Alternative 12: 75.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -420:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+73}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -420.0)
   (* -9.0 (* z (* y t)))
   (if (<= z 1.7e+73) (- (* x 2.0) (* a (* b -27.0))) (* 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 tmp;
	if (z <= -420.0) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= 1.7e+73) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} 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) :: tmp
    if (z <= (-420.0d0)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (z <= 1.7d+73) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    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 tmp;
	if (z <= -420.0) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= 1.7e+73) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} 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):
	tmp = 0
	if z <= -420.0:
		tmp = -9.0 * (z * (y * t))
	elif z <= 1.7e+73:
		tmp = (x * 2.0) - (a * (b * -27.0))
	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)
	tmp = 0.0
	if (z <= -420.0)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (z <= 1.7e+73)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	else
		tmp = Float64(z * Float64(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)
	tmp = 0.0;
	if (z <= -420.0)
		tmp = -9.0 * (z * (y * t));
	elseif (z <= 1.7e+73)
		tmp = (x * 2.0) - (a * (b * -27.0));
	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_] := If[LessEqual[z, -420.0], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+73], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -420

   1. Initial program 87.6%

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

   2. Taylor expanded in y around 0 87.7%

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

   3. Taylor expanded in y around inf 44.5%

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

      1. associate-*r* 50.1%

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

   5. Simplified 50.1%

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

   if -420 < z < 1.7000000000000001e73

   1. Initial program 96.4%

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

      1. associate-+l- 96.4%

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

      2. sub-neg 96.4%

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

      3. neg-mul-1 96.4%

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

      4. metadata-eval 96.4%

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

      5. metadata-eval 96.4%

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

      6. cancel-sign-sub-inv 96.4%

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

      7. metadata-eval 96.4%

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

      8. *-lft-identity 96.4%

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

      9. associate-*l* 99.1%

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

      10. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-*r* 75.5%

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

   6. Simplified 75.5%

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

   if 1.7000000000000001e73 < z

   1. Initial program 79.5%

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

   2. Taylor expanded in y around 0 79.5%

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

   3. Taylor expanded in y around inf 62.3%

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

      1. *-commutative 62.3%

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

      2. *-commutative 62.3%

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

      3. associate-*r* 62.3%

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

      4. *-commutative 62.3%

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

      5. associate-*l* 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in y around 0 62.3%

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

      1. *-commutative 62.3%

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

      2. associate-*r* 70.7%

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

      3. *-commutative 70.7%

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

      4. *-commutative 70.7%

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

      5. associate-*l* 70.5%

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

      6. *-commutative 70.5%

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

   8. Simplified 70.5%

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

   9. Taylor expanded in y around 0 70.5%

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

       1. *-commutative 70.5%

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

       2. associate-*r* 70.6%

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

       3. *-commutative 70.6%

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

       4. associate-*l* 70.6%

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

   11. Simplified 70.6%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -420:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+73}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 13: 75.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -31:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+70}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -31.0)
   (* -9.0 (* z (* y t)))
   (if (<= z 1.45e+70)
     (- (* x 2.0) (* b (* a -27.0)))
     (* 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 tmp;
	if (z <= -31.0) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= 1.45e+70) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} 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) :: tmp
    if (z <= (-31.0d0)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (z <= 1.45d+70) then
        tmp = (x * 2.0d0) - (b * (a * (-27.0d0)))
    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 tmp;
	if (z <= -31.0) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= 1.45e+70) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} 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):
	tmp = 0
	if z <= -31.0:
		tmp = -9.0 * (z * (y * t))
	elif z <= 1.45e+70:
		tmp = (x * 2.0) - (b * (a * -27.0))
	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)
	tmp = 0.0
	if (z <= -31.0)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (z <= 1.45e+70)
		tmp = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)));
	else
		tmp = Float64(z * Float64(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)
	tmp = 0.0;
	if (z <= -31.0)
		tmp = -9.0 * (z * (y * t));
	elseif (z <= 1.45e+70)
		tmp = (x * 2.0) - (b * (a * -27.0));
	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_] := If[LessEqual[z, -31.0], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+70], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -31

   1. Initial program 87.6%

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

   2. Taylor expanded in y around 0 87.7%

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

   3. Taylor expanded in y around inf 44.5%

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

      1. associate-*r* 50.1%

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

   5. Simplified 50.1%

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

   if -31 < z < 1.4499999999999999e70

   1. Initial program 96.4%

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

      1. associate-+l- 96.4%

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

      2. sub-neg 96.4%

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

      3. neg-mul-1 96.4%

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

      4. metadata-eval 96.4%

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

      5. metadata-eval 96.4%

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

      6. cancel-sign-sub-inv 96.4%

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

      7. metadata-eval 96.4%

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

      8. *-lft-identity 96.4%

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

      9. associate-*l* 99.1%

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

      10. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

      1. sub-neg 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*r* 99.1%

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

      4. associate-*r* 96.3%

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

      5. distribute-rgt-neg-in 96.3%

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

      6. *-commutative 96.3%

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

      7. distribute-rgt-neg-in 96.3%

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

      8. metadata-eval 96.3%

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

   5. Applied egg-rr 96.3%

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

   6. Taylor expanded in y around 0 75.5%

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

      1. associate-*r* 75.5%

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

      2. *-commutative 75.5%

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

   8. Simplified 75.5%

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

   if 1.4499999999999999e70 < z

   1. Initial program 79.5%

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

   2. Taylor expanded in y around 0 79.5%

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

   3. Taylor expanded in y around inf 62.3%

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

      1. *-commutative 62.3%

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

      2. *-commutative 62.3%

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

      3. associate-*r* 62.3%

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

      4. *-commutative 62.3%

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

      5. associate-*l* 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in y around 0 62.3%

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

      1. *-commutative 62.3%

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

      2. associate-*r* 70.7%

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

      3. *-commutative 70.7%

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

      4. *-commutative 70.7%

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

      5. associate-*l* 70.5%

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

      6. *-commutative 70.5%

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

   8. Simplified 70.5%

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

   9. Taylor expanded in y around 0 70.5%

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

       1. *-commutative 70.5%

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

       2. associate-*r* 70.6%

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

       3. *-commutative 70.6%

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

       4. associate-*l* 70.6%

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

   11. Simplified 70.6%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -31:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+70}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 14: 75.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -135:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+73}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -135.0)
   (* -9.0 (* z (* y t)))
   (if (<= z 1.36e+73)
     (- (* x 2.0) (* (* a b) -27.0))
     (* 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 tmp;
	if (z <= -135.0) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= 1.36e+73) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} 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) :: tmp
    if (z <= (-135.0d0)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (z <= 1.36d+73) then
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    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 tmp;
	if (z <= -135.0) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= 1.36e+73) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} 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):
	tmp = 0
	if z <= -135.0:
		tmp = -9.0 * (z * (y * t))
	elif z <= 1.36e+73:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	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)
	tmp = 0.0
	if (z <= -135.0)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (z <= 1.36e+73)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	else
		tmp = Float64(z * Float64(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)
	tmp = 0.0;
	if (z <= -135.0)
		tmp = -9.0 * (z * (y * t));
	elseif (z <= 1.36e+73)
		tmp = (x * 2.0) - ((a * b) * -27.0);
	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_] := If[LessEqual[z, -135.0], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.36e+73], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -135

   1. Initial program 87.6%

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

   2. Taylor expanded in y around 0 87.7%

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

   3. Taylor expanded in y around inf 44.5%

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

      1. associate-*r* 50.1%

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

   5. Simplified 50.1%

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

   if -135 < z < 1.3599999999999999e73

   1. Initial program 96.4%

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

      1. associate-+l- 96.4%

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

      2. sub-neg 96.4%

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

      3. neg-mul-1 96.4%

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

      4. metadata-eval 96.4%

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

      5. metadata-eval 96.4%

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

      6. cancel-sign-sub-inv 96.4%

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

      7. metadata-eval 96.4%

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

      8. *-lft-identity 96.4%

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

      9. associate-*l* 99.1%

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

      10. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 75.5%

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

      1. *-commutative 75.5%

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

   6. Simplified 75.5%

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

   if 1.3599999999999999e73 < z

   1. Initial program 79.5%

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

   2. Taylor expanded in y around 0 79.5%

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

   3. Taylor expanded in y around inf 62.3%

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

      1. *-commutative 62.3%

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

      2. *-commutative 62.3%

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

      3. associate-*r* 62.3%

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

      4. *-commutative 62.3%

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

      5. associate-*l* 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in y around 0 62.3%

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

      1. *-commutative 62.3%

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

      2. associate-*r* 70.7%

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

      3. *-commutative 70.7%

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

      4. *-commutative 70.7%

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

      5. associate-*l* 70.5%

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

      6. *-commutative 70.5%

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

   8. Simplified 70.5%

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

   9. Taylor expanded in y around 0 70.5%

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

       1. *-commutative 70.5%

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

       2. associate-*r* 70.6%

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

       3. *-commutative 70.6%

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

       4. associate-*l* 70.6%

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

   11. Simplified 70.6%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -135:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+73}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 15: 45.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+105}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-112}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.8e+105) (* x 2.0) (if (<= x 3e-112) (* 27.0 (* a b)) (* x 2.0))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+105) {
		tmp = x * 2.0;
	} else if (x <= 3e-112) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.8d+105)) then
        tmp = x * 2.0d0
    else if (x <= 3d-112) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+105) {
		tmp = x * 2.0;
	} else if (x <= 3e-112) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.8e+105:
		tmp = x * 2.0
	elif x <= 3e-112:
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.8e+105)
		tmp = Float64(x * 2.0);
	elseif (x <= 3e-112)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.8e+105)
		tmp = x * 2.0;
	elseif (x <= 3e-112)
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.8e+105], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, 3e-112], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.80000000000000027e105 or 3.0000000000000001e-112 < x

   1. Initial program 90.4%

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

   2. Taylor expanded in x around inf 52.4%

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

   if -8.80000000000000027e105 < x < 3.0000000000000001e-112

   1. Initial program 92.1%

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

   2. Taylor expanded in a around inf 45.7%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+105}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-112}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 16: 30.3% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.3%

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

2. Taylor expanded in x around inf 30.3%

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

3. Final simplification 30.3%

   \[\leadsto x \cdot 2 \]

Developer target: 95.4% 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 2023182 
(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)))