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

Percentage Accurate: 95.2% → 98.8%

Time: 17.1s

Alternatives: 13

Speedup: 0.8×

• 27.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -2 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(\left(-9 \cdot z\right) \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 + 27 \cdot \left(a \cdot b\right)\right) - \left(y \cdot t\right) \cdot \left(9 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* y 9.0) -2e-22)
   (fma a (* 27.0 b) (fma x 2.0 (* y (* (* -9.0 z) t))))
   (- (+ (* x 2.0) (* 27.0 (* a b))) (* (* y t) (* 9.0 z)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y * 9.0) <= -2e-22) {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (y * ((-9.0 * z) * t))));
	} else {
		tmp = ((x * 2.0) + (27.0 * (a * b))) - ((y * t) * (9.0 * z));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(y * 9.0) <= -2e-22)
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(y * Float64(Float64(-9.0 * z) * t))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b))) - Float64(Float64(y * t) * Float64(9.0 * z)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(y * 9.0), $MachinePrecision], -2e-22], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(y * N[(N[(-9.0 * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * t), $MachinePrecision] * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y 9) < -2.0000000000000001e-22

   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. +-commutative 92.6%

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

      2. sub-neg 92.6%

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

      3. associate-+r+ 92.6%

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

      4. associate-*l* 98.4%

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

      5. distribute-rgt-neg-in 98.4%

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

      6. *-commutative 98.4%

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

      7. distribute-rgt-neg-in 98.4%

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

      8. associate-*l* 89.1%

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

      9. associate-+r+ 89.1%

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

      10. sub-neg 89.1%

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

      11. associate-*l* 89.1%

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

      12. fma-define 89.1%

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

      13. fma-neg 89.1%

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

      14. *-commutative 89.1%

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

      15. distribute-lft-neg-in 89.1%

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

      16. associate-*l* 92.5%

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

   3. Simplified 99.7%

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

   if -2.0000000000000001e-22 < (*.f64 y 9)

   1. Initial program 93.9%

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

      1. associate-*l* 93.5%

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

      2. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

      1. +-commutative 93.5%

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

      2. associate-+r- 93.5%

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

      3. *-commutative 93.5%

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

      4. associate-*l* 93.4%

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

      5. associate-*r* 93.9%

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

      6. *-commutative 93.9%

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

      7. associate-*l* 93.9%

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

      8. associate-*r* 96.2%

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

   6. Applied egg-rr 96.2%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -2 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(\left(-9 \cdot z\right) \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 + 27 \cdot \left(a \cdot b\right)\right) - \left(y \cdot t\right) \cdot \left(9 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-11} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-60}\right):\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, 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 (* b (* a 27.0))))
   (if (or (<= t_1 -1e-11) (not (<= t_1 2e-60)))
     (+ (* t (* z (* y -9.0))) (* a (* 27.0 b)))
     (- (* x 2.0) (* 9.0 (* t (* y z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if ((t_1 <= -1e-11) || !(t_1 <= 2e-60)) {
		tmp = (t * (z * (y * -9.0))) + (a * (27.0 * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, 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 = b * (a * 27.0d0)
    if ((t_1 <= (-1d-11)) .or. (.not. (t_1 <= 2d-60))) then
        tmp = (t * (z * (y * (-9.0d0)))) + (a * (27.0d0 * b))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if ((t_1 <= -1e-11) || !(t_1 <= 2e-60)) {
		tmp = (t * (z * (y * -9.0))) + (a * (27.0 * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	tmp = 0
	if (t_1 <= -1e-11) or not (t_1 <= 2e-60):
		tmp = (t * (z * (y * -9.0))) + (a * (27.0 * b))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if ((t_1 <= -1e-11) || !(t_1 <= 2e-60))
		tmp = Float64(Float64(t * Float64(z * Float64(y * -9.0))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if ((t_1 <= -1e-11) || ~((t_1 <= 2e-60)))
		tmp = (t * (z * (y * -9.0))) + (a * (27.0 * b));
	else
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, 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[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-11], N[Not[LessEqual[t$95$1, 2e-60]], $MachinePrecision]], N[(N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a 27) b) < -9.99999999999999939e-12 or 1.9999999999999999e-60 < (*.f64 (*.f64 a 27) b)

   1. Initial program 95.5%

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

      1. associate-*l* 95.3%

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

      2. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in x around 0 85.5%

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

      1. *-commutative 85.5%

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

      2. associate-*r* 85.6%

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

      3. *-commutative 85.6%

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

      4. associate-*l* 85.6%

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

   7. Simplified 85.6%

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

   if -9.99999999999999939e-12 < (*.f64 (*.f64 a 27) b) < 1.9999999999999999e-60

   1. Initial program 91.0%

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

      1. associate-*l* 93.7%

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

      2. associate-*l* 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in a around 0 87.6%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -1 \cdot 10^{-11} \lor \neg \left(b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{-60}\right):\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-11}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-60}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, 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 (* b (* a 27.0))))
   (if (<= t_1 -1e-11)
     (+ (* t (* z (* y -9.0))) (* a (* 27.0 b)))
     (if (<= t_1 2e-60)
       (- (* x 2.0) (* 9.0 (* t (* y z))))
       (+ t_1 (* z (* -9.0 (* y t))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -1e-11) {
		tmp = (t * (z * (y * -9.0))) + (a * (27.0 * b));
	} else if (t_1 <= 2e-60) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else {
		tmp = t_1 + (z * (-9.0 * (y * t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, 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 = b * (a * 27.0d0)
    if (t_1 <= (-1d-11)) then
        tmp = (t * (z * (y * (-9.0d0)))) + (a * (27.0d0 * b))
    else if (t_1 <= 2d-60) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    else
        tmp = t_1 + (z * ((-9.0d0) * (y * t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -1e-11) {
		tmp = (t * (z * (y * -9.0))) + (a * (27.0 * b));
	} else if (t_1 <= 2e-60) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else {
		tmp = t_1 + (z * (-9.0 * (y * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	tmp = 0
	if t_1 <= -1e-11:
		tmp = (t * (z * (y * -9.0))) + (a * (27.0 * b))
	elif t_1 <= 2e-60:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	else:
		tmp = t_1 + (z * (-9.0 * (y * t)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (t_1 <= -1e-11)
		tmp = Float64(Float64(t * Float64(z * Float64(y * -9.0))) + Float64(a * Float64(27.0 * b)));
	elseif (t_1 <= 2e-60)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	else
		tmp = Float64(t_1 + Float64(z * Float64(-9.0 * Float64(y * t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if (t_1 <= -1e-11)
		tmp = (t * (z * (y * -9.0))) + (a * (27.0 * b));
	elseif (t_1 <= 2e-60)
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	else
		tmp = t_1 + (z * (-9.0 * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, 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[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-11], N[(N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-60], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a 27) b) < -9.99999999999999939e-12

   1. Initial program 97.0%

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

      1. associate-*l* 95.5%

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

      2. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in x around 0 90.8%

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

      1. *-commutative 90.8%

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

      2. associate-*r* 90.8%

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

      3. *-commutative 90.8%

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

      4. associate-*l* 90.9%

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

   7. Simplified 90.9%

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

   if -9.99999999999999939e-12 < (*.f64 (*.f64 a 27) b) < 1.9999999999999999e-60

   1. Initial program 91.0%

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

      1. associate-*l* 93.7%

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

      2. associate-*l* 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in a around 0 87.6%

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

   if 1.9999999999999999e-60 < (*.f64 (*.f64 a 27) b)

   1. Initial program 94.1%

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

   3. Taylor expanded in y around 0 94.1%

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

   4. Taylor expanded in x around 0 82.2%

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

      1. *-commutative 82.2%

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

      2. *-commutative 82.2%

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

      3. *-commutative 82.2%

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

      4. associate-*r* 79.7%

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

      5. metadata-eval 79.7%

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

      6. distribute-rgt-neg-in 79.7%

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

      7. associate-*r* 79.6%

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

      8. distribute-rgt-neg-in 79.6%

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

      9. associate-*l* 79.7%

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

      10. *-commutative 79.7%

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

      11. distribute-rgt-neg-in 79.7%

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

      12. *-commutative 79.7%

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

      13. distribute-rgt-neg-in 79.7%

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

      14. metadata-eval 79.7%

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

   6. Simplified 79.7%

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

   7. Taylor expanded in y around 0 79.6%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -1 \cdot 10^{-11}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{-60}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-11}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-60}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, 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 (* b (* a 27.0))))
   (if (<= t_1 -1e-11)
     (+ (* t (* z (* y -9.0))) (* a (* 27.0 b)))
     (if (<= t_1 2e-60)
       (- (* x 2.0) (* 9.0 (* t (* y z))))
       (+ t_1 (* z (* t (* y -9.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -1e-11) {
		tmp = (t * (z * (y * -9.0))) + (a * (27.0 * b));
	} else if (t_1 <= 2e-60) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else {
		tmp = t_1 + (z * (t * (y * -9.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, 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 = b * (a * 27.0d0)
    if (t_1 <= (-1d-11)) then
        tmp = (t * (z * (y * (-9.0d0)))) + (a * (27.0d0 * b))
    else if (t_1 <= 2d-60) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    else
        tmp = t_1 + (z * (t * (y * (-9.0d0))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -1e-11) {
		tmp = (t * (z * (y * -9.0))) + (a * (27.0 * b));
	} else if (t_1 <= 2e-60) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else {
		tmp = t_1 + (z * (t * (y * -9.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	tmp = 0
	if t_1 <= -1e-11:
		tmp = (t * (z * (y * -9.0))) + (a * (27.0 * b))
	elif t_1 <= 2e-60:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	else:
		tmp = t_1 + (z * (t * (y * -9.0)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (t_1 <= -1e-11)
		tmp = Float64(Float64(t * Float64(z * Float64(y * -9.0))) + Float64(a * Float64(27.0 * b)));
	elseif (t_1 <= 2e-60)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	else
		tmp = Float64(t_1 + Float64(z * Float64(t * Float64(y * -9.0))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if (t_1 <= -1e-11)
		tmp = (t * (z * (y * -9.0))) + (a * (27.0 * b));
	elseif (t_1 <= 2e-60)
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	else
		tmp = t_1 + (z * (t * (y * -9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, 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[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-11], N[(N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-60], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a 27) b) < -9.99999999999999939e-12

   1. Initial program 97.0%

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

      1. associate-*l* 95.5%

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

      2. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in x around 0 90.8%

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

      1. *-commutative 90.8%

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

      2. associate-*r* 90.8%

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

      3. *-commutative 90.8%

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

      4. associate-*l* 90.9%

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

   7. Simplified 90.9%

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

   if -9.99999999999999939e-12 < (*.f64 (*.f64 a 27) b) < 1.9999999999999999e-60

   1. Initial program 91.0%

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

      1. associate-*l* 93.7%

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

      2. associate-*l* 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in a around 0 87.6%

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

   if 1.9999999999999999e-60 < (*.f64 (*.f64 a 27) b)

   1. Initial program 94.1%

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

   3. Taylor expanded in y around 0 94.1%

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

   4. Taylor expanded in x around 0 82.2%

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

      1. *-commutative 82.2%

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

      2. *-commutative 82.2%

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

      3. *-commutative 82.2%

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

      4. associate-*r* 79.7%

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

      5. metadata-eval 79.7%

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

      6. distribute-rgt-neg-in 79.7%

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

      7. associate-*r* 79.6%

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

      8. distribute-rgt-neg-in 79.6%

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

      9. associate-*l* 79.7%

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

      10. *-commutative 79.7%

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

      11. distribute-rgt-neg-in 79.7%

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

      12. *-commutative 79.7%

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

      13. distribute-rgt-neg-in 79.7%

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

      14. metadata-eval 79.7%

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

   6. Simplified 79.7%

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

   7. Taylor expanded in y around 0 79.6%

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

      1. associate-*r* 79.7%

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

      2. *-commutative 79.7%

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

      3. associate-*l* 79.7%

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

   9. Simplified 79.7%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -1 \cdot 10^{-11}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{-60}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{-48} \lor \neg \left(b \leq 2.6 \cdot 10^{-31}\right) \land \left(b \leq 3.3 \cdot 10^{+25} \lor \neg \left(b \leq 9.2 \cdot 10^{+64}\right)\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.95e-48)
         (and (not (<= b 2.6e-31)) (or (<= b 3.3e+25) (not (<= b 9.2e+64)))))
   (* 27.0 (* a b))
   (* x 2.0)))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.95e-48) || (!(b <= 2.6e-31) && ((b <= 3.3e+25) || !(b <= 9.2e+64)))) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.95d-48)) .or. (.not. (b <= 2.6d-31)) .and. (b <= 3.3d+25) .or. (.not. (b <= 9.2d+64))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.95e-48) || (!(b <= 2.6e-31) && ((b <= 3.3e+25) || !(b <= 9.2e+64)))) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.95e-48) or (not (b <= 2.6e-31) and ((b <= 3.3e+25) or not (b <= 9.2e+64))):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.95e-48) || (!(b <= 2.6e-31) && ((b <= 3.3e+25) || !(b <= 9.2e+64))))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.95e-48) || (~((b <= 2.6e-31)) && ((b <= 3.3e+25) || ~((b <= 9.2e+64)))))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.95e-48], And[N[Not[LessEqual[b, 2.6e-31]], $MachinePrecision], Or[LessEqual[b, 3.3e+25], N[Not[LessEqual[b, 9.2e+64]], $MachinePrecision]]]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.95e-48 or 2.59999999999999995e-31 < b < 3.3000000000000001e25 or 9.2e64 < b

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0 94.9%

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

   4. Taylor expanded in x around 0 83.6%

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

      1. *-commutative 83.6%

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

      2. *-commutative 83.6%

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

      3. *-commutative 83.6%

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

      4. associate-*r* 82.8%

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

      5. metadata-eval 82.8%

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

      6. distribute-rgt-neg-in 82.8%

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

      7. associate-*r* 82.1%

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

      8. distribute-rgt-neg-in 82.1%

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

      9. associate-*l* 82.1%

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

      10. *-commutative 82.1%

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

      11. distribute-rgt-neg-in 82.1%

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

      12. *-commutative 82.1%

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

      13. distribute-rgt-neg-in 82.1%

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

      14. metadata-eval 82.1%

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

   6. Simplified 82.1%

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

   7. Taylor expanded in y around 0 82.1%

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

   8. Taylor expanded in z around 0 59.5%

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

   if -1.95e-48 < b < 2.59999999999999995e-31 or 3.3000000000000001e25 < b < 9.2e64

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. sub-neg 91.8%

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

      3. associate-+r+ 91.8%

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

      4. associate-*l* 93.6%

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

      5. distribute-rgt-neg-in 93.6%

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

      6. *-commutative 93.6%

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

      7. distribute-rgt-neg-in 93.6%

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

      8. associate-*l* 93.4%

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

      9. associate-+r+ 93.4%

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

      10. sub-neg 93.4%

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

      11. associate-*l* 93.4%

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

      12. fma-define 93.4%

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

      13. fma-neg 93.4%

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

      14. distribute-rgt-neg-in 93.4%

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

      15. *-commutative 93.4%

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

      16. associate-*r* 91.8%

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

   3. Simplified 92.6%

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

      1. fma-undefine 92.6%

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

      2. fma-undefine 92.6%

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

      3. associate-+r+ 92.6%

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

      4. *-commutative 92.6%

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

      5. associate-*l* 92.6%

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

      6. *-commutative 92.6%

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

      7. associate-*r* 94.5%

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

      8. *-commutative 94.5%

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

      9. *-commutative 94.5%

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

      10. associate-*r* 94.5%

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

   6. Applied egg-rr 94.5%

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

   7. Taylor expanded in x around inf 45.0%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{-48} \lor \neg \left(b \leq 2.6 \cdot 10^{-31}\right) \land \left(b \leq 3.3 \cdot 10^{+25} \lor \neg \left(b \leq 9.2 \cdot 10^{+64}\right)\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{-51}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-30} \lor \neg \left(b \leq 8.5 \cdot 10^{+26}\right) \land b \leq 1.05 \cdot 10^{+65}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.8e-51)
   (* a (* 27.0 b))
   (if (or (<= b 7.5e-30) (and (not (<= b 8.5e+26)) (<= b 1.05e+65)))
     (* x 2.0)
     (* 27.0 (* a b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.8e-51) {
		tmp = a * (27.0 * b);
	} else if ((b <= 7.5e-30) || (!(b <= 8.5e+26) && (b <= 1.05e+65))) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.8d-51)) then
        tmp = a * (27.0d0 * b)
    else if ((b <= 7.5d-30) .or. (.not. (b <= 8.5d+26)) .and. (b <= 1.05d+65)) then
        tmp = x * 2.0d0
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.8e-51) {
		tmp = a * (27.0 * b);
	} else if ((b <= 7.5e-30) || (!(b <= 8.5e+26) && (b <= 1.05e+65))) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.8e-51:
		tmp = a * (27.0 * b)
	elif (b <= 7.5e-30) or (not (b <= 8.5e+26) and (b <= 1.05e+65)):
		tmp = x * 2.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.8e-51)
		tmp = Float64(a * Float64(27.0 * b));
	elseif ((b <= 7.5e-30) || (!(b <= 8.5e+26) && (b <= 1.05e+65)))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.8e-51)
		tmp = a * (27.0 * b);
	elseif ((b <= 7.5e-30) || (~((b <= 8.5e+26)) && (b <= 1.05e+65)))
		tmp = x * 2.0;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.8e-51], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 7.5e-30], And[N[Not[LessEqual[b, 8.5e+26]], $MachinePrecision], LessEqual[b, 1.05e+65]]], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8e-51

   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. Add Preprocessing

   3. Taylor expanded in y around 0 96.4%

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

   4. Taylor expanded in x around 0 86.6%

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

      1. *-commutative 86.6%

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

      2. *-commutative 86.6%

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

      3. *-commutative 86.6%

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

      4. associate-*r* 86.4%

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

      5. metadata-eval 86.4%

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

      6. distribute-rgt-neg-in 86.4%

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

      7. associate-*r* 86.4%

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

      8. distribute-rgt-neg-in 86.4%

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

      9. associate-*l* 86.4%

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

      10. *-commutative 86.4%

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

      11. distribute-rgt-neg-in 86.4%

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

      12. *-commutative 86.4%

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

      13. distribute-rgt-neg-in 86.4%

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

      14. metadata-eval 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in y around 0 86.4%

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

   8. Taylor expanded in z around 0 55.7%

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

      1. associate-*r* 55.7%

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

      2. *-commutative 55.7%

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

      3. associate-*r* 55.7%

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

   10. Simplified 55.7%

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

   if -1.8e-51 < b < 7.5000000000000006e-30 or 8.5e26 < b < 1.04999999999999996e65

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. sub-neg 91.8%

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

      3. associate-+r+ 91.8%

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

      4. associate-*l* 93.6%

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

      5. distribute-rgt-neg-in 93.6%

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

      6. *-commutative 93.6%

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

      7. distribute-rgt-neg-in 93.6%

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

      8. associate-*l* 93.4%

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

      9. associate-+r+ 93.4%

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

      10. sub-neg 93.4%

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

      11. associate-*l* 93.4%

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

      12. fma-define 93.4%

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

      13. fma-neg 93.4%

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

      14. distribute-rgt-neg-in 93.4%

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

      15. *-commutative 93.4%

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

      16. associate-*r* 91.8%

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

   3. Simplified 92.6%

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

      1. fma-undefine 92.6%

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

      2. fma-undefine 92.6%

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

      3. associate-+r+ 92.6%

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

      4. *-commutative 92.6%

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

      5. associate-*l* 92.6%

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

      6. *-commutative 92.6%

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

      7. associate-*r* 94.5%

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

      8. *-commutative 94.5%

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

      9. *-commutative 94.5%

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

      10. associate-*r* 94.5%

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

   6. Applied egg-rr 94.5%

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

   7. Taylor expanded in x around inf 45.0%

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

   if 7.5000000000000006e-30 < b < 8.5e26 or 1.04999999999999996e65 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 93.1%

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

   4. Taylor expanded in x around 0 80.1%

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

      1. *-commutative 80.1%

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

      2. *-commutative 80.1%

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

      3. *-commutative 80.1%

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

      4. associate-*r* 78.6%

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

      5. metadata-eval 78.6%

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

      6. distribute-rgt-neg-in 78.6%

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

      7. associate-*r* 77.3%

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

      8. distribute-rgt-neg-in 77.3%

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

      9. associate-*l* 77.2%

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

      10. *-commutative 77.2%

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

      11. distribute-rgt-neg-in 77.2%

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

      12. *-commutative 77.2%

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

      13. distribute-rgt-neg-in 77.2%

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

      14. metadata-eval 77.2%

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

   6. Simplified 77.2%

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

   7. Taylor expanded in y around 0 77.3%

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

   8. Taylor expanded in z around 0 63.7%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{-51}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-30} \lor \neg \left(b \leq 8.5 \cdot 10^{+26}\right) \land b \leq 1.05 \cdot 10^{+65}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 96.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 6.8 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot 2 + 27 \cdot \left(a \cdot b\right)\right) + y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 6.8e+70)
   (+ (+ (* x 2.0) (* 27.0 (* a b))) (* y (* z (* -9.0 t))))
   (- (* x 2.0) (* 9.0 (* t (* y z))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 6.8e+70) {
		tmp = ((x * 2.0) + (27.0 * (a * b))) + (y * (z * (-9.0 * t)));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, 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 <= 6.8d+70) then
        tmp = ((x * 2.0d0) + (27.0d0 * (a * b))) + (y * (z * ((-9.0d0) * t)))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 6.8e+70) {
		tmp = ((x * 2.0) + (27.0 * (a * b))) + (y * (z * (-9.0 * t)));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 6.8e+70:
		tmp = ((x * 2.0) + (27.0 * (a * b))) + (y * (z * (-9.0 * t)))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 6.8e+70)
		tmp = Float64(Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b))) + Float64(y * Float64(z * Float64(-9.0 * t))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 6.8e+70)
		tmp = ((x * 2.0) + (27.0 * (a * b))) + (y * (z * (-9.0 * t)));
	else
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 6.8e+70], N[(N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.8000000000000002e70

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. sub-neg 96.6%

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

      3. associate-+r+ 96.6%

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

      4. associate-*l* 96.5%

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

      5. distribute-rgt-neg-in 96.5%

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

      6. *-commutative 96.5%

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

      7. distribute-rgt-neg-in 96.5%

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

      8. associate-*l* 93.7%

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

      9. associate-+r+ 93.7%

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

      10. sub-neg 93.7%

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

      11. associate-*l* 93.7%

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

      12. fma-define 93.7%

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

      13. fma-neg 93.7%

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

      14. distribute-rgt-neg-in 93.7%

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

      15. *-commutative 93.7%

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

      16. associate-*r* 96.6%

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

   3. Simplified 97.0%

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

      1. fma-undefine 97.0%

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

      2. fma-undefine 97.0%

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

      3. associate-+r+ 97.0%

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

      4. *-commutative 97.0%

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

      5. associate-*l* 97.0%

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

      6. *-commutative 97.0%

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

      7. associate-*r* 97.0%

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

      8. *-commutative 97.0%

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

      9. *-commutative 97.0%

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

      10. associate-*r* 97.0%

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

   6. Applied egg-rr 97.0%

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

   if 6.8000000000000002e70 < z

   1. Initial program 82.7%

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

      1. associate-*l* 87.7%

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

      2. associate-*l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in a around 0 63.5%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6.8 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot 2 + 27 \cdot \left(a \cdot b\right)\right) + y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 9.5 \cdot 10^{+54}:\\ \;\;\;\;\left(x \cdot 2 + 27 \cdot \left(a \cdot b\right)\right) + y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 9.5e+54)
   (+ (+ (* x 2.0) (* 27.0 (* a b))) (* y (* z (* -9.0 t))))
   (+ (- (* x 2.0) (* t (* 9.0 (* y z)))) (* b (* a 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 9.5e+54) {
		tmp = ((x * 2.0) + (27.0 * (a * b))) + (y * (z * (-9.0 * t)));
	} else {
		tmp = ((x * 2.0) - (t * (9.0 * (y * z)))) + (b * (a * 27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, 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 <= 9.5d+54) then
        tmp = ((x * 2.0d0) + (27.0d0 * (a * b))) + (y * (z * ((-9.0d0) * t)))
    else
        tmp = ((x * 2.0d0) - (t * (9.0d0 * (y * z)))) + (b * (a * 27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 9.5e+54) {
		tmp = ((x * 2.0) + (27.0 * (a * b))) + (y * (z * (-9.0 * t)));
	} else {
		tmp = ((x * 2.0) - (t * (9.0 * (y * z)))) + (b * (a * 27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 9.5e+54:
		tmp = ((x * 2.0) + (27.0 * (a * b))) + (y * (z * (-9.0 * t)))
	else:
		tmp = ((x * 2.0) - (t * (9.0 * (y * z)))) + (b * (a * 27.0))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 9.5e+54)
		tmp = Float64(Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b))) + Float64(y * Float64(z * Float64(-9.0 * t))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(9.0 * Float64(y * z)))) + Float64(b * Float64(a * 27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 9.5e+54)
		tmp = ((x * 2.0) + (27.0 * (a * b))) + (y * (z * (-9.0 * t)));
	else
		tmp = ((x * 2.0) - (t * (9.0 * (y * z)))) + (b * (a * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 9.5e+54], N[(N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 9.4999999999999999e54

   1. Initial program 96.5%

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

      1. +-commutative 96.5%

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

      2. sub-neg 96.5%

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

      3. associate-+r+ 96.5%

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

      4. associate-*l* 96.5%

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

      5. distribute-rgt-neg-in 96.5%

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

      6. *-commutative 96.5%

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

      7. distribute-rgt-neg-in 96.5%

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

      8. associate-*l* 93.7%

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

      9. associate-+r+ 93.7%

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

      10. sub-neg 93.7%

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

      11. associate-*l* 93.7%

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

      12. fma-define 93.7%

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

      13. fma-neg 93.7%

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

      14. distribute-rgt-neg-in 93.7%

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

      15. *-commutative 93.7%

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

      16. associate-*r* 96.5%

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

   3. Simplified 97.0%

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

      1. fma-undefine 97.0%

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

      2. fma-undefine 97.0%

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

      3. associate-+r+ 97.0%

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

      4. *-commutative 97.0%

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

      5. associate-*l* 97.0%

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

      6. *-commutative 97.0%

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

      7. associate-*r* 96.9%

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

      8. *-commutative 96.9%

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

      9. *-commutative 96.9%

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

      10. associate-*r* 96.9%

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

   6. Applied egg-rr 96.9%

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

   if 9.4999999999999999e54 < z

   1. Initial program 83.3%

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

   3. Taylor expanded in y around 0 83.3%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 9.5 \cdot 10^{+54}:\\ \;\;\;\;\left(x \cdot 2 + 27 \cdot \left(a \cdot b\right)\right) + y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq 1.05 \cdot 10^{+55}:\\ \;\;\;\;t\_1 + y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \left(y \cdot t\right) \cdot \left(9 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x 2.0) (* 27.0 (* a b)))))
   (if (<= z 1.05e+55)
     (+ t_1 (* y (* z (* -9.0 t))))
     (- t_1 (* (* y t) (* 9.0 z))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) + (27.0 * (a * b));
	double tmp;
	if (z <= 1.05e+55) {
		tmp = t_1 + (y * (z * (-9.0 * t)));
	} else {
		tmp = t_1 - ((y * t) * (9.0 * z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) + (27.0d0 * (a * b))
    if (z <= 1.05d+55) then
        tmp = t_1 + (y * (z * ((-9.0d0) * t)))
    else
        tmp = t_1 - ((y * t) * (9.0d0 * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) + (27.0 * (a * b));
	double tmp;
	if (z <= 1.05e+55) {
		tmp = t_1 + (y * (z * (-9.0 * t)));
	} else {
		tmp = t_1 - ((y * t) * (9.0 * z));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) + (27.0 * (a * b))
	tmp = 0
	if z <= 1.05e+55:
		tmp = t_1 + (y * (z * (-9.0 * t)))
	else:
		tmp = t_1 - ((y * t) * (9.0 * z))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)))
	tmp = 0.0
	if (z <= 1.05e+55)
		tmp = Float64(t_1 + Float64(y * Float64(z * Float64(-9.0 * t))));
	else
		tmp = Float64(t_1 - Float64(Float64(y * t) * Float64(9.0 * z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) + (27.0 * (a * b));
	tmp = 0.0;
	if (z <= 1.05e+55)
		tmp = t_1 + (y * (z * (-9.0 * t)));
	else
		tmp = t_1 - ((y * t) * (9.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 1.05e+55], N[(t$95$1 + N[(y * N[(z * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(y * t), $MachinePrecision] * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 1.05e55

   1. Initial program 96.5%

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

      1. +-commutative 96.5%

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

      2. sub-neg 96.5%

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

      3. associate-+r+ 96.5%

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

      4. associate-*l* 96.5%

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

      5. distribute-rgt-neg-in 96.5%

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

      6. *-commutative 96.5%

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

      7. distribute-rgt-neg-in 96.5%

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

      8. associate-*l* 93.7%

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

      9. associate-+r+ 93.7%

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

      10. sub-neg 93.7%

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

      11. associate-*l* 93.7%

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

      12. fma-define 93.7%

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

      13. fma-neg 93.7%

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

      14. distribute-rgt-neg-in 93.7%

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

      15. *-commutative 93.7%

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

      16. associate-*r* 96.5%

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

   3. Simplified 97.0%

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

      1. fma-undefine 97.0%

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

      2. fma-undefine 97.0%

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

      3. associate-+r+ 97.0%

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

      4. *-commutative 97.0%

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

      5. associate-*l* 97.0%

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

      6. *-commutative 97.0%

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

      7. associate-*r* 96.9%

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

      8. *-commutative 96.9%

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

      9. *-commutative 96.9%

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

      10. associate-*r* 96.9%

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

   6. Applied egg-rr 96.9%

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

   if 1.05e55 < z

   1. Initial program 83.3%

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

      1. associate-*l* 88.2%

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

      2. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

      1. +-commutative 88.2%

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

      2. associate-+r- 88.2%

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

      3. *-commutative 88.2%

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

      4. associate-*l* 88.2%

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

      5. associate-*r* 83.4%

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

      6. *-commutative 83.4%

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

      7. associate-*l* 83.3%

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

      8. associate-*r* 97.5%

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

   6. Applied egg-rr 97.5%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.05 \cdot 10^{+55}:\\ \;\;\;\;\left(x \cdot 2 + 27 \cdot \left(a \cdot b\right)\right) + y \cdot \left(z \cdot \left(-9 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 + 27 \cdot \left(a \cdot b\right)\right) - \left(y \cdot t\right) \cdot \left(9 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-47}:\\ \;\;\;\;x \cdot 2 + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{+66}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.3e-47)
   (+ (* x 2.0) (* a (* 27.0 b)))
   (if (<= b 3.9e+66)
     (- (* x 2.0) (* 9.0 (* t (* y z))))
     (+ (* b (* a 27.0)) (* x 2.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.3e-47) {
		tmp = (x * 2.0) + (a * (27.0 * b));
	} else if (b <= 3.9e+66) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else {
		tmp = (b * (a * 27.0)) + (x * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.3d-47)) then
        tmp = (x * 2.0d0) + (a * (27.0d0 * b))
    else if (b <= 3.9d+66) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    else
        tmp = (b * (a * 27.0d0)) + (x * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.3e-47) {
		tmp = (x * 2.0) + (a * (27.0 * b));
	} else if (b <= 3.9e+66) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else {
		tmp = (b * (a * 27.0)) + (x * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.3e-47:
		tmp = (x * 2.0) + (a * (27.0 * b))
	elif b <= 3.9e+66:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	else:
		tmp = (b * (a * 27.0)) + (x * 2.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.3e-47)
		tmp = Float64(Float64(x * 2.0) + Float64(a * Float64(27.0 * b)));
	elseif (b <= 3.9e+66)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	else
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(x * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.3e-47)
		tmp = (x * 2.0) + (a * (27.0 * b));
	elseif (b <= 3.9e+66)
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	else
		tmp = (b * (a * 27.0)) + (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.3e-47], N[(N[(x * 2.0), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.9e+66], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.3e-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. Step-by-step derivation

      1. associate-*l* 93.9%

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

      2. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around inf 67.1%

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

   if -1.3e-47 < b < 3.9000000000000004e66

   1. Initial program 91.1%

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

      1. associate-*l* 94.3%

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

      2. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in a around 0 79.8%

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

   if 3.9000000000000004e66 < b

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0 94.9%

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

   4. Taylor expanded in x around inf 83.4%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-47}:\\ \;\;\;\;x \cdot 2 + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{+66}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.4% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

   1. associate-*l* 94.7%

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

   2. associate-*l* 94.7%

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

3. Simplified 94.7%

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

5. Taylor expanded in y around 0 65.0%

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

6. Final simplification 65.0%

   \[\leadsto x \cdot 2 + 27 \cdot \left(a \cdot b\right) \]
7. Add Preprocessing

Alternative 12: 63.4% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, 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 = (b * (a * 27.0d0)) + (x * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

3. Taylor expanded in y around 0 93.9%

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

4. Taylor expanded in x around inf 65.0%

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

5. Final simplification 65.0%

   \[\leadsto b \cdot \left(a \cdot 27\right) + x \cdot 2 \]
6. Add Preprocessing

Alternative 13: 29.8% accurate, 5.7× speedup

Math

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

FPCore

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, 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 93.6%

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

   1. +-commutative 93.6%

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

   2. sub-neg 93.6%

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

   3. associate-+r+ 93.6%

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

   4. associate-*l* 94.7%

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

   5. distribute-rgt-neg-in 94.7%

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

   6. *-commutative 94.7%

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

   7. distribute-rgt-neg-in 94.7%

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

   8. associate-*l* 94.5%

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

   9. associate-+r+ 94.5%

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

   10. sub-neg 94.5%

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

   11. associate-*l* 94.2%

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

   12. fma-define 94.2%

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

   13. fma-neg 94.2%

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

   14. distribute-rgt-neg-in 94.2%

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

   15. *-commutative 94.2%

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

   16. associate-*r* 93.2%

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

3. Simplified 93.6%

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

   1. fma-undefine 93.6%

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

   2. fma-undefine 93.6%

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

   3. associate-+r+ 93.6%

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

   4. *-commutative 93.6%

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

   5. associate-*l* 93.9%

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

   6. *-commutative 93.9%

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

   7. associate-*r* 95.0%

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

   8. *-commutative 95.0%

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

   9. *-commutative 95.0%

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

   10. associate-*r* 95.0%

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

6. Applied egg-rr 95.0%

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

7. Taylor expanded in x around inf 27.8%

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

8. Final simplification 27.8%

   \[\leadsto x \cdot 2 \]
9. Add Preprocessing

Developer target: 94.7% accurate, 0.8× 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 2024034 
(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)))