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

Percentage Accurate: 85.3% → 89.6%

Time: 29.0s

Alternatives: 22

Speedup: 0.9×

• 50.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Alternative 1: 89.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 4\right) \cdot i\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := t \cdot \left(a \cdot 4\right)\\ \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t\_3\right) + b \cdot c\right) - t\_1\right) - t\_2 \leq \infty:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right) - t\_3\right)\right) - t\_1\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* x 4.0) i)) (t_2 (* (* j 27.0) k)) (t_3 (* t (* a 4.0))))
   (if (<=
        (- (- (+ (- (* (* (* (* x 18.0) y) z) t) t_3) (* b c)) t_1) t_2)
        INFINITY)
     (- (- (+ (* b c) (- (* (* z t) (* 18.0 (* x y))) t_3)) t_1) t_2)
     (* x (+ (* (* 18.0 t) (* y z)) (* i -4.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * 4.0) * i;
	double t_2 = (j * 27.0) * k;
	double t_3 = t * (a * 4.0);
	double tmp;
	if (((((((((x * 18.0) * y) * z) * t) - t_3) + (b * c)) - t_1) - t_2) <= ((double) INFINITY)) {
		tmp = (((b * c) + (((z * t) * (18.0 * (x * y))) - t_3)) - t_1) - t_2;
	} else {
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * 4.0) * i;
	double t_2 = (j * 27.0) * k;
	double t_3 = t * (a * 4.0);
	double tmp;
	if (((((((((x * 18.0) * y) * z) * t) - t_3) + (b * c)) - t_1) - t_2) <= Double.POSITIVE_INFINITY) {
		tmp = (((b * c) + (((z * t) * (18.0 * (x * y))) - t_3)) - t_1) - t_2;
	} else {
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * 4.0) * i
	t_2 = (j * 27.0) * k
	t_3 = t * (a * 4.0)
	tmp = 0
	if ((((((((x * 18.0) * y) * z) * t) - t_3) + (b * c)) - t_1) - t_2) <= math.inf:
		tmp = (((b * c) + (((z * t) * (18.0 * (x * y))) - t_3)) - t_1) - t_2
	else:
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * 4.0) * i)
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(t * Float64(a * 4.0))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - t_3) + Float64(b * c)) - t_1) - t_2) <= Inf)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(Float64(z * t) * Float64(18.0 * Float64(x * y))) - t_3)) - t_1) - t_2);
	else
		tmp = Float64(x * Float64(Float64(Float64(18.0 * t) * Float64(y * z)) + Float64(i * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * 4.0) * i;
	t_2 = (j * 27.0) * k;
	t_3 = t * (a * 4.0);
	tmp = 0.0;
	if (((((((((x * 18.0) * y) * z) * t) - t_3) + (b * c)) - t_1) - t_2) <= Inf)
		tmp = (((b * c) + (((z * t) * (18.0 * (x * y))) - t_3)) - t_1) - t_2;
	else
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - t$95$3), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], Infinity], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] * N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(x * N[(N[(N[(18.0 * t), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k)) < +inf.0

   1. Initial program 92.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. pow1 92.4%

         \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      2. associate-*r* 92.1%

         \[\leadsto \left(\left(\left({\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)} \cdot t\right)}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 92.1%

         \[\leadsto \left(\left(\left({\color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right)}}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      4. associate-*r* 92.4%

         \[\leadsto \left(\left(\left({\left(t \cdot \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)}\right)}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      5. *-commutative 92.4%

         \[\leadsto \left(\left(\left({\left(t \cdot \color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)}\right)}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      6. *-commutative 92.4%

         \[\leadsto \left(\left(\left({\left(t \cdot \left(z \cdot \color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)}\right)\right)}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied egg-rr 92.4%

      \[\leadsto \left(\left(\left(\color{blue}{{\left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)\right)}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   5. Step-by-step derivation

      1. unpow1 92.4%

         \[\leadsto \left(\left(\left(\color{blue}{t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      2. associate-*r* 93.0%

         \[\leadsto \left(\left(\left(\color{blue}{\left(t \cdot z\right) \cdot \left(y \cdot \left(x \cdot 18\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 93.0%

         \[\leadsto \left(\left(\left(\left(t \cdot z\right) \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative 93.0%

         \[\leadsto \left(\left(\left(\left(t \cdot z\right) \cdot \left(\color{blue}{\left(18 \cdot x\right)} \cdot y\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      5. associate-*r* 93.0%

         \[\leadsto \left(\left(\left(\left(t \cdot z\right) \cdot \color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   6. Simplified 93.0%

      \[\leadsto \left(\left(\left(\color{blue}{\left(t \cdot z\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 25.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 59.4%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 59.4%

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(-4\right) \cdot i\right)} \]

      2. associate-*r* 59.4%

         \[\leadsto x \cdot \left(\color{blue}{\left(18 \cdot t\right) \cdot \left(y \cdot z\right)} + \left(-4\right) \cdot i\right) \]

      3. *-commutative 59.4%

         \[\leadsto x \cdot \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(z \cdot y\right)} + \left(-4\right) \cdot i\right) \]

      4. metadata-eval 59.4%

         \[\leadsto x \cdot \left(\left(18 \cdot t\right) \cdot \left(z \cdot y\right) + \color{blue}{-4} \cdot i\right) \]

   7. Applied egg-rr 59.4%

      \[\leadsto x \cdot \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(z \cdot y\right) + -4 \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(z \cdot t\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 59.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_3 := b \cdot c + t\_1\\ t_4 := x \cdot \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + i \cdot -4\right)\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{-7}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-144}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-251}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-265}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{-232}:\\ \;\;\;\;t\_1 + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 15500000:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ (* b c) (* -4.0 (* t a))))
        (t_3 (+ (* b c) t_1))
        (t_4 (* x (+ (* (* 18.0 t) (* y z)) (* i -4.0)))))
   (if (<= x -2.15e-7)
     t_4
     (if (<= x -2e-144)
       t_3
       (if (<= x -1.15e-251)
         t_2
         (if (<= x -3.2e-265)
           t_3
           (if (<= x 2.95e-232)
             (+ t_1 (* t (* a -4.0)))
             (if (<= x 9.2e-88) t_2 (if (<= x 15500000.0) t_3 t_4)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + (-4.0 * (t * a));
	double t_3 = (b * c) + t_1;
	double t_4 = x * (((18.0 * t) * (y * z)) + (i * -4.0));
	double tmp;
	if (x <= -2.15e-7) {
		tmp = t_4;
	} else if (x <= -2e-144) {
		tmp = t_3;
	} else if (x <= -1.15e-251) {
		tmp = t_2;
	} else if (x <= -3.2e-265) {
		tmp = t_3;
	} else if (x <= 2.95e-232) {
		tmp = t_1 + (t * (a * -4.0));
	} else if (x <= 9.2e-88) {
		tmp = t_2;
	} else if (x <= 15500000.0) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + ((-4.0d0) * (t * a))
    t_3 = (b * c) + t_1
    t_4 = x * (((18.0d0 * t) * (y * z)) + (i * (-4.0d0)))
    if (x <= (-2.15d-7)) then
        tmp = t_4
    else if (x <= (-2d-144)) then
        tmp = t_3
    else if (x <= (-1.15d-251)) then
        tmp = t_2
    else if (x <= (-3.2d-265)) then
        tmp = t_3
    else if (x <= 2.95d-232) then
        tmp = t_1 + (t * (a * (-4.0d0)))
    else if (x <= 9.2d-88) then
        tmp = t_2
    else if (x <= 15500000.0d0) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + (-4.0 * (t * a));
	double t_3 = (b * c) + t_1;
	double t_4 = x * (((18.0 * t) * (y * z)) + (i * -4.0));
	double tmp;
	if (x <= -2.15e-7) {
		tmp = t_4;
	} else if (x <= -2e-144) {
		tmp = t_3;
	} else if (x <= -1.15e-251) {
		tmp = t_2;
	} else if (x <= -3.2e-265) {
		tmp = t_3;
	} else if (x <= 2.95e-232) {
		tmp = t_1 + (t * (a * -4.0));
	} else if (x <= 9.2e-88) {
		tmp = t_2;
	} else if (x <= 15500000.0) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + (-4.0 * (t * a))
	t_3 = (b * c) + t_1
	t_4 = x * (((18.0 * t) * (y * z)) + (i * -4.0))
	tmp = 0
	if x <= -2.15e-7:
		tmp = t_4
	elif x <= -2e-144:
		tmp = t_3
	elif x <= -1.15e-251:
		tmp = t_2
	elif x <= -3.2e-265:
		tmp = t_3
	elif x <= 2.95e-232:
		tmp = t_1 + (t * (a * -4.0))
	elif x <= 9.2e-88:
		tmp = t_2
	elif x <= 15500000.0:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_3 = Float64(Float64(b * c) + t_1)
	t_4 = Float64(x * Float64(Float64(Float64(18.0 * t) * Float64(y * z)) + Float64(i * -4.0)))
	tmp = 0.0
	if (x <= -2.15e-7)
		tmp = t_4;
	elseif (x <= -2e-144)
		tmp = t_3;
	elseif (x <= -1.15e-251)
		tmp = t_2;
	elseif (x <= -3.2e-265)
		tmp = t_3;
	elseif (x <= 2.95e-232)
		tmp = Float64(t_1 + Float64(t * Float64(a * -4.0)));
	elseif (x <= 9.2e-88)
		tmp = t_2;
	elseif (x <= 15500000.0)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + (-4.0 * (t * a));
	t_3 = (b * c) + t_1;
	t_4 = x * (((18.0 * t) * (y * z)) + (i * -4.0));
	tmp = 0.0;
	if (x <= -2.15e-7)
		tmp = t_4;
	elseif (x <= -2e-144)
		tmp = t_3;
	elseif (x <= -1.15e-251)
		tmp = t_2;
	elseif (x <= -3.2e-265)
		tmp = t_3;
	elseif (x <= 2.95e-232)
		tmp = t_1 + (t * (a * -4.0));
	elseif (x <= 9.2e-88)
		tmp = t_2;
	elseif (x <= 15500000.0)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(N[(18.0 * t), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.15e-7], t$95$4, If[LessEqual[x, -2e-144], t$95$3, If[LessEqual[x, -1.15e-251], t$95$2, If[LessEqual[x, -3.2e-265], t$95$3, If[LessEqual[x, 2.95e-232], N[(t$95$1 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.2e-88], t$95$2, If[LessEqual[x, 15500000.0], t$95$3, t$95$4]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.1500000000000001e-7 or 1.55e7 < x

   1. Initial program 71.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 80.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 70.2%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 70.2%

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(-4\right) \cdot i\right)} \]

      2. associate-*r* 70.2%

         \[\leadsto x \cdot \left(\color{blue}{\left(18 \cdot t\right) \cdot \left(y \cdot z\right)} + \left(-4\right) \cdot i\right) \]

      3. *-commutative 70.2%

         \[\leadsto x \cdot \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(z \cdot y\right)} + \left(-4\right) \cdot i\right) \]

      4. metadata-eval 70.2%

         \[\leadsto x \cdot \left(\left(18 \cdot t\right) \cdot \left(z \cdot y\right) + \color{blue}{-4} \cdot i\right) \]

   7. Applied egg-rr 70.2%

      \[\leadsto x \cdot \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(z \cdot y\right) + -4 \cdot i\right)} \]

   if -2.1500000000000001e-7 < x < -1.9999999999999999e-144 or -1.15000000000000009e-251 < x < -3.2e-265 or 9.19999999999999945e-88 < x < 1.55e7

   1. Initial program 92.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 76.4%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]

   if -1.9999999999999999e-144 < x < -1.15000000000000009e-251 or 2.95000000000000008e-232 < x < 9.19999999999999945e-88

   1. Initial program 94.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 78.0%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]

   6. Taylor expanded in j around 0 64.7%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]

   if -3.2e-265 < x < 2.95000000000000008e-232

   1. Initial program 95.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 82.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 79.3%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 79.3%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 79.3%

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 79.3%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-144}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-251}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-265}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{-232}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-88}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 15500000:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_3 := b \cdot c + t\_1\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -2.02 \cdot 10^{-144}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-250}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-268}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-232}:\\ \;\;\;\;t\_1 + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 16500000:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ (* b c) (* -4.0 (* t a))))
        (t_3 (+ (* b c) t_1)))
   (if (<= x -1.1e-8)
     (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
     (if (<= x -2.02e-144)
       t_3
       (if (<= x -1.3e-250)
         t_2
         (if (<= x -1.8e-268)
           t_3
           (if (<= x 8e-232)
             (+ t_1 (* t (* a -4.0)))
             (if (<= x 1.6e-88)
               t_2
               (if (<= x 16500000.0)
                 t_3
                 (* x (+ (* (* 18.0 t) (* y z)) (* i -4.0))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + (-4.0 * (t * a));
	double t_3 = (b * c) + t_1;
	double tmp;
	if (x <= -1.1e-8) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (x <= -2.02e-144) {
		tmp = t_3;
	} else if (x <= -1.3e-250) {
		tmp = t_2;
	} else if (x <= -1.8e-268) {
		tmp = t_3;
	} else if (x <= 8e-232) {
		tmp = t_1 + (t * (a * -4.0));
	} else if (x <= 1.6e-88) {
		tmp = t_2;
	} else if (x <= 16500000.0) {
		tmp = t_3;
	} else {
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + ((-4.0d0) * (t * a))
    t_3 = (b * c) + t_1
    if (x <= (-1.1d-8)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (x <= (-2.02d-144)) then
        tmp = t_3
    else if (x <= (-1.3d-250)) then
        tmp = t_2
    else if (x <= (-1.8d-268)) then
        tmp = t_3
    else if (x <= 8d-232) then
        tmp = t_1 + (t * (a * (-4.0d0)))
    else if (x <= 1.6d-88) then
        tmp = t_2
    else if (x <= 16500000.0d0) then
        tmp = t_3
    else
        tmp = x * (((18.0d0 * t) * (y * z)) + (i * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + (-4.0 * (t * a));
	double t_3 = (b * c) + t_1;
	double tmp;
	if (x <= -1.1e-8) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (x <= -2.02e-144) {
		tmp = t_3;
	} else if (x <= -1.3e-250) {
		tmp = t_2;
	} else if (x <= -1.8e-268) {
		tmp = t_3;
	} else if (x <= 8e-232) {
		tmp = t_1 + (t * (a * -4.0));
	} else if (x <= 1.6e-88) {
		tmp = t_2;
	} else if (x <= 16500000.0) {
		tmp = t_3;
	} else {
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + (-4.0 * (t * a))
	t_3 = (b * c) + t_1
	tmp = 0
	if x <= -1.1e-8:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif x <= -2.02e-144:
		tmp = t_3
	elif x <= -1.3e-250:
		tmp = t_2
	elif x <= -1.8e-268:
		tmp = t_3
	elif x <= 8e-232:
		tmp = t_1 + (t * (a * -4.0))
	elif x <= 1.6e-88:
		tmp = t_2
	elif x <= 16500000.0:
		tmp = t_3
	else:
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_3 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (x <= -1.1e-8)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (x <= -2.02e-144)
		tmp = t_3;
	elseif (x <= -1.3e-250)
		tmp = t_2;
	elseif (x <= -1.8e-268)
		tmp = t_3;
	elseif (x <= 8e-232)
		tmp = Float64(t_1 + Float64(t * Float64(a * -4.0)));
	elseif (x <= 1.6e-88)
		tmp = t_2;
	elseif (x <= 16500000.0)
		tmp = t_3;
	else
		tmp = Float64(x * Float64(Float64(Float64(18.0 * t) * Float64(y * z)) + Float64(i * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + (-4.0 * (t * a));
	t_3 = (b * c) + t_1;
	tmp = 0.0;
	if (x <= -1.1e-8)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (x <= -2.02e-144)
		tmp = t_3;
	elseif (x <= -1.3e-250)
		tmp = t_2;
	elseif (x <= -1.8e-268)
		tmp = t_3;
	elseif (x <= 8e-232)
		tmp = t_1 + (t * (a * -4.0));
	elseif (x <= 1.6e-88)
		tmp = t_2;
	elseif (x <= 16500000.0)
		tmp = t_3;
	else
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[x, -1.1e-8], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.02e-144], t$95$3, If[LessEqual[x, -1.3e-250], t$95$2, If[LessEqual[x, -1.8e-268], t$95$3, If[LessEqual[x, 8e-232], N[(t$95$1 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e-88], t$95$2, If[LessEqual[x, 16500000.0], t$95$3, N[(x * N[(N[(N[(18.0 * t), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.0999999999999999e-8

   1. Initial program 73.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 80.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 67.3%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   if -1.0999999999999999e-8 < x < -2.0200000000000001e-144 or -1.30000000000000004e-250 < x < -1.8000000000000001e-268 or 1.60000000000000006e-88 < x < 1.65e7

   1. Initial program 92.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 76.4%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]

   if -2.0200000000000001e-144 < x < -1.30000000000000004e-250 or 8.0000000000000002e-232 < x < 1.60000000000000006e-88

   1. Initial program 94.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 78.0%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]

   6. Taylor expanded in j around 0 64.7%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]

   if -1.8000000000000001e-268 < x < 8.0000000000000002e-232

   1. Initial program 95.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 82.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 79.3%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 79.3%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 79.3%

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 79.3%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   if 1.65e7 < x

   1. Initial program 70.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 80.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 73.6%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 73.6%

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(-4\right) \cdot i\right)} \]

      2. associate-*r* 73.6%

         \[\leadsto x \cdot \left(\color{blue}{\left(18 \cdot t\right) \cdot \left(y \cdot z\right)} + \left(-4\right) \cdot i\right) \]

      3. *-commutative 73.6%

         \[\leadsto x \cdot \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(z \cdot y\right)} + \left(-4\right) \cdot i\right) \]

      4. metadata-eval 73.6%

         \[\leadsto x \cdot \left(\left(18 \cdot t\right) \cdot \left(z \cdot y\right) + \color{blue}{-4} \cdot i\right) \]

   7. Applied egg-rr 73.6%

      \[\leadsto x \cdot \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(z \cdot y\right) + -4 \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -2.02 \cdot 10^{-144}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-250}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-268}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-232}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-88}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 16500000:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t\_2 + i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-159}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-308}:\\ \;\;\;\;t\_2 + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 0.005:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+203}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* i (* x -4.0)))))
   (if (<= (* b c) -2e+182)
     t_1
     (if (<= (* b c) -1e-159)
       t_3
       (if (<= (* b c) -5e-308)
         (+ t_2 (* t (* a -4.0)))
         (if (<= (* b c) 0.005)
           t_3
           (if (<= (* b c) 2e+203)
             (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
             t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (i * (x * -4.0));
	double tmp;
	if ((b * c) <= -2e+182) {
		tmp = t_1;
	} else if ((b * c) <= -1e-159) {
		tmp = t_3;
	} else if ((b * c) <= -5e-308) {
		tmp = t_2 + (t * (a * -4.0));
	} else if ((b * c) <= 0.005) {
		tmp = t_3;
	} else if ((b * c) <= 2e+203) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + (i * (x * (-4.0d0)))
    if ((b * c) <= (-2d+182)) then
        tmp = t_1
    else if ((b * c) <= (-1d-159)) then
        tmp = t_3
    else if ((b * c) <= (-5d-308)) then
        tmp = t_2 + (t * (a * (-4.0d0)))
    else if ((b * c) <= 0.005d0) then
        tmp = t_3
    else if ((b * c) <= 2d+203) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (i * (x * -4.0));
	double tmp;
	if ((b * c) <= -2e+182) {
		tmp = t_1;
	} else if ((b * c) <= -1e-159) {
		tmp = t_3;
	} else if ((b * c) <= -5e-308) {
		tmp = t_2 + (t * (a * -4.0));
	} else if ((b * c) <= 0.005) {
		tmp = t_3;
	} else if ((b * c) <= 2e+203) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (i * (x * -4.0))
	tmp = 0
	if (b * c) <= -2e+182:
		tmp = t_1
	elif (b * c) <= -1e-159:
		tmp = t_3
	elif (b * c) <= -5e-308:
		tmp = t_2 + (t * (a * -4.0))
	elif (b * c) <= 0.005:
		tmp = t_3
	elif (b * c) <= 2e+203:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(i * Float64(x * -4.0)))
	tmp = 0.0
	if (Float64(b * c) <= -2e+182)
		tmp = t_1;
	elseif (Float64(b * c) <= -1e-159)
		tmp = t_3;
	elseif (Float64(b * c) <= -5e-308)
		tmp = Float64(t_2 + Float64(t * Float64(a * -4.0)));
	elseif (Float64(b * c) <= 0.005)
		tmp = t_3;
	elseif (Float64(b * c) <= 2e+203)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (i * (x * -4.0));
	tmp = 0.0;
	if ((b * c) <= -2e+182)
		tmp = t_1;
	elseif ((b * c) <= -1e-159)
		tmp = t_3;
	elseif ((b * c) <= -5e-308)
		tmp = t_2 + (t * (a * -4.0));
	elseif ((b * c) <= 0.005)
		tmp = t_3;
	elseif ((b * c) <= 2e+203)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+182], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1e-159], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], -5e-308], N[(t$95$2 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 0.005], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 2e+203], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.0000000000000001e182 or 2e203 < (*.f64 b c)

   1. Initial program 80.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 79.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 80.8%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]

   6. Taylor expanded in j around 0 82.3%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]

   if -2.0000000000000001e182 < (*.f64 b c) < -9.99999999999999989e-160 or -4.99999999999999955e-308 < (*.f64 b c) < 0.0050000000000000001

   1. Initial program 83.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 60.8%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 60.8%

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 60.8%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} + j \cdot \left(k \cdot -27\right) \]

      3. associate-*r* 60.8%

         \[\leadsto \color{blue}{\left(x \cdot -4\right) \cdot i} + j \cdot \left(k \cdot -27\right) \]

      4. *-commutative 60.8%

         \[\leadsto \color{blue}{\left(-4 \cdot x\right)} \cdot i + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 60.8%

      \[\leadsto \color{blue}{\left(-4 \cdot x\right) \cdot i} + j \cdot \left(k \cdot -27\right) \]

   if -9.99999999999999989e-160 < (*.f64 b c) < -4.99999999999999955e-308

   1. Initial program 84.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 94.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 79.3%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 79.3%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 79.3%

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 79.3%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   if 0.0050000000000000001 < (*.f64 b c) < 2e203

   1. Initial program 82.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. pow1 89.3%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. associate-*r* 89.4%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 89.4%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 89.4%

         \[\leadsto \left(t \cdot \left({\left(z \cdot \color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)}\right)}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 89.4%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 89.4%

         \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(y \cdot \left(x \cdot 18\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 89.4%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 89.4%

         \[\leadsto \left(t \cdot \left(z \cdot \left(\color{blue}{\left(18 \cdot x\right)} \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*r* 89.4%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 89.4%

      \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in k around inf 62.0%

      \[\leadsto \color{blue}{k \cdot \left(\left(\frac{b \cdot c}{k} + \frac{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)}{k}\right) - \left(4 \cdot \frac{i \cdot x}{k} + 27 \cdot j\right)\right)} \]

   10. Taylor expanded in t around -inf 62.1%

       \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+182}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-159}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-308}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 0.005:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+203}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t\_2 + i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-159}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-308}:\\ \;\;\;\;t\_2 + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+101}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* i (* x -4.0)))))
   (if (<= (* b c) -2e+182)
     t_1
     (if (<= (* b c) -1e-159)
       t_3
       (if (<= (* b c) -5e-308)
         (+ t_2 (* t (* a -4.0)))
         (if (<= (* b c) 2e+101) t_3 t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (i * (x * -4.0));
	double tmp;
	if ((b * c) <= -2e+182) {
		tmp = t_1;
	} else if ((b * c) <= -1e-159) {
		tmp = t_3;
	} else if ((b * c) <= -5e-308) {
		tmp = t_2 + (t * (a * -4.0));
	} else if ((b * c) <= 2e+101) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + (i * (x * (-4.0d0)))
    if ((b * c) <= (-2d+182)) then
        tmp = t_1
    else if ((b * c) <= (-1d-159)) then
        tmp = t_3
    else if ((b * c) <= (-5d-308)) then
        tmp = t_2 + (t * (a * (-4.0d0)))
    else if ((b * c) <= 2d+101) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (i * (x * -4.0));
	double tmp;
	if ((b * c) <= -2e+182) {
		tmp = t_1;
	} else if ((b * c) <= -1e-159) {
		tmp = t_3;
	} else if ((b * c) <= -5e-308) {
		tmp = t_2 + (t * (a * -4.0));
	} else if ((b * c) <= 2e+101) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (i * (x * -4.0))
	tmp = 0
	if (b * c) <= -2e+182:
		tmp = t_1
	elif (b * c) <= -1e-159:
		tmp = t_3
	elif (b * c) <= -5e-308:
		tmp = t_2 + (t * (a * -4.0))
	elif (b * c) <= 2e+101:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(i * Float64(x * -4.0)))
	tmp = 0.0
	if (Float64(b * c) <= -2e+182)
		tmp = t_1;
	elseif (Float64(b * c) <= -1e-159)
		tmp = t_3;
	elseif (Float64(b * c) <= -5e-308)
		tmp = Float64(t_2 + Float64(t * Float64(a * -4.0)));
	elseif (Float64(b * c) <= 2e+101)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (i * (x * -4.0));
	tmp = 0.0;
	if ((b * c) <= -2e+182)
		tmp = t_1;
	elseif ((b * c) <= -1e-159)
		tmp = t_3;
	elseif ((b * c) <= -5e-308)
		tmp = t_2 + (t * (a * -4.0));
	elseif ((b * c) <= 2e+101)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+182], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1e-159], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], -5e-308], N[(t$95$2 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+101], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.0000000000000001e182 or 2e101 < (*.f64 b c)

   1. Initial program 83.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 81.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 76.6%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]

   6. Taylor expanded in j around 0 75.4%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]

   if -2.0000000000000001e182 < (*.f64 b c) < -9.99999999999999989e-160 or -4.99999999999999955e-308 < (*.f64 b c) < 2e101

   1. Initial program 82.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 86.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 59.0%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 59.0%

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 59.0%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} + j \cdot \left(k \cdot -27\right) \]

      3. associate-*r* 59.0%

         \[\leadsto \color{blue}{\left(x \cdot -4\right) \cdot i} + j \cdot \left(k \cdot -27\right) \]

      4. *-commutative 59.0%

         \[\leadsto \color{blue}{\left(-4 \cdot x\right)} \cdot i + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 59.0%

      \[\leadsto \color{blue}{\left(-4 \cdot x\right) \cdot i} + j \cdot \left(k \cdot -27\right) \]

   if -9.99999999999999989e-160 < (*.f64 b c) < -4.99999999999999955e-308

   1. Initial program 84.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 94.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 79.3%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 79.3%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 79.3%

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 79.3%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+182}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-159}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-308}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+101}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ t_3 := \left(b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\right) - t\_2\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{+68}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-141}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-6}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(t\_1 + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z))))
        (t_2 (* 4.0 (* x i)))
        (t_3 (- (+ (* b c) (* t (- t_1 (* a 4.0)))) t_2)))
   (if (<= t -1.85e+68)
     t_3
     (if (<= t 5.8e-141)
       (- (- (- (* b c) (* 4.0 (* t a))) (* (* x 4.0) i)) (* (* j 27.0) k))
       (if (<= t 1.2e-6)
         t_3
         (if (<= t 4e+87)
           (- (* b c) (+ (* 27.0 (* j k)) t_2))
           (+ (* t (+ t_1 (* a -4.0))) (* j (* k -27.0)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = 4.0 * (x * i);
	double t_3 = ((b * c) + (t * (t_1 - (a * 4.0)))) - t_2;
	double tmp;
	if (t <= -1.85e+68) {
		tmp = t_3;
	} else if (t <= 5.8e-141) {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else if (t <= 1.2e-6) {
		tmp = t_3;
	} else if (t <= 4e+87) {
		tmp = (b * c) - ((27.0 * (j * k)) + t_2);
	} else {
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    t_2 = 4.0d0 * (x * i)
    t_3 = ((b * c) + (t * (t_1 - (a * 4.0d0)))) - t_2
    if (t <= (-1.85d+68)) then
        tmp = t_3
    else if (t <= 5.8d-141) then
        tmp = (((b * c) - (4.0d0 * (t * a))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    else if (t <= 1.2d-6) then
        tmp = t_3
    else if (t <= 4d+87) then
        tmp = (b * c) - ((27.0d0 * (j * k)) + t_2)
    else
        tmp = (t * (t_1 + (a * (-4.0d0)))) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = 4.0 * (x * i);
	double t_3 = ((b * c) + (t * (t_1 - (a * 4.0)))) - t_2;
	double tmp;
	if (t <= -1.85e+68) {
		tmp = t_3;
	} else if (t <= 5.8e-141) {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else if (t <= 1.2e-6) {
		tmp = t_3;
	} else if (t <= 4e+87) {
		tmp = (b * c) - ((27.0 * (j * k)) + t_2);
	} else {
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	t_2 = 4.0 * (x * i)
	t_3 = ((b * c) + (t * (t_1 - (a * 4.0)))) - t_2
	tmp = 0
	if t <= -1.85e+68:
		tmp = t_3
	elif t <= 5.8e-141:
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	elif t <= 1.2e-6:
		tmp = t_3
	elif t <= 4e+87:
		tmp = (b * c) - ((27.0 * (j * k)) + t_2)
	else:
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	t_2 = Float64(4.0 * Float64(x * i))
	t_3 = Float64(Float64(Float64(b * c) + Float64(t * Float64(t_1 - Float64(a * 4.0)))) - t_2)
	tmp = 0.0
	if (t <= -1.85e+68)
		tmp = t_3;
	elseif (t <= 5.8e-141)
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 1.2e-6)
		tmp = t_3;
	elseif (t <= 4e+87)
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + t_2));
	else
		tmp = Float64(Float64(t * Float64(t_1 + Float64(a * -4.0))) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	t_2 = 4.0 * (x * i);
	t_3 = ((b * c) + (t * (t_1 - (a * 4.0)))) - t_2;
	tmp = 0.0;
	if (t <= -1.85e+68)
		tmp = t_3;
	elseif (t <= 5.8e-141)
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	elseif (t <= 1.2e-6)
		tmp = t_3;
	elseif (t <= 4e+87)
		tmp = (b * c) - ((27.0 * (j * k)) + t_2);
	else
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[t, -1.85e+68], t$95$3, If[LessEqual[t, 5.8e-141], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-6], t$95$3, If[LessEqual[t, 4e+87], N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.84999999999999999e68 or 5.7999999999999999e-141 < t < 1.1999999999999999e-6

   1. Initial program 80.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 82.6%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   if -1.84999999999999999e68 < t < 5.7999999999999999e-141

   1. Initial program 83.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.8%

      \[\leadsto \left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   if 1.1999999999999999e-6 < t < 3.9999999999999998e87

   1. Initial program 89.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 84.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   if 3.9999999999999998e87 < t

   1. Initial program 81.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 86.3%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+68}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-141}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-6}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ t_3 := b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\\ t_4 := 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+136}:\\ \;\;\;\;t\_3 - t\_4\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-141}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-6}:\\ \;\;\;\;t\_3 - t\_2\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c - \left(t\_4 + t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(t\_1 + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z))))
        (t_2 (* 4.0 (* x i)))
        (t_3 (+ (* b c) (* t (- t_1 (* a 4.0)))))
        (t_4 (* 27.0 (* j k))))
   (if (<= t -2.6e+136)
     (- t_3 t_4)
     (if (<= t 6.6e-141)
       (- (- (- (* b c) (* 4.0 (* t a))) (* (* x 4.0) i)) (* (* j 27.0) k))
       (if (<= t 1.35e-6)
         (- t_3 t_2)
         (if (<= t 1.3e+88)
           (- (* b c) (+ t_4 t_2))
           (+ (* t (+ t_1 (* a -4.0))) (* j (* k -27.0)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = 4.0 * (x * i);
	double t_3 = (b * c) + (t * (t_1 - (a * 4.0)));
	double t_4 = 27.0 * (j * k);
	double tmp;
	if (t <= -2.6e+136) {
		tmp = t_3 - t_4;
	} else if (t <= 6.6e-141) {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else if (t <= 1.35e-6) {
		tmp = t_3 - t_2;
	} else if (t <= 1.3e+88) {
		tmp = (b * c) - (t_4 + t_2);
	} else {
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    t_2 = 4.0d0 * (x * i)
    t_3 = (b * c) + (t * (t_1 - (a * 4.0d0)))
    t_4 = 27.0d0 * (j * k)
    if (t <= (-2.6d+136)) then
        tmp = t_3 - t_4
    else if (t <= 6.6d-141) then
        tmp = (((b * c) - (4.0d0 * (t * a))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    else if (t <= 1.35d-6) then
        tmp = t_3 - t_2
    else if (t <= 1.3d+88) then
        tmp = (b * c) - (t_4 + t_2)
    else
        tmp = (t * (t_1 + (a * (-4.0d0)))) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = 4.0 * (x * i);
	double t_3 = (b * c) + (t * (t_1 - (a * 4.0)));
	double t_4 = 27.0 * (j * k);
	double tmp;
	if (t <= -2.6e+136) {
		tmp = t_3 - t_4;
	} else if (t <= 6.6e-141) {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else if (t <= 1.35e-6) {
		tmp = t_3 - t_2;
	} else if (t <= 1.3e+88) {
		tmp = (b * c) - (t_4 + t_2);
	} else {
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	t_2 = 4.0 * (x * i)
	t_3 = (b * c) + (t * (t_1 - (a * 4.0)))
	t_4 = 27.0 * (j * k)
	tmp = 0
	if t <= -2.6e+136:
		tmp = t_3 - t_4
	elif t <= 6.6e-141:
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	elif t <= 1.35e-6:
		tmp = t_3 - t_2
	elif t <= 1.3e+88:
		tmp = (b * c) - (t_4 + t_2)
	else:
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	t_2 = Float64(4.0 * Float64(x * i))
	t_3 = Float64(Float64(b * c) + Float64(t * Float64(t_1 - Float64(a * 4.0))))
	t_4 = Float64(27.0 * Float64(j * k))
	tmp = 0.0
	if (t <= -2.6e+136)
		tmp = Float64(t_3 - t_4);
	elseif (t <= 6.6e-141)
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 1.35e-6)
		tmp = Float64(t_3 - t_2);
	elseif (t <= 1.3e+88)
		tmp = Float64(Float64(b * c) - Float64(t_4 + t_2));
	else
		tmp = Float64(Float64(t * Float64(t_1 + Float64(a * -4.0))) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	t_2 = 4.0 * (x * i);
	t_3 = (b * c) + (t * (t_1 - (a * 4.0)));
	t_4 = 27.0 * (j * k);
	tmp = 0.0;
	if (t <= -2.6e+136)
		tmp = t_3 - t_4;
	elseif (t <= 6.6e-141)
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	elseif (t <= 1.35e-6)
		tmp = t_3 - t_2;
	elseif (t <= 1.3e+88)
		tmp = (b * c) - (t_4 + t_2);
	else
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e+136], N[(t$95$3 - t$95$4), $MachinePrecision], If[LessEqual[t, 6.6e-141], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-6], N[(t$95$3 - t$95$2), $MachinePrecision], If[LessEqual[t, 1.3e+88], N[(N[(b * c), $MachinePrecision] - N[(t$95$4 + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.6000000000000001e136

   1. Initial program 84.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. pow1 93.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. associate-*r* 93.7%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 93.7%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 93.7%

         \[\leadsto \left(t \cdot \left({\left(z \cdot \color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)}\right)}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 93.7%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 93.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(y \cdot \left(x \cdot 18\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 93.7%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 93.7%

         \[\leadsto \left(t \cdot \left(z \cdot \left(\color{blue}{\left(18 \cdot x\right)} \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*r* 93.7%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 93.7%

      \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in i around 0 90.5%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

   if -2.6000000000000001e136 < t < 6.59999999999999998e-141

   1. Initial program 83.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.2%

      \[\leadsto \left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   if 6.59999999999999998e-141 < t < 1.34999999999999999e-6

   1. Initial program 70.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 80.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around 0 83.3%

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   if 1.34999999999999999e-6 < t < 1.3e88

   1. Initial program 89.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 84.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   if 1.3e88 < t

   1. Initial program 81.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 86.3%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+136}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-141}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-6}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.6 \cdot 10^{+177}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -6 \cdot 10^{-274}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 1.65 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.5 \cdot 10^{+204}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -3.6e+177)
   (* b c)
   (if (<= (* b c) -6e-274)
     (* (* j k) -27.0)
     (if (<= (* b c) 1.65e-115)
       (* x (* i -4.0))
       (if (<= (* b c) 1.5e+204) (* x (* 18.0 (* t (* y z)))) (* b c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -3.6e+177) {
		tmp = b * c;
	} else if ((b * c) <= -6e-274) {
		tmp = (j * k) * -27.0;
	} else if ((b * c) <= 1.65e-115) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 1.5e+204) {
		tmp = x * (18.0 * (t * (y * z)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-3.6d+177)) then
        tmp = b * c
    else if ((b * c) <= (-6d-274)) then
        tmp = (j * k) * (-27.0d0)
    else if ((b * c) <= 1.65d-115) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= 1.5d+204) then
        tmp = x * (18.0d0 * (t * (y * z)))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -3.6e+177) {
		tmp = b * c;
	} else if ((b * c) <= -6e-274) {
		tmp = (j * k) * -27.0;
	} else if ((b * c) <= 1.65e-115) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 1.5e+204) {
		tmp = x * (18.0 * (t * (y * z)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -3.6e+177:
		tmp = b * c
	elif (b * c) <= -6e-274:
		tmp = (j * k) * -27.0
	elif (b * c) <= 1.65e-115:
		tmp = x * (i * -4.0)
	elif (b * c) <= 1.5e+204:
		tmp = x * (18.0 * (t * (y * z)))
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -3.6e+177)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -6e-274)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (Float64(b * c) <= 1.65e-115)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= 1.5e+204)
		tmp = Float64(x * Float64(18.0 * Float64(t * Float64(y * z))));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -3.6e+177)
		tmp = b * c;
	elseif ((b * c) <= -6e-274)
		tmp = (j * k) * -27.0;
	elseif ((b * c) <= 1.65e-115)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= 1.5e+204)
		tmp = x * (18.0 * (t * (y * z)));
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -3.6e+177], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -6e-274], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.65e-115], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.5e+204], N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -3.60000000000000003e177 or 1.49999999999999991e204 < (*.f64 b c)

   1. Initial program 81.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. pow1 79.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. associate-*r* 79.5%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 79.5%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 79.5%

         \[\leadsto \left(t \cdot \left({\left(z \cdot \color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)}\right)}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 79.5%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 79.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(y \cdot \left(x \cdot 18\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 79.5%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 79.5%

         \[\leadsto \left(t \cdot \left(z \cdot \left(\color{blue}{\left(18 \cdot x\right)} \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*r* 79.5%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 79.5%

      \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in k around inf 60.9%

      \[\leadsto \color{blue}{k \cdot \left(\left(\frac{b \cdot c}{k} + \frac{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)}{k}\right) - \left(4 \cdot \frac{i \cdot x}{k} + 27 \cdot j\right)\right)} \]

   10. Taylor expanded in b around inf 71.2%

       \[\leadsto \color{blue}{b \cdot c} \]

   if -3.60000000000000003e177 < (*.f64 b c) < -5.99999999999999954e-274

   1. Initial program 84.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 35.5%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -5.99999999999999954e-274 < (*.f64 b c) < 1.64999999999999995e-115

   1. Initial program 79.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 62.0%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   6. Taylor expanded in t around 0 43.6%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. metadata-eval 43.6%

         \[\leadsto \color{blue}{\left(-4\right)} \cdot \left(i \cdot x\right) \]

      2. distribute-lft-neg-in 43.6%

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

      3. associate-*r* 43.6%

         \[\leadsto -\color{blue}{\left(4 \cdot i\right) \cdot x} \]

      4. *-commutative 43.6%

         \[\leadsto -\color{blue}{x \cdot \left(4 \cdot i\right)} \]

      5. distribute-rgt-neg-in 43.6%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

      6. distribute-lft-neg-in 43.6%

         \[\leadsto x \cdot \color{blue}{\left(\left(-4\right) \cdot i\right)} \]

      7. metadata-eval 43.6%

         \[\leadsto x \cdot \left(\color{blue}{-4} \cdot i\right) \]

   8. Simplified 43.6%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

   if 1.64999999999999995e-115 < (*.f64 b c) < 1.49999999999999991e204

   1. Initial program 85.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 42.7%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   6. Taylor expanded in t around inf 35.7%

      \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.6 \cdot 10^{+177}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -6 \cdot 10^{-274}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 1.65 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.5 \cdot 10^{+204}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.2 \cdot 10^{+178}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5.2 \cdot 10^{-293}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 3.6 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.25 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1.2e+178)
   (* b c)
   (if (<= (* b c) -5.2e-293)
     (* (* j k) -27.0)
     (if (<= (* b c) 3.6e-123)
       (* x (* i -4.0))
       (if (<= (* b c) 1.25e+203) (* x (* 18.0 (* y (* z t)))) (* b c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.2e+178) {
		tmp = b * c;
	} else if ((b * c) <= -5.2e-293) {
		tmp = (j * k) * -27.0;
	} else if ((b * c) <= 3.6e-123) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 1.25e+203) {
		tmp = x * (18.0 * (y * (z * t)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-1.2d+178)) then
        tmp = b * c
    else if ((b * c) <= (-5.2d-293)) then
        tmp = (j * k) * (-27.0d0)
    else if ((b * c) <= 3.6d-123) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= 1.25d+203) then
        tmp = x * (18.0d0 * (y * (z * t)))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.2e+178) {
		tmp = b * c;
	} else if ((b * c) <= -5.2e-293) {
		tmp = (j * k) * -27.0;
	} else if ((b * c) <= 3.6e-123) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 1.25e+203) {
		tmp = x * (18.0 * (y * (z * t)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.2e+178:
		tmp = b * c
	elif (b * c) <= -5.2e-293:
		tmp = (j * k) * -27.0
	elif (b * c) <= 3.6e-123:
		tmp = x * (i * -4.0)
	elif (b * c) <= 1.25e+203:
		tmp = x * (18.0 * (y * (z * t)))
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1.2e+178)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -5.2e-293)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (Float64(b * c) <= 3.6e-123)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= 1.25e+203)
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1.2e+178)
		tmp = b * c;
	elseif ((b * c) <= -5.2e-293)
		tmp = (j * k) * -27.0;
	elseif ((b * c) <= 3.6e-123)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= 1.25e+203)
		tmp = x * (18.0 * (y * (z * t)));
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1.2e+178], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5.2e-293], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.6e-123], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.25e+203], N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.2e178 or 1.24999999999999999e203 < (*.f64 b c)

   1. Initial program 81.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. pow1 79.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. associate-*r* 79.5%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 79.5%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 79.5%

         \[\leadsto \left(t \cdot \left({\left(z \cdot \color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)}\right)}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 79.5%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 79.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(y \cdot \left(x \cdot 18\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 79.5%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 79.5%

         \[\leadsto \left(t \cdot \left(z \cdot \left(\color{blue}{\left(18 \cdot x\right)} \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*r* 79.5%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 79.5%

      \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in k around inf 60.9%

      \[\leadsto \color{blue}{k \cdot \left(\left(\frac{b \cdot c}{k} + \frac{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)}{k}\right) - \left(4 \cdot \frac{i \cdot x}{k} + 27 \cdot j\right)\right)} \]

   10. Taylor expanded in b around inf 71.2%

       \[\leadsto \color{blue}{b \cdot c} \]

   if -1.2e178 < (*.f64 b c) < -5.1999999999999996e-293

   1. Initial program 84.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 35.5%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -5.1999999999999996e-293 < (*.f64 b c) < 3.5999999999999997e-123

   1. Initial program 79.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 62.0%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   6. Taylor expanded in t around 0 43.6%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. metadata-eval 43.6%

         \[\leadsto \color{blue}{\left(-4\right)} \cdot \left(i \cdot x\right) \]

      2. distribute-lft-neg-in 43.6%

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

      3. associate-*r* 43.6%

         \[\leadsto -\color{blue}{\left(4 \cdot i\right) \cdot x} \]

      4. *-commutative 43.6%

         \[\leadsto -\color{blue}{x \cdot \left(4 \cdot i\right)} \]

      5. distribute-rgt-neg-in 43.6%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

      6. distribute-lft-neg-in 43.6%

         \[\leadsto x \cdot \color{blue}{\left(\left(-4\right) \cdot i\right)} \]

      7. metadata-eval 43.6%

         \[\leadsto x \cdot \left(\color{blue}{-4} \cdot i\right) \]

   8. Simplified 43.6%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

   if 3.5999999999999997e-123 < (*.f64 b c) < 1.24999999999999999e203

   1. Initial program 85.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 42.7%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   6. Taylor expanded in t around inf 35.7%

      \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 35.7%

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \color{blue}{\left(z \cdot y\right)}\right)\right) \]

      2. associate-*r* 35.5%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right) \]

   8. Simplified 35.5%

      \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(\left(t \cdot z\right) \cdot y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.2 \cdot 10^{+178}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -5.2 \cdot 10^{-293}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 3.6 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.25 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+193}:\\ \;\;\;\;b \cdot \left(\left(c + -4 \cdot \frac{t \cdot a}{b}\right) - 27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(z \cdot \left(18 \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -4e+193)
   (* b (- (+ c (* -4.0 (/ (* t a) b))) (* 27.0 (/ (* j k) b))))
   (-
    (+ (* b c) (* t (- (* z (* 18.0 (* x y))) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4e+193) {
		tmp = b * ((c + (-4.0 * ((t * a) / b))) - (27.0 * ((j * k) / b)));
	} else {
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-4d+193)) then
        tmp = b * ((c + ((-4.0d0) * ((t * a) / b))) - (27.0d0 * ((j * k) / b)))
    else
        tmp = ((b * c) + (t * ((z * (18.0d0 * (x * y))) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4e+193) {
		tmp = b * ((c + (-4.0 * ((t * a) / b))) - (27.0 * ((j * k) / b)));
	} else {
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -4e+193:
		tmp = b * ((c + (-4.0 * ((t * a) / b))) - (27.0 * ((j * k) / b)))
	else:
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -4e+193)
		tmp = Float64(b * Float64(Float64(c + Float64(-4.0 * Float64(Float64(t * a) / b))) - Float64(27.0 * Float64(Float64(j * k) / b))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(z * Float64(18.0 * Float64(x * y))) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -4e+193)
		tmp = b * ((c + (-4.0 * ((t * a) / b))) - (27.0 * ((j * k) / b)));
	else
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -4e+193], N[(b * N[(N[(c + N[(-4.0 * N[(N[(t * a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(N[(j * k), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(z * N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -4.00000000000000026e193

   1. Initial program 76.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 72.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 89.7%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]

   6. Taylor expanded in b around inf 93.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(c + -4 \cdot \frac{a \cdot t}{b}\right) - 27 \cdot \frac{j \cdot k}{b}\right)} \]

   if -4.00000000000000026e193 < (*.f64 b c)

   1. Initial program 83.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. pow1 86.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. associate-*r* 86.1%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 86.1%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 86.1%

         \[\leadsto \left(t \cdot \left({\left(z \cdot \color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)}\right)}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 86.1%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 86.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(y \cdot \left(x \cdot 18\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 86.1%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 86.1%

         \[\leadsto \left(t \cdot \left(z \cdot \left(\color{blue}{\left(18 \cdot x\right)} \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*r* 86.1%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 86.1%

      \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+193}:\\ \;\;\;\;b \cdot \left(\left(c + -4 \cdot \frac{t \cdot a}{b}\right) - 27 \cdot \frac{j \cdot k}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(z \cdot \left(18 \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+32} \lor \neg \left(x \leq -2.15 \cdot 10^{-7}\right) \land x \leq 16500000:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) + \left(b \cdot c - \left(j \cdot 27\right) \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1.06e+52)
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (if (or (<= x -2.8e+32) (and (not (<= x -2.15e-7)) (<= x 16500000.0)))
     (+ (* t (* a -4.0)) (- (* b c) (* (* j 27.0) k)))
     (* x (+ (* (* 18.0 t) (* y z)) (* i -4.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -1.06e+52) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if ((x <= -2.8e+32) || (!(x <= -2.15e-7) && (x <= 16500000.0))) {
		tmp = (t * (a * -4.0)) + ((b * c) - ((j * 27.0) * k));
	} else {
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-1.06d+52)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if ((x <= (-2.8d+32)) .or. (.not. (x <= (-2.15d-7))) .and. (x <= 16500000.0d0)) then
        tmp = (t * (a * (-4.0d0))) + ((b * c) - ((j * 27.0d0) * k))
    else
        tmp = x * (((18.0d0 * t) * (y * z)) + (i * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -1.06e+52) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if ((x <= -2.8e+32) || (!(x <= -2.15e-7) && (x <= 16500000.0))) {
		tmp = (t * (a * -4.0)) + ((b * c) - ((j * 27.0) * k));
	} else {
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -1.06e+52:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif (x <= -2.8e+32) or (not (x <= -2.15e-7) and (x <= 16500000.0)):
		tmp = (t * (a * -4.0)) + ((b * c) - ((j * 27.0) * k))
	else:
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -1.06e+52)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif ((x <= -2.8e+32) || (!(x <= -2.15e-7) && (x <= 16500000.0)))
		tmp = Float64(Float64(t * Float64(a * -4.0)) + Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k)));
	else
		tmp = Float64(x * Float64(Float64(Float64(18.0 * t) * Float64(y * z)) + Float64(i * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -1.06e+52)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif ((x <= -2.8e+32) || (~((x <= -2.15e-7)) && (x <= 16500000.0)))
		tmp = (t * (a * -4.0)) + ((b * c) - ((j * 27.0) * k));
	else
		tmp = x * (((18.0 * t) * (y * z)) + (i * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -1.06e+52], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -2.8e+32], And[N[Not[LessEqual[x, -2.15e-7]], $MachinePrecision], LessEqual[x, 16500000.0]]], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(18.0 * t), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.0599999999999999e52

   1. Initial program 70.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 77.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 70.1%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   if -1.0599999999999999e52 < x < -2.8e32 or -2.1500000000000001e-7 < x < 1.65e7

   1. Initial program 92.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 85.0%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. associate--l+ 85.0%

         \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

      2. associate-*r* 85.0%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      3. associate-*r* 84.2%

         \[\leadsto \left(-4 \cdot a\right) \cdot t + \left(b \cdot c - \color{blue}{\left(27 \cdot j\right) \cdot k}\right) \]

   7. Applied egg-rr 84.2%

      \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t + \left(b \cdot c - \left(27 \cdot j\right) \cdot k\right)} \]

   if -2.8e32 < x < -2.1500000000000001e-7 or 1.65e7 < x

   1. Initial program 73.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 75.3%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 75.3%

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(-4\right) \cdot i\right)} \]

      2. associate-*r* 75.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(18 \cdot t\right) \cdot \left(y \cdot z\right)} + \left(-4\right) \cdot i\right) \]

      3. *-commutative 75.3%

         \[\leadsto x \cdot \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(z \cdot y\right)} + \left(-4\right) \cdot i\right) \]

      4. metadata-eval 75.3%

         \[\leadsto x \cdot \left(\left(18 \cdot t\right) \cdot \left(z \cdot y\right) + \color{blue}{-4} \cdot i\right) \]

   7. Applied egg-rr 75.3%

      \[\leadsto x \cdot \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(z \cdot y\right) + -4 \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+32} \lor \neg \left(x \leq -2.15 \cdot 10^{-7}\right) \land x \leq 16500000:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) + \left(b \cdot c - \left(j \cdot 27\right) \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 85.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 1.1 \cdot 10^{+160}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= c 1.1e+160)
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (- (- (- (* b c) (* 4.0 (* t a))) (* (* x 4.0) i)) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (c <= 1.1e+160) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (c <= 1.1d+160) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = (((b * c) - (4.0d0 * (t * a))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (c <= 1.1e+160) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if c <= 1.1e+160:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (c <= 1.1e+160)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (c <= 1.1e+160)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[c, 1.1e+160], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 1.09999999999999996e160

   1. Initial program 83.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   if 1.09999999999999996e160 < c

   1. Initial program 80.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.2%

      \[\leadsto \left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.1 \cdot 10^{+160}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;b \cdot c \leq -4.5 \cdot 10^{+176}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -8 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 8 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.1 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j k) -27.0)))
   (if (<= (* b c) -4.5e+176)
     (* b c)
     (if (<= (* b c) -8e-287)
       t_1
       (if (<= (* b c) 8e-121)
         (* x (* i -4.0))
         (if (<= (* b c) 3.1e+121) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * k) * -27.0;
	double tmp;
	if ((b * c) <= -4.5e+176) {
		tmp = b * c;
	} else if ((b * c) <= -8e-287) {
		tmp = t_1;
	} else if ((b * c) <= 8e-121) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 3.1e+121) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * k) * (-27.0d0)
    if ((b * c) <= (-4.5d+176)) then
        tmp = b * c
    else if ((b * c) <= (-8d-287)) then
        tmp = t_1
    else if ((b * c) <= 8d-121) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= 3.1d+121) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * k) * -27.0;
	double tmp;
	if ((b * c) <= -4.5e+176) {
		tmp = b * c;
	} else if ((b * c) <= -8e-287) {
		tmp = t_1;
	} else if ((b * c) <= 8e-121) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 3.1e+121) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * k) * -27.0
	tmp = 0
	if (b * c) <= -4.5e+176:
		tmp = b * c
	elif (b * c) <= -8e-287:
		tmp = t_1
	elif (b * c) <= 8e-121:
		tmp = x * (i * -4.0)
	elif (b * c) <= 3.1e+121:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * k) * -27.0)
	tmp = 0.0
	if (Float64(b * c) <= -4.5e+176)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -8e-287)
		tmp = t_1;
	elseif (Float64(b * c) <= 8e-121)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= 3.1e+121)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * k) * -27.0;
	tmp = 0.0;
	if ((b * c) <= -4.5e+176)
		tmp = b * c;
	elseif ((b * c) <= -8e-287)
		tmp = t_1;
	elseif ((b * c) <= 8e-121)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= 3.1e+121)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -4.5e+176], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -8e-287], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 8e-121], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.1e+121], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -4.50000000000000003e176 or 3.10000000000000008e121 < (*.f64 b c)

   1. Initial program 82.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. pow1 81.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. associate-*r* 81.2%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 81.2%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 81.2%

         \[\leadsto \left(t \cdot \left({\left(z \cdot \color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)}\right)}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 81.2%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 81.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(y \cdot \left(x \cdot 18\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 81.2%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 81.2%

         \[\leadsto \left(t \cdot \left(z \cdot \left(\color{blue}{\left(18 \cdot x\right)} \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*r* 81.2%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 81.2%

      \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in k around inf 60.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(\frac{b \cdot c}{k} + \frac{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)}{k}\right) - \left(4 \cdot \frac{i \cdot x}{k} + 27 \cdot j\right)\right)} \]

   10. Taylor expanded in b around inf 65.9%

       \[\leadsto \color{blue}{b \cdot c} \]

   if -4.50000000000000003e176 < (*.f64 b c) < -8.00000000000000017e-287 or 7.9999999999999998e-121 < (*.f64 b c) < 3.10000000000000008e121

   1. Initial program 84.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 35.5%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -8.00000000000000017e-287 < (*.f64 b c) < 7.9999999999999998e-121

   1. Initial program 79.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 62.0%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   6. Taylor expanded in t around 0 43.6%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. metadata-eval 43.6%

         \[\leadsto \color{blue}{\left(-4\right)} \cdot \left(i \cdot x\right) \]

      2. distribute-lft-neg-in 43.6%

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

      3. associate-*r* 43.6%

         \[\leadsto -\color{blue}{\left(4 \cdot i\right) \cdot x} \]

      4. *-commutative 43.6%

         \[\leadsto -\color{blue}{x \cdot \left(4 \cdot i\right)} \]

      5. distribute-rgt-neg-in 43.6%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

      6. distribute-lft-neg-in 43.6%

         \[\leadsto x \cdot \color{blue}{\left(\left(-4\right) \cdot i\right)} \]

      7. metadata-eval 43.6%

         \[\leadsto x \cdot \left(\color{blue}{-4} \cdot i\right) \]

   8. Simplified 43.6%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.5 \cdot 10^{+176}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -8 \cdot 10^{-287}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 8 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.1 \cdot 10^{+121}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 81.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+136} \lor \neg \left(t \leq 10^{+88}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.05e+136) (not (<= t 1e+88)))
   (+ (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))) (* j (* k -27.0)))
   (- (- (- (* b c) (* 4.0 (* t a))) (* (* x 4.0) i)) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.05e+136) || !(t <= 1e+88)) {
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0));
	} else {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-1.05d+136)) .or. (.not. (t <= 1d+88))) then
        tmp = (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))) + (j * (k * (-27.0d0)))
    else
        tmp = (((b * c) - (4.0d0 * (t * a))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.05e+136) || !(t <= 1e+88)) {
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0));
	} else {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.05e+136) or not (t <= 1e+88):
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0))
	else:
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.05e+136) || !(t <= 1e+88))
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.05e+136) || ~((t <= 1e+88)))
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0));
	else
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.05e+136], N[Not[LessEqual[t, 1e+88]], $MachinePrecision]], N[(N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e136 or 9.99999999999999959e87 < t

   1. Initial program 82.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 91.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 84.2%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   if -1.05e136 < t < 9.99999999999999959e87

   1. Initial program 82.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 86.6%

      \[\leadsto \left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+136} \lor \neg \left(t \leq 10^{+88}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27\\ t_2 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;j \leq -3.7 \cdot 10^{+233}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq -4.7 \cdot 10^{+210}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7.6 \cdot 10^{-125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j k) -27.0)) (t_2 (+ (* b c) (* -4.0 (* t a)))))
   (if (<= j -3.7e+233)
     (* k (* j -27.0))
     (if (<= j -4.7e+210)
       t_2
       (if (<= j -3.4e+138)
         t_1
         (if (<= j 7.6e-125)
           t_2
           (if (<= j 1.55e+96) (* x (* i -4.0)) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * k) * -27.0;
	double t_2 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if (j <= -3.7e+233) {
		tmp = k * (j * -27.0);
	} else if (j <= -4.7e+210) {
		tmp = t_2;
	} else if (j <= -3.4e+138) {
		tmp = t_1;
	} else if (j <= 7.6e-125) {
		tmp = t_2;
	} else if (j <= 1.55e+96) {
		tmp = x * (i * -4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * k) * (-27.0d0)
    t_2 = (b * c) + ((-4.0d0) * (t * a))
    if (j <= (-3.7d+233)) then
        tmp = k * (j * (-27.0d0))
    else if (j <= (-4.7d+210)) then
        tmp = t_2
    else if (j <= (-3.4d+138)) then
        tmp = t_1
    else if (j <= 7.6d-125) then
        tmp = t_2
    else if (j <= 1.55d+96) then
        tmp = x * (i * (-4.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * k) * -27.0;
	double t_2 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if (j <= -3.7e+233) {
		tmp = k * (j * -27.0);
	} else if (j <= -4.7e+210) {
		tmp = t_2;
	} else if (j <= -3.4e+138) {
		tmp = t_1;
	} else if (j <= 7.6e-125) {
		tmp = t_2;
	} else if (j <= 1.55e+96) {
		tmp = x * (i * -4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * k) * -27.0
	t_2 = (b * c) + (-4.0 * (t * a))
	tmp = 0
	if j <= -3.7e+233:
		tmp = k * (j * -27.0)
	elif j <= -4.7e+210:
		tmp = t_2
	elif j <= -3.4e+138:
		tmp = t_1
	elif j <= 7.6e-125:
		tmp = t_2
	elif j <= 1.55e+96:
		tmp = x * (i * -4.0)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * k) * -27.0)
	t_2 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (j <= -3.7e+233)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (j <= -4.7e+210)
		tmp = t_2;
	elseif (j <= -3.4e+138)
		tmp = t_1;
	elseif (j <= 7.6e-125)
		tmp = t_2;
	elseif (j <= 1.55e+96)
		tmp = Float64(x * Float64(i * -4.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * k) * -27.0;
	t_2 = (b * c) + (-4.0 * (t * a));
	tmp = 0.0;
	if (j <= -3.7e+233)
		tmp = k * (j * -27.0);
	elseif (j <= -4.7e+210)
		tmp = t_2;
	elseif (j <= -3.4e+138)
		tmp = t_1;
	elseif (j <= 7.6e-125)
		tmp = t_2;
	elseif (j <= 1.55e+96)
		tmp = x * (i * -4.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.7e+233], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.7e+210], t$95$2, If[LessEqual[j, -3.4e+138], t$95$1, If[LessEqual[j, 7.6e-125], t$95$2, If[LessEqual[j, 1.55e+96], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.6999999999999998e233

   1. Initial program 76.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 71.8%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.9%

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

   7. Simplified 71.9%

      \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

   if -3.6999999999999998e233 < j < -4.7000000000000001e210 or -3.40000000000000011e138 < j < 7.6000000000000002e-125

   1. Initial program 81.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 84.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 58.7%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]

   6. Taylor expanded in j around 0 53.1%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]

   if -4.7000000000000001e210 < j < -3.40000000000000011e138 or 1.5499999999999999e96 < j

   1. Initial program 84.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 47.5%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if 7.6000000000000002e-125 < j < 1.5499999999999999e96

   1. Initial program 85.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 46.1%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   6. Taylor expanded in t around 0 23.9%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. metadata-eval 23.9%

         \[\leadsto \color{blue}{\left(-4\right)} \cdot \left(i \cdot x\right) \]

      2. distribute-lft-neg-in 23.9%

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

      3. associate-*r* 23.9%

         \[\leadsto -\color{blue}{\left(4 \cdot i\right) \cdot x} \]

      4. *-commutative 23.9%

         \[\leadsto -\color{blue}{x \cdot \left(4 \cdot i\right)} \]

      5. distribute-rgt-neg-in 23.9%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

      6. distribute-lft-neg-in 23.9%

         \[\leadsto x \cdot \color{blue}{\left(\left(-4\right) \cdot i\right)} \]

      7. metadata-eval 23.9%

         \[\leadsto x \cdot \left(\color{blue}{-4} \cdot i\right) \]

   8. Simplified 23.9%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.7 \cdot 10^{+233}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq -4.7 \cdot 10^{+210}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq -3.4 \cdot 10^{+138}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;j \leq 7.6 \cdot 10^{-125}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 68.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+182} \lor \neg \left(b \cdot c \leq 5 \cdot 10^{+120}\right):\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -2e+182) (not (<= (* b c) 5e+120)))
   (+ (* b c) (* -4.0 (* t a)))
   (+ (* k (* j -27.0)) (* -4.0 (+ (* t a) (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2e+182) || !((b * c) <= 5e+120)) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (k * (j * -27.0)) + (-4.0 * ((t * a) + (x * i)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-2d+182)) .or. (.not. ((b * c) <= 5d+120))) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = (k * (j * (-27.0d0))) + ((-4.0d0) * ((t * a) + (x * i)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2e+182) || !((b * c) <= 5e+120)) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (k * (j * -27.0)) + (-4.0 * ((t * a) + (x * i)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -2e+182) or not ((b * c) <= 5e+120):
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = (k * (j * -27.0)) + (-4.0 * ((t * a) + (x * i)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -2e+182) || !(Float64(b * c) <= 5e+120))
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(k * Float64(j * -27.0)) + Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -2e+182) || ~(((b * c) <= 5e+120)))
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = (k * (j * -27.0)) + (-4.0 * ((t * a) + (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -2e+182], N[Not[LessEqual[N[(b * c), $MachinePrecision], 5e+120]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.0000000000000001e182 or 5.00000000000000019e120 < (*.f64 b c)

   1. Initial program 82.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 80.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 76.6%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]

   6. Taylor expanded in j around 0 76.6%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]

   if -2.0000000000000001e182 < (*.f64 b c) < 5.00000000000000019e120

   1. Initial program 82.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. pow1 82.9%

         \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      2. associate-*r* 83.5%

         \[\leadsto \left(\left(\left({\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)} \cdot t\right)}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 83.5%

         \[\leadsto \left(\left(\left({\color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right)}}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      4. associate-*r* 82.9%

         \[\leadsto \left(\left(\left({\left(t \cdot \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)}\right)}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      5. *-commutative 82.9%

         \[\leadsto \left(\left(\left({\left(t \cdot \color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)}\right)}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      6. *-commutative 82.9%

         \[\leadsto \left(\left(\left({\left(t \cdot \left(z \cdot \color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)}\right)\right)}^{1} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied egg-rr 82.9%

      \[\leadsto \left(\left(\left(\color{blue}{{\left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)\right)}^{1}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   5. Step-by-step derivation

      1. unpow1 82.9%

         \[\leadsto \left(\left(\left(\color{blue}{t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      2. associate-*r* 83.7%

         \[\leadsto \left(\left(\left(\color{blue}{\left(t \cdot z\right) \cdot \left(y \cdot \left(x \cdot 18\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 83.7%

         \[\leadsto \left(\left(\left(\left(t \cdot z\right) \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative 83.7%

         \[\leadsto \left(\left(\left(\left(t \cdot z\right) \cdot \left(\color{blue}{\left(18 \cdot x\right)} \cdot y\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      5. associate-*r* 83.7%

         \[\leadsto \left(\left(\left(\left(t \cdot z\right) \cdot \color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   6. Simplified 83.7%

      \[\leadsto \left(\left(\left(\color{blue}{\left(t \cdot z\right) \cdot \left(18 \cdot \left(x \cdot y\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   7. Taylor expanded in a around inf 74.1%

      \[\leadsto \left(\color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   8. Step-by-step derivation

      1. associate-*r* 74.1%

         \[\leadsto \left(\color{blue}{\left(-4 \cdot a\right) \cdot t} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 74.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(-4 \cdot a\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 74.1%

         \[\leadsto \left(t \cdot \color{blue}{\left(a \cdot -4\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   9. Simplified 74.1%

      \[\leadsto \left(\color{blue}{t \cdot \left(a \cdot -4\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   10. Taylor expanded in t around 0 74.7%

       \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   11. Step-by-step derivation

       1. +-commutative 74.7%

          \[\leadsto -4 \cdot \left(a \cdot t\right) - \color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

       2. associate-*r* 74.1%

          \[\leadsto -4 \cdot \left(a \cdot t\right) - \left(\color{blue}{\left(27 \cdot j\right) \cdot k} + 4 \cdot \left(i \cdot x\right)\right) \]

       3. *-commutative 74.1%

          \[\leadsto -4 \cdot \left(a \cdot t\right) - \left(\color{blue}{\left(j \cdot 27\right)} \cdot k + 4 \cdot \left(i \cdot x\right)\right) \]

       4. associate-*r* 74.6%

          \[\leadsto -4 \cdot \left(a \cdot t\right) - \left(\color{blue}{j \cdot \left(27 \cdot k\right)} + 4 \cdot \left(i \cdot x\right)\right) \]

       5. *-commutative 74.6%

          \[\leadsto -4 \cdot \left(a \cdot t\right) - \left(j \cdot \left(27 \cdot k\right) + \color{blue}{\left(i \cdot x\right) \cdot 4}\right) \]

       6. associate-*r* 74.6%

          \[\leadsto -4 \cdot \left(a \cdot t\right) - \left(j \cdot \left(27 \cdot k\right) + \color{blue}{i \cdot \left(x \cdot 4\right)}\right) \]

       7. associate--r+ 74.6%

          \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) - j \cdot \left(27 \cdot k\right)\right) - i \cdot \left(x \cdot 4\right)} \]

       8. associate-*r* 74.1%

          \[\leadsto \left(-4 \cdot \left(a \cdot t\right) - \color{blue}{\left(j \cdot 27\right) \cdot k}\right) - i \cdot \left(x \cdot 4\right) \]

       9. *-commutative 74.1%

          \[\leadsto \left(-4 \cdot \left(a \cdot t\right) - \color{blue}{\left(27 \cdot j\right)} \cdot k\right) - i \cdot \left(x \cdot 4\right) \]

       10. associate-*r* 74.7%

           \[\leadsto \left(-4 \cdot \left(a \cdot t\right) - \color{blue}{27 \cdot \left(j \cdot k\right)}\right) - i \cdot \left(x \cdot 4\right) \]

       11. cancel-sign-sub-inv 74.7%

           \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(-27\right) \cdot \left(j \cdot k\right)\right)} - i \cdot \left(x \cdot 4\right) \]

       12. metadata-eval 74.7%

           \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) - i \cdot \left(x \cdot 4\right) \]

       13. +-commutative 74.7%

           \[\leadsto \color{blue}{\left(-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(a \cdot t\right)\right)} - i \cdot \left(x \cdot 4\right) \]

       14. associate-*r* 74.7%

           \[\leadsto \left(-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(a \cdot t\right)\right) - \color{blue}{\left(i \cdot x\right) \cdot 4} \]

       15. *-commutative 74.7%

           \[\leadsto \left(-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(a \cdot t\right)\right) - \color{blue}{4 \cdot \left(i \cdot x\right)} \]

       16. associate--l+ 74.7%

           \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(-4 \cdot \left(a \cdot t\right) - 4 \cdot \left(i \cdot x\right)\right)} \]

   12. Simplified 74.1%

       \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j\right) + -4 \cdot \left(a \cdot t + x \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+182} \lor \neg \left(b \cdot c \leq 5 \cdot 10^{+120}\right):\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 73.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+126} \lor \neg \left(t \leq 1.8 \cdot 10^{+87}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -6.5e+126) (not (<= t 1.8e+87)))
   (+ (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))) (* j (* k -27.0)))
   (- (* b c) (+ (* 27.0 (* j k)) (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -6.5e+126) || !(t <= 1.8e+87)) {
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0));
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-6.5d+126)) .or. (.not. (t <= 1.8d+87))) then
        tmp = (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))) + (j * (k * (-27.0d0)))
    else
        tmp = (b * c) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -6.5e+126) || !(t <= 1.8e+87)) {
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0));
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -6.5e+126) or not (t <= 1.8e+87):
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0))
	else:
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -6.5e+126) || !(t <= 1.8e+87))
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * i))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -6.5e+126) || ~((t <= 1.8e+87)))
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0));
	else
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -6.5e+126], N[Not[LessEqual[t, 1.8e+87]], $MachinePrecision]], N[(N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5000000000000005e126 or 1.79999999999999997e87 < t

   1. Initial program 83.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 83.4%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   if -6.5000000000000005e126 < t < 1.79999999999999997e87

   1. Initial program 82.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 78.6%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+126} \lor \neg \left(t \leq 1.8 \cdot 10^{+87}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 54.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.5 \cdot 10^{+176} \lor \neg \left(b \cdot c \leq 1.02 \cdot 10^{+126}\right):\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -2.5e+176) (not (<= (* b c) 1.02e+126)))
   (+ (* b c) (* -4.0 (* t a)))
   (+ (* j (* k -27.0)) (* t (* a -4.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.5e+176) || !((b * c) <= 1.02e+126)) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (j * (k * -27.0)) + (t * (a * -4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-2.5d+176)) .or. (.not. ((b * c) <= 1.02d+126))) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = (j * (k * (-27.0d0))) + (t * (a * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.5e+176) || !((b * c) <= 1.02e+126)) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (j * (k * -27.0)) + (t * (a * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -2.5e+176) or not ((b * c) <= 1.02e+126):
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = (j * (k * -27.0)) + (t * (a * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -2.5e+176) || !(Float64(b * c) <= 1.02e+126))
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(a * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -2.5e+176) || ~(((b * c) <= 1.02e+126)))
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = (j * (k * -27.0)) + (t * (a * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -2.5e+176], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.02e+126]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.5e176 or 1.02e126 < (*.f64 b c)

   1. Initial program 82.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 75.7%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]

   6. Taylor expanded in j around 0 75.7%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]

   if -2.5e176 < (*.f64 b c) < 1.02e126

   1. Initial program 82.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 50.5%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. associate-*r* 50.5%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + j \cdot \left(k \cdot -27\right) \]

      2. *-commutative 50.5%

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Simplified 50.5%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.5 \cdot 10^{+176} \lor \neg \left(b \cdot c \leq 1.02 \cdot 10^{+126}\right):\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 71.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+128} \lor \neg \left(t \leq 3 \cdot 10^{+87}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -5.8e+128) (not (<= t 3e+87)))
   (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
   (- (* b c) (+ (* 27.0 (* j k)) (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -5.8e+128) || !(t <= 3e+87)) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-5.8d+128)) .or. (.not. (t <= 3d+87))) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else
        tmp = (b * c) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -5.8e+128) || !(t <= 3e+87)) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -5.8e+128) or not (t <= 3e+87):
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	else:
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -5.8e+128) || !(t <= 3e+87))
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * i))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -5.8e+128) || ~((t <= 3e+87)))
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	else
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -5.8e+128], N[Not[LessEqual[t, 3e+87]], $MachinePrecision]], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.8000000000000001e128 or 2.9999999999999999e87 < t

   1. Initial program 83.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. pow1 88.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. associate-*r* 88.3%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 88.3%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 88.3%

         \[\leadsto \left(t \cdot \left({\left(z \cdot \color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)}\right)}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 88.3%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 88.3%

         \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(y \cdot \left(x \cdot 18\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 88.3%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 88.3%

         \[\leadsto \left(t \cdot \left(z \cdot \left(\color{blue}{\left(18 \cdot x\right)} \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*r* 88.3%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 88.3%

      \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in k around inf 73.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(\frac{b \cdot c}{k} + \frac{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)}{k}\right) - \left(4 \cdot \frac{i \cdot x}{k} + 27 \cdot j\right)\right)} \]

   10. Taylor expanded in t around -inf 76.3%

       \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]

   if -5.8000000000000001e128 < t < 2.9999999999999999e87

   1. Initial program 82.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 78.6%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+128} \lor \neg \left(t \leq 3 \cdot 10^{+87}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 49.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -1.9 \cdot 10^{-13}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-125}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= j -1.9e-13)
   (+ (* b c) (* j (* k -27.0)))
   (if (<= j 5.5e-125)
     (+ (* b c) (* -4.0 (* t a)))
     (if (<= j 1.1e+113) (* x (* i -4.0)) (* (* j k) -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -1.9e-13) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (j <= 5.5e-125) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (j <= 1.1e+113) {
		tmp = x * (i * -4.0);
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (j <= (-1.9d-13)) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (j <= 5.5d-125) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (j <= 1.1d+113) then
        tmp = x * (i * (-4.0d0))
    else
        tmp = (j * k) * (-27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -1.9e-13) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (j <= 5.5e-125) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (j <= 1.1e+113) {
		tmp = x * (i * -4.0);
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if j <= -1.9e-13:
		tmp = (b * c) + (j * (k * -27.0))
	elif j <= 5.5e-125:
		tmp = (b * c) + (-4.0 * (t * a))
	elif j <= 1.1e+113:
		tmp = x * (i * -4.0)
	else:
		tmp = (j * k) * -27.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (j <= -1.9e-13)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (j <= 5.5e-125)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (j <= 1.1e+113)
		tmp = Float64(x * Float64(i * -4.0));
	else
		tmp = Float64(Float64(j * k) * -27.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (j <= -1.9e-13)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (j <= 5.5e-125)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (j <= 1.1e+113)
		tmp = x * (i * -4.0);
	else
		tmp = (j * k) * -27.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[j, -1.9e-13], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.5e-125], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.1e+113], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.9e-13

   1. Initial program 72.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 75.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 61.0%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]

   if -1.9e-13 < j < 5.4999999999999997e-125

   1. Initial program 83.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 56.6%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]

   6. Taylor expanded in j around 0 54.4%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]

   if 5.4999999999999997e-125 < j < 1.10000000000000005e113

   1. Initial program 84.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 46.7%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   6. Taylor expanded in t around 0 27.5%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. metadata-eval 27.5%

         \[\leadsto \color{blue}{\left(-4\right)} \cdot \left(i \cdot x\right) \]

      2. distribute-lft-neg-in 27.5%

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

      3. associate-*r* 27.5%

         \[\leadsto -\color{blue}{\left(4 \cdot i\right) \cdot x} \]

      4. *-commutative 27.5%

         \[\leadsto -\color{blue}{x \cdot \left(4 \cdot i\right)} \]

      5. distribute-rgt-neg-in 27.5%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

      6. distribute-lft-neg-in 27.5%

         \[\leadsto x \cdot \color{blue}{\left(\left(-4\right) \cdot i\right)} \]

      7. metadata-eval 27.5%

         \[\leadsto x \cdot \left(\color{blue}{-4} \cdot i\right) \]

   8. Simplified 27.5%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

   if 1.10000000000000005e113 < j

   1. Initial program 93.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 52.2%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.9 \cdot 10^{-13}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-125}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 37.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.9 \cdot 10^{+176} \lor \neg \left(b \cdot c \leq 2.9 \cdot 10^{+122}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -4.9e+176) (not (<= (* b c) 2.9e+122)))
   (* b c)
   (* (* j k) -27.0)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -4.9e+176) || !((b * c) <= 2.9e+122)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-4.9d+176)) .or. (.not. ((b * c) <= 2.9d+122))) then
        tmp = b * c
    else
        tmp = (j * k) * (-27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -4.9e+176) || !((b * c) <= 2.9e+122)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -4.9e+176) or not ((b * c) <= 2.9e+122):
		tmp = b * c
	else:
		tmp = (j * k) * -27.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -4.9e+176) || !(Float64(b * c) <= 2.9e+122))
		tmp = Float64(b * c);
	else
		tmp = Float64(Float64(j * k) * -27.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -4.9e+176) || ~(((b * c) <= 2.9e+122)))
		tmp = b * c;
	else
		tmp = (j * k) * -27.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -4.9e+176], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2.9e+122]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -4.9e176 or 2.9000000000000001e122 < (*.f64 b c)

   1. Initial program 82.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. pow1 81.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. associate-*r* 81.2%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 81.2%

         \[\leadsto \left(t \cdot \left({\color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 81.2%

         \[\leadsto \left(t \cdot \left({\left(z \cdot \color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)}\right)}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 81.2%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. unpow1 81.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(y \cdot \left(x \cdot 18\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 81.2%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 81.2%

         \[\leadsto \left(t \cdot \left(z \cdot \left(\color{blue}{\left(18 \cdot x\right)} \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*r* 81.2%

         \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 81.2%

      \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in k around inf 60.2%

      \[\leadsto \color{blue}{k \cdot \left(\left(\frac{b \cdot c}{k} + \frac{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)}{k}\right) - \left(4 \cdot \frac{i \cdot x}{k} + 27 \cdot j\right)\right)} \]

   10. Taylor expanded in b around inf 65.9%

       \[\leadsto \color{blue}{b \cdot c} \]

   if -4.9e176 < (*.f64 b c) < 2.9000000000000001e122

   1. Initial program 82.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 32.2%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.9 \cdot 10^{+176} \lor \neg \left(b \cdot c \leq 2.9 \cdot 10^{+122}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 24.2% accurate, 10.3× speedup

Math

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

FPCore

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

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Fortran

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

Java

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

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.7%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

3. Simplified 85.1%

   \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. pow1 85.1%

      \[\leadsto \left(t \cdot \left(\color{blue}{{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   2. associate-*r* 84.6%

      \[\leadsto \left(t \cdot \left({\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   3. *-commutative 84.6%

      \[\leadsto \left(t \cdot \left({\color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)}}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   4. *-commutative 84.6%

      \[\leadsto \left(t \cdot \left({\left(z \cdot \color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)}\right)}^{1} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

6. Applied egg-rr 84.6%

   \[\leadsto \left(t \cdot \left(\color{blue}{{\left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)}^{1}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
7. Step-by-step derivation

   1. unpow1 84.6%

      \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(y \cdot \left(x \cdot 18\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   2. *-commutative 84.6%

      \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   3. *-commutative 84.6%

      \[\leadsto \left(t \cdot \left(z \cdot \left(\color{blue}{\left(18 \cdot x\right)} \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   4. associate-*r* 84.6%

      \[\leadsto \left(t \cdot \left(z \cdot \color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

8. Simplified 84.6%

   \[\leadsto \left(t \cdot \left(\color{blue}{z \cdot \left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

9. Taylor expanded in k around inf 72.3%

   \[\leadsto \color{blue}{k \cdot \left(\left(\frac{b \cdot c}{k} + \frac{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)}{k}\right) - \left(4 \cdot \frac{i \cdot x}{k} + 27 \cdot j\right)\right)} \]

10. Taylor expanded in b around inf 24.2%

    \[\leadsto \color{blue}{b \cdot c} \]

11. Final simplification 24.2%

    \[\leadsto b \cdot c \]
12. Add Preprocessing

Developer target: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024080 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))