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

Percentage Accurate: 85.3% → 93.6%

Time: 38.4s

Alternatives: 28

Speedup: 0.8×

• 51.2% 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: 93.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - t\_1\\ t_3 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ t_4 := \left(\left(b \cdot c + t\_3\right) - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+245}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2
         (-
          (-
           (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
           (* (* x 4.0) i))
          t_1))
        (t_3 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
        (t_4 (- (- (+ (* b c) t_3) (* 4.0 (* t a))) t_1)))
   (if (<= t_2 (- INFINITY))
     t_4
     (if (<= t_2 5e+245) t_2 (if (<= t_2 INFINITY) t_4 t_3)))))

C

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 * 27.0) * k;
	double t_2 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1;
	double t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_4 = (((b * c) + t_3) - (4.0 * (t * a))) - t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_2 <= 5e+245) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

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 * 27.0) * k;
	double t_2 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1;
	double t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_4 = (((b * c) + t_3) - (4.0 * (t * a))) - t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_2 <= 5e+245) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[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 * 27.0) * k
	t_2 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1
	t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	t_4 = (((b * c) + t_3) - (4.0 * (t * a))) - t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_4
	elif t_2 <= 5e+245:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

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 * 27.0) * k)
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - t_1)
	t_3 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	t_4 = Float64(Float64(Float64(Float64(b * c) + t_3) - Float64(4.0 * Float64(t * a))) - t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_2 <= 5e+245)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_4;
	else
		tmp = t_3;
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1;
	t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	t_4 = (((b * c) + t_3) - (4.0 * (t * a))) - t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_4;
	elseif (t_2 <= 5e+245)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_4;
	else
		tmp = t_3;
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(b * c), $MachinePrecision] + t$95$3), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$4, If[LessEqual[t$95$2, 5e+245], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$4, t$95$3]]]]]]]

Derivation

1. Split input into 3 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 or 5.00000000000000034e245 < (-.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 91.8%

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

   3. Taylor expanded in x around 0 97.1%

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

   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)) < 5.00000000000000034e245

   1. Initial program 99.5%

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

   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 29.0%

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

   5. Taylor expanded in x around inf 80.7%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq -\infty:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+245}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 53.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(t \cdot a\right) \cdot -4\\ t_2 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_3 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+113}:\\ \;\;\;\;b \cdot c - t\_3\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{-253}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{-152}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+186}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* t a) -4.0))
        (t_2 (- (* b c) (* 4.0 (* x i))))
        (t_3 (* (* j 27.0) k)))
   (if (<= t_3 -2e+113)
     (- (* b c) t_3)
     (if (<= t_3 -5e-23)
       t_2
       (if (<= t_3 -5e-49)
         (* x (* 18.0 (* t (* y z))))
         (if (<= t_3 2e-253)
           t_2
           (if (<= t_3 5e-152)
             (+ (* b c) t_1)
             (if (<= t_3 2e+186) t_2 (+ (* j (* k -27.0)) t_1)))))))))

C

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 = (t * a) * -4.0;
	double t_2 = (b * c) - (4.0 * (x * i));
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (t_3 <= -2e+113) {
		tmp = (b * c) - t_3;
	} else if (t_3 <= -5e-23) {
		tmp = t_2;
	} else if (t_3 <= -5e-49) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if (t_3 <= 2e-253) {
		tmp = t_2;
	} else if (t_3 <= 5e-152) {
		tmp = (b * c) + t_1;
	} else if (t_3 <= 2e+186) {
		tmp = t_2;
	} else {
		tmp = (j * (k * -27.0)) + 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.
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 = (t * a) * (-4.0d0)
    t_2 = (b * c) - (4.0d0 * (x * i))
    t_3 = (j * 27.0d0) * k
    if (t_3 <= (-2d+113)) then
        tmp = (b * c) - t_3
    else if (t_3 <= (-5d-23)) then
        tmp = t_2
    else if (t_3 <= (-5d-49)) then
        tmp = x * (18.0d0 * (t * (y * z)))
    else if (t_3 <= 2d-253) then
        tmp = t_2
    else if (t_3 <= 5d-152) then
        tmp = (b * c) + t_1
    else if (t_3 <= 2d+186) then
        tmp = t_2
    else
        tmp = (j * (k * (-27.0d0))) + 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;
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 = (t * a) * -4.0;
	double t_2 = (b * c) - (4.0 * (x * i));
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (t_3 <= -2e+113) {
		tmp = (b * c) - t_3;
	} else if (t_3 <= -5e-23) {
		tmp = t_2;
	} else if (t_3 <= -5e-49) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if (t_3 <= 2e-253) {
		tmp = t_2;
	} else if (t_3 <= 5e-152) {
		tmp = (b * c) + t_1;
	} else if (t_3 <= 2e+186) {
		tmp = t_2;
	} else {
		tmp = (j * (k * -27.0)) + 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (t * a) * -4.0
	t_2 = (b * c) - (4.0 * (x * i))
	t_3 = (j * 27.0) * k
	tmp = 0
	if t_3 <= -2e+113:
		tmp = (b * c) - t_3
	elif t_3 <= -5e-23:
		tmp = t_2
	elif t_3 <= -5e-49:
		tmp = x * (18.0 * (t * (y * z)))
	elif t_3 <= 2e-253:
		tmp = t_2
	elif t_3 <= 5e-152:
		tmp = (b * c) + t_1
	elif t_3 <= 2e+186:
		tmp = t_2
	else:
		tmp = (j * (k * -27.0)) + 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(t * a) * -4.0)
	t_2 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	t_3 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_3 <= -2e+113)
		tmp = Float64(Float64(b * c) - t_3);
	elseif (t_3 <= -5e-23)
		tmp = t_2;
	elseif (t_3 <= -5e-49)
		tmp = Float64(x * Float64(18.0 * Float64(t * Float64(y * z))));
	elseif (t_3 <= 2e-253)
		tmp = t_2;
	elseif (t_3 <= 5e-152)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (t_3 <= 2e+186)
		tmp = t_2;
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (t * a) * -4.0;
	t_2 = (b * c) - (4.0 * (x * i));
	t_3 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_3 <= -2e+113)
		tmp = (b * c) - t_3;
	elseif (t_3 <= -5e-23)
		tmp = t_2;
	elseif (t_3 <= -5e-49)
		tmp = x * (18.0 * (t * (y * z)));
	elseif (t_3 <= 2e-253)
		tmp = t_2;
	elseif (t_3 <= 5e-152)
		tmp = (b * c) + t_1;
	elseif (t_3 <= 2e+186)
		tmp = t_2;
	else
		tmp = (j * (k * -27.0)) + 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+113], N[(N[(b * c), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[t$95$3, -5e-23], t$95$2, If[LessEqual[t$95$3, -5e-49], N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e-253], t$95$2, If[LessEqual[t$95$3, 5e-152], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 2e+186], t$95$2, N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j 27) k) < -2e113

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0 88.8%

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

   4. Taylor expanded in b around inf 78.1%

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

   if -2e113 < (*.f64 (*.f64 j 27) k) < -5.0000000000000002e-23 or -4.9999999999999999e-49 < (*.f64 (*.f64 j 27) k) < 2.0000000000000001e-253 or 4.9999999999999997e-152 < (*.f64 (*.f64 j 27) k) < 1.99999999999999996e186

   1. Initial program 86.8%

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

   3. Taylor expanded in t around 0 61.3%

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

   4. Taylor expanded in j around 0 55.8%

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

   if -5.0000000000000002e-23 < (*.f64 (*.f64 j 27) k) < -4.9999999999999999e-49

   1. Initial program 56.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in x around inf 67.7%

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

   6. Taylor expanded in t around inf 67.7%

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

   if 2.0000000000000001e-253 < (*.f64 (*.f64 j 27) k) < 4.9999999999999997e-152

   1. Initial program 76.7%

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

   3. Simplified 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 x around inf 88.9%

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

      1. associate-*r* 88.9%

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

      2. *-commutative 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in x around 0 60.1%

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

   if 1.99999999999999996e186 < (*.f64 (*.f64 j 27) k)

   1. Initial program 79.2%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in a around inf 85.5%

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

      1. *-commutative 85.5%

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

   7. Simplified 85.5%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+113}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{-23}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-253}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{-152}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+186}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+113}:\\ \;\;\;\;b \cdot c - t\_2\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-152}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;t\_2 \leq 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* x i)))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+113)
     (- (* b c) t_2)
     (if (<= t_2 -5e-23)
       t_1
       (if (<= t_2 -5e-49)
         (* x (* 18.0 (* t (* y z))))
         (if (<= t_2 2e-253)
           t_1
           (if (<= t_2 5e-152)
             (+ (* b c) (* (* t a) -4.0))
             (if (<= t_2 1e+118) t_1 (+ (* 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);
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 * (x * i));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+113) {
		tmp = (b * c) - t_2;
	} else if (t_2 <= -5e-23) {
		tmp = t_1;
	} else if (t_2 <= -5e-49) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if (t_2 <= 2e-253) {
		tmp = t_1;
	} else if (t_2 <= 5e-152) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if (t_2 <= 1e+118) {
		tmp = t_1;
	} else {
		tmp = (b * c) + (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.
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 = (b * c) - (4.0d0 * (x * i))
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-2d+113)) then
        tmp = (b * c) - t_2
    else if (t_2 <= (-5d-23)) then
        tmp = t_1
    else if (t_2 <= (-5d-49)) then
        tmp = x * (18.0d0 * (t * (y * z)))
    else if (t_2 <= 2d-253) then
        tmp = t_1
    else if (t_2 <= 5d-152) then
        tmp = (b * c) + ((t * a) * (-4.0d0))
    else if (t_2 <= 1d+118) then
        tmp = t_1
    else
        tmp = (b * c) + (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;
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 * (x * i));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+113) {
		tmp = (b * c) - t_2;
	} else if (t_2 <= -5e-23) {
		tmp = t_1;
	} else if (t_2 <= -5e-49) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if (t_2 <= 2e-253) {
		tmp = t_1;
	} else if (t_2 <= 5e-152) {
		tmp = (b * c) + ((t * a) * -4.0);
	} else if (t_2 <= 1e+118) {
		tmp = t_1;
	} else {
		tmp = (b * c) + (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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (x * i))
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -2e+113:
		tmp = (b * c) - t_2
	elif t_2 <= -5e-23:
		tmp = t_1
	elif t_2 <= -5e-49:
		tmp = x * (18.0 * (t * (y * z)))
	elif t_2 <= 2e-253:
		tmp = t_1
	elif t_2 <= 5e-152:
		tmp = (b * c) + ((t * a) * -4.0)
	elif t_2 <= 1e+118:
		tmp = t_1
	else:
		tmp = (b * c) + (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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+113)
		tmp = Float64(Float64(b * c) - t_2);
	elseif (t_2 <= -5e-23)
		tmp = t_1;
	elseif (t_2 <= -5e-49)
		tmp = Float64(x * Float64(18.0 * Float64(t * Float64(y * z))));
	elseif (t_2 <= 2e-253)
		tmp = t_1;
	elseif (t_2 <= 5e-152)
		tmp = Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0));
	elseif (t_2 <= 1e+118)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) + 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (x * i));
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -2e+113)
		tmp = (b * c) - t_2;
	elseif (t_2 <= -5e-23)
		tmp = t_1;
	elseif (t_2 <= -5e-49)
		tmp = x * (18.0 * (t * (y * z)));
	elseif (t_2 <= 2e-253)
		tmp = t_1;
	elseif (t_2 <= 5e-152)
		tmp = (b * c) + ((t * a) * -4.0);
	elseif (t_2 <= 1e+118)
		tmp = t_1;
	else
		tmp = (b * c) + (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+113], N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$2, -5e-23], t$95$1, If[LessEqual[t$95$2, -5e-49], N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e-253], t$95$1, If[LessEqual[t$95$2, 5e-152], N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+118], t$95$1, N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j 27) k) < -2e113

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0 88.8%

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

   4. Taylor expanded in b around inf 78.1%

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

   if -2e113 < (*.f64 (*.f64 j 27) k) < -5.0000000000000002e-23 or -4.9999999999999999e-49 < (*.f64 (*.f64 j 27) k) < 2.0000000000000001e-253 or 4.9999999999999997e-152 < (*.f64 (*.f64 j 27) k) < 9.99999999999999967e117

   1. Initial program 86.1%

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

   3. Taylor expanded in t around 0 60.0%

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

   4. Taylor expanded in j around 0 56.0%

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

   if -5.0000000000000002e-23 < (*.f64 (*.f64 j 27) k) < -4.9999999999999999e-49

   1. Initial program 56.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in x around inf 67.7%

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

   6. Taylor expanded in t around inf 67.7%

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

   if 2.0000000000000001e-253 < (*.f64 (*.f64 j 27) k) < 4.9999999999999997e-152

   1. Initial program 76.7%

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

   3. Simplified 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 x around inf 88.9%

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

      1. associate-*r* 88.9%

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

      2. *-commutative 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in x around 0 60.1%

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

   if 9.99999999999999967e117 < (*.f64 (*.f64 j 27) k)

   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 87.7%

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

   5. Taylor expanded in b around inf 75.8%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+113}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{-23}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-253}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{-152}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+118}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.5 \cdot 10^{+104}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.35 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{-302}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-170}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 7 \cdot 10^{-79}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.35 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.48 \cdot 10^{+181}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -5.5e+104)
   (* b c)
   (if (<= (* b c) -1.35e-92)
     (* x (* 18.0 (* z (* y t))))
     (if (<= (* b c) 3.5e-302)
       (* k (* j -27.0))
       (if (<= (* b c) 2e-170)
         (* (* x i) -4.0)
         (if (<= (* b c) 7e-79)
           (* -27.0 (* j k))
           (if (<= (* b c) 1.35e+40)
             (* t (* a -4.0))
             (if (<= (* b c) 1.48e+181)
               (* 18.0 (* t (* x (* y z))))
               (* b c)))))))))

C

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) <= -5.5e+104) {
		tmp = b * c;
	} else if ((b * c) <= -1.35e-92) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if ((b * c) <= 3.5e-302) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 2e-170) {
		tmp = (x * i) * -4.0;
	} else if ((b * c) <= 7e-79) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 1.35e+40) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 1.48e+181) {
		tmp = 18.0 * (t * (x * (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.
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) <= (-5.5d+104)) then
        tmp = b * c
    else if ((b * c) <= (-1.35d-92)) then
        tmp = x * (18.0d0 * (z * (y * t)))
    else if ((b * c) <= 3.5d-302) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 2d-170) then
        tmp = (x * i) * (-4.0d0)
    else if ((b * c) <= 7d-79) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 1.35d+40) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= 1.48d+181) then
        tmp = 18.0d0 * (t * (x * (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;
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) <= -5.5e+104) {
		tmp = b * c;
	} else if ((b * c) <= -1.35e-92) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if ((b * c) <= 3.5e-302) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 2e-170) {
		tmp = (x * i) * -4.0;
	} else if ((b * c) <= 7e-79) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 1.35e+40) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 1.48e+181) {
		tmp = 18.0 * (t * (x * (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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -5.5e+104:
		tmp = b * c
	elif (b * c) <= -1.35e-92:
		tmp = x * (18.0 * (z * (y * t)))
	elif (b * c) <= 3.5e-302:
		tmp = k * (j * -27.0)
	elif (b * c) <= 2e-170:
		tmp = (x * i) * -4.0
	elif (b * c) <= 7e-79:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 1.35e+40:
		tmp = t * (a * -4.0)
	elif (b * c) <= 1.48e+181:
		tmp = 18.0 * (t * (x * (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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -5.5e+104)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.35e-92)
		tmp = Float64(x * Float64(18.0 * Float64(z * Float64(y * t))));
	elseif (Float64(b * c) <= 3.5e-302)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 2e-170)
		tmp = Float64(Float64(x * i) * -4.0);
	elseif (Float64(b * c) <= 7e-79)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 1.35e+40)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= 1.48e+181)
		tmp = Float64(18.0 * Float64(t * Float64(x * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -5.5e+104)
		tmp = b * c;
	elseif ((b * c) <= -1.35e-92)
		tmp = x * (18.0 * (z * (y * t)));
	elseif ((b * c) <= 3.5e-302)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 2e-170)
		tmp = (x * i) * -4.0;
	elseif ((b * c) <= 7e-79)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 1.35e+40)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= 1.48e+181)
		tmp = 18.0 * (t * (x * (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -5.5e+104], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.35e-92], N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.5e-302], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e-170], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7e-79], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.35e+40], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.48e+181], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if (*.f64 b c) < -5.50000000000000017e104 or 1.4800000000000001e181 < (*.f64 b c)

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0 87.7%

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

   4. Taylor expanded in a around 0 83.0%

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

   5. Taylor expanded in b around inf 60.4%

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

   if -5.50000000000000017e104 < (*.f64 b c) < -1.34999999999999998e-92

   1. Initial program 87.5%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf 61.6%

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

   6. Taylor expanded in t around inf 42.6%

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

      1. associate-*r* 42.6%

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

   8. Simplified 42.6%

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

   if -1.34999999999999998e-92 < (*.f64 b c) < 3.5000000000000001e-302

   1. Initial program 87.2%

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

   3. Taylor expanded in x around 0 86.4%

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

   4. Taylor expanded in a around 0 79.6%

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

   5. Taylor expanded in j around inf 46.4%

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

      1. associate-*r* 46.4%

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

   7. Simplified 46.4%

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

   if 3.5000000000000001e-302 < (*.f64 b c) < 1.99999999999999997e-170

   1. Initial program 79.9%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in x around inf 72.8%

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

   6. Taylor expanded in t around 0 49.5%

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

   if 1.99999999999999997e-170 < (*.f64 b c) < 7.00000000000000059e-79

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in j around inf 51.3%

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

   if 7.00000000000000059e-79 < (*.f64 b c) < 1.35000000000000005e40

   1. Initial program 78.0%

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

   3. Taylor expanded in x around 0 86.3%

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

   4. Taylor expanded in t around 0 72.2%

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

      1. *-commutative 72.2%

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

      2. *-commutative 72.2%

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

      3. associate-*r* 72.2%

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

      4. *-commutative 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in a around inf 41.2%

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

      1. associate-*r* 41.2%

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

   9. Simplified 41.2%

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

   if 1.35000000000000005e40 < (*.f64 b c) < 1.4800000000000001e181

   1. Initial program 71.2%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in x around inf 60.3%

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

   6. Taylor expanded in t around inf 42.1%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.5 \cdot 10^{+104}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.35 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{-302}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-170}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 7 \cdot 10^{-79}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.35 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.48 \cdot 10^{+181}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + \left(t \cdot a\right) \cdot -4\\ t_2 := \left(y \cdot \left(x \cdot z\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{if}\;b \cdot c \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -1.6 \cdot 10^{-91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 5.5 \cdot 10^{-302}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 4.5 \cdot 10^{-78}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 1.55 \cdot 10^{+46} \lor \neg \left(b \cdot c \leq 7.6 \cdot 10^{+168}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* (* t a) -4.0))) (t_2 (* (* y (* x z)) (* 18.0 t))))
   (if (<= (* b c) -3.8e+73)
     t_1
     (if (<= (* b c) -1.6e-91)
       t_2
       (if (<= (* b c) 5.5e-302)
         (* k (* j -27.0))
         (if (<= (* b c) 4.5e-78)
           (* (* x i) -4.0)
           (if (or (<= (* b c) 1.55e+46) (not (<= (* b c) 7.6e+168)))
             t_1
             t_2)))))))

C

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) + ((t * a) * -4.0);
	double t_2 = (y * (x * z)) * (18.0 * t);
	double tmp;
	if ((b * c) <= -3.8e+73) {
		tmp = t_1;
	} else if ((b * c) <= -1.6e-91) {
		tmp = t_2;
	} else if ((b * c) <= 5.5e-302) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 4.5e-78) {
		tmp = (x * i) * -4.0;
	} else if (((b * c) <= 1.55e+46) || !((b * c) <= 7.6e+168)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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.
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 = (b * c) + ((t * a) * (-4.0d0))
    t_2 = (y * (x * z)) * (18.0d0 * t)
    if ((b * c) <= (-3.8d+73)) then
        tmp = t_1
    else if ((b * c) <= (-1.6d-91)) then
        tmp = t_2
    else if ((b * c) <= 5.5d-302) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 4.5d-78) then
        tmp = (x * i) * (-4.0d0)
    else if (((b * c) <= 1.55d+46) .or. (.not. ((b * c) <= 7.6d+168))) then
        tmp = t_1
    else
        tmp = t_2
    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;
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) + ((t * a) * -4.0);
	double t_2 = (y * (x * z)) * (18.0 * t);
	double tmp;
	if ((b * c) <= -3.8e+73) {
		tmp = t_1;
	} else if ((b * c) <= -1.6e-91) {
		tmp = t_2;
	} else if ((b * c) <= 5.5e-302) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 4.5e-78) {
		tmp = (x * i) * -4.0;
	} else if (((b * c) <= 1.55e+46) || !((b * c) <= 7.6e+168)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[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) + ((t * a) * -4.0)
	t_2 = (y * (x * z)) * (18.0 * t)
	tmp = 0
	if (b * c) <= -3.8e+73:
		tmp = t_1
	elif (b * c) <= -1.6e-91:
		tmp = t_2
	elif (b * c) <= 5.5e-302:
		tmp = k * (j * -27.0)
	elif (b * c) <= 4.5e-78:
		tmp = (x * i) * -4.0
	elif ((b * c) <= 1.55e+46) or not ((b * c) <= 7.6e+168):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

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(Float64(t * a) * -4.0))
	t_2 = Float64(Float64(y * Float64(x * z)) * Float64(18.0 * t))
	tmp = 0.0
	if (Float64(b * c) <= -3.8e+73)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.6e-91)
		tmp = t_2;
	elseif (Float64(b * c) <= 5.5e-302)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 4.5e-78)
		tmp = Float64(Float64(x * i) * -4.0);
	elseif ((Float64(b * c) <= 1.55e+46) || !(Float64(b * c) <= 7.6e+168))
		tmp = t_1;
	else
		tmp = t_2;
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + ((t * a) * -4.0);
	t_2 = (y * (x * z)) * (18.0 * t);
	tmp = 0.0;
	if ((b * c) <= -3.8e+73)
		tmp = t_1;
	elseif ((b * c) <= -1.6e-91)
		tmp = t_2;
	elseif ((b * c) <= 5.5e-302)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 4.5e-78)
		tmp = (x * i) * -4.0;
	elseif (((b * c) <= 1.55e+46) || ~(((b * c) <= 7.6e+168)))
		tmp = t_1;
	else
		tmp = t_2;
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3.8e+73], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.6e-91], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 5.5e-302], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.5e-78], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], If[Or[LessEqual[N[(b * c), $MachinePrecision], 1.55e+46], N[Not[LessEqual[N[(b * c), $MachinePrecision], 7.6e+168]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -3.80000000000000022e73 or 4.5e-78 < (*.f64 b c) < 1.54999999999999988e46 or 7.6000000000000005e168 < (*.f64 b c)

   1. Initial program 82.9%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in x around inf 79.6%

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

      1. associate-*r* 79.6%

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

      2. *-commutative 79.6%

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

   7. Simplified 79.6%

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

   8. Taylor expanded in x around 0 61.5%

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

   if -3.80000000000000022e73 < (*.f64 b c) < -1.59999999999999998e-91 or 1.54999999999999988e46 < (*.f64 b c) < 7.6000000000000005e168

   1. Initial program 77.8%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in x around inf 75.0%

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

      1. associate-*r* 75.0%

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

      2. *-commutative 75.0%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in y around inf 46.9%

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

      1. *-commutative 46.9%

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

      2. *-commutative 46.9%

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

      3. associate-*l* 47.0%

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

      4. *-commutative 47.0%

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

      5. associate-*l* 48.7%

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

   10. Simplified 48.7%

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

   if -1.59999999999999998e-91 < (*.f64 b c) < 5.5000000000000001e-302

   1. Initial program 87.2%

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

   3. Taylor expanded in x around 0 86.4%

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

   4. Taylor expanded in a around 0 79.6%

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

   5. Taylor expanded in j around inf 46.4%

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

      1. associate-*r* 46.4%

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

   7. Simplified 46.4%

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

   if 5.5000000000000001e-302 < (*.f64 b c) < 4.5e-78

   1. Initial program 86.6%

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

   3. Simplified 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. Taylor expanded in x around inf 64.1%

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

   6. Taylor expanded in t around 0 43.6%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq -1.6 \cdot 10^{-91}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 5.5 \cdot 10^{-302}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 4.5 \cdot 10^{-78}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 1.55 \cdot 10^{+46} \lor \neg \left(b \cdot c \leq 7.6 \cdot 10^{+168}\right):\\ \;\;\;\;b \cdot c + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right)\right) \cdot \left(18 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9.5 \cdot 10^{+152}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{-302}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 5.6 \cdot 10^{-171}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 6.5 \cdot 10^{-79}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.3 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.7 \cdot 10^{+185}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -9.5e+152)
   (* b c)
   (if (<= (* b c) 1.9e-302)
     (* k (* j -27.0))
     (if (<= (* b c) 5.6e-171)
       (* (* x i) -4.0)
       (if (<= (* b c) 6.5e-79)
         (* -27.0 (* j k))
         (if (<= (* b c) 1.3e+40)
           (* t (* a -4.0))
           (if (<= (* b c) 3.7e+185)
             (* 18.0 (* t (* x (* y z))))
             (* b c))))))))

C

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) <= -9.5e+152) {
		tmp = b * c;
	} else if ((b * c) <= 1.9e-302) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 5.6e-171) {
		tmp = (x * i) * -4.0;
	} else if ((b * c) <= 6.5e-79) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 1.3e+40) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 3.7e+185) {
		tmp = 18.0 * (t * (x * (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.
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) <= (-9.5d+152)) then
        tmp = b * c
    else if ((b * c) <= 1.9d-302) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 5.6d-171) then
        tmp = (x * i) * (-4.0d0)
    else if ((b * c) <= 6.5d-79) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 1.3d+40) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= 3.7d+185) then
        tmp = 18.0d0 * (t * (x * (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;
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) <= -9.5e+152) {
		tmp = b * c;
	} else if ((b * c) <= 1.9e-302) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 5.6e-171) {
		tmp = (x * i) * -4.0;
	} else if ((b * c) <= 6.5e-79) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 1.3e+40) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 3.7e+185) {
		tmp = 18.0 * (t * (x * (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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -9.5e+152:
		tmp = b * c
	elif (b * c) <= 1.9e-302:
		tmp = k * (j * -27.0)
	elif (b * c) <= 5.6e-171:
		tmp = (x * i) * -4.0
	elif (b * c) <= 6.5e-79:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 1.3e+40:
		tmp = t * (a * -4.0)
	elif (b * c) <= 3.7e+185:
		tmp = 18.0 * (t * (x * (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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -9.5e+152)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 1.9e-302)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 5.6e-171)
		tmp = Float64(Float64(x * i) * -4.0);
	elseif (Float64(b * c) <= 6.5e-79)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 1.3e+40)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= 3.7e+185)
		tmp = Float64(18.0 * Float64(t * Float64(x * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -9.5e+152)
		tmp = b * c;
	elseif ((b * c) <= 1.9e-302)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 5.6e-171)
		tmp = (x * i) * -4.0;
	elseif ((b * c) <= 6.5e-79)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 1.3e+40)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= 3.7e+185)
		tmp = 18.0 * (t * (x * (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -9.5e+152], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.9e-302], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5.6e-171], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6.5e-79], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.3e+40], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.7e+185], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 b c) < -9.49999999999999916e152 or 3.6999999999999997e185 < (*.f64 b c)

   1. Initial program 81.9%

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

   3. Taylor expanded in x around 0 86.8%

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

   4. Taylor expanded in a around 0 83.0%

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

   5. Taylor expanded in b around inf 64.9%

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

   if -9.49999999999999916e152 < (*.f64 b c) < 1.9e-302

   1. Initial program 88.1%

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

   3. Taylor expanded in x around 0 87.8%

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

   4. Taylor expanded in a around 0 79.6%

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

   5. Taylor expanded in j around inf 38.4%

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

      1. associate-*r* 38.4%

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

   7. Simplified 38.4%

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

   if 1.9e-302 < (*.f64 b c) < 5.60000000000000046e-171

   1. Initial program 79.9%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in x around inf 72.8%

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

   6. Taylor expanded in t around 0 49.5%

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

   if 5.60000000000000046e-171 < (*.f64 b c) < 6.5000000000000003e-79

   1. Initial program 99.4%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in j around inf 51.3%

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

   if 6.5000000000000003e-79 < (*.f64 b c) < 1.3e40

   1. Initial program 78.0%

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

   3. Taylor expanded in x around 0 86.3%

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

   4. Taylor expanded in t around 0 72.2%

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

      1. *-commutative 72.2%

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

      2. *-commutative 72.2%

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

      3. associate-*r* 72.2%

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

      4. *-commutative 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in a around inf 41.2%

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

      1. associate-*r* 41.2%

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

   9. Simplified 41.2%

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

   if 1.3e40 < (*.f64 b c) < 3.6999999999999997e185

   1. Initial program 71.2%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in x around inf 60.3%

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

   6. Taylor expanded in t around inf 42.1%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9.5 \cdot 10^{+152}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{-302}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 5.6 \cdot 10^{-171}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 6.5 \cdot 10^{-79}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.3 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.7 \cdot 10^{+185}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(y \cdot \left(x \cdot z\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{if}\;b \cdot c \leq -1.75 \cdot 10^{+205}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -7.8 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{-302}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{-78}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{+181}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* y (* x z)) (* 18.0 t))))
   (if (<= (* b c) -1.75e+205)
     (* b c)
     (if (<= (* b c) -7.8e-87)
       t_1
       (if (<= (* b c) 3.2e-302)
         (* k (* j -27.0))
         (if (<= (* b c) 3.8e-78)
           (* (* x i) -4.0)
           (if (<= (* b c) 1.6e+32)
             (* t (* a -4.0))
             (if (<= (* b c) 7.5e+181) t_1 (* b c)))))))))

C

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 = (y * (x * z)) * (18.0 * t);
	double tmp;
	if ((b * c) <= -1.75e+205) {
		tmp = b * c;
	} else if ((b * c) <= -7.8e-87) {
		tmp = t_1;
	} else if ((b * c) <= 3.2e-302) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 3.8e-78) {
		tmp = (x * i) * -4.0;
	} else if ((b * c) <= 1.6e+32) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 7.5e+181) {
		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.
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 = (y * (x * z)) * (18.0d0 * t)
    if ((b * c) <= (-1.75d+205)) then
        tmp = b * c
    else if ((b * c) <= (-7.8d-87)) then
        tmp = t_1
    else if ((b * c) <= 3.2d-302) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 3.8d-78) then
        tmp = (x * i) * (-4.0d0)
    else if ((b * c) <= 1.6d+32) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= 7.5d+181) 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;
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 = (y * (x * z)) * (18.0 * t);
	double tmp;
	if ((b * c) <= -1.75e+205) {
		tmp = b * c;
	} else if ((b * c) <= -7.8e-87) {
		tmp = t_1;
	} else if ((b * c) <= 3.2e-302) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 3.8e-78) {
		tmp = (x * i) * -4.0;
	} else if ((b * c) <= 1.6e+32) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 7.5e+181) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (y * (x * z)) * (18.0 * t)
	tmp = 0
	if (b * c) <= -1.75e+205:
		tmp = b * c
	elif (b * c) <= -7.8e-87:
		tmp = t_1
	elif (b * c) <= 3.2e-302:
		tmp = k * (j * -27.0)
	elif (b * c) <= 3.8e-78:
		tmp = (x * i) * -4.0
	elif (b * c) <= 1.6e+32:
		tmp = t * (a * -4.0)
	elif (b * c) <= 7.5e+181:
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(y * Float64(x * z)) * Float64(18.0 * t))
	tmp = 0.0
	if (Float64(b * c) <= -1.75e+205)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -7.8e-87)
		tmp = t_1;
	elseif (Float64(b * c) <= 3.2e-302)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 3.8e-78)
		tmp = Float64(Float64(x * i) * -4.0);
	elseif (Float64(b * c) <= 1.6e+32)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= 7.5e+181)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (y * (x * z)) * (18.0 * t);
	tmp = 0.0;
	if ((b * c) <= -1.75e+205)
		tmp = b * c;
	elseif ((b * c) <= -7.8e-87)
		tmp = t_1;
	elseif ((b * c) <= 3.2e-302)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 3.8e-78)
		tmp = (x * i) * -4.0;
	elseif ((b * c) <= 1.6e+32)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= 7.5e+181)
		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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.75e+205], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -7.8e-87], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 3.2e-302], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.8e-78], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.6e+32], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7.5e+181], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -1.7499999999999999e205 or 7.5000000000000005e181 < (*.f64 b c)

   1. Initial program 83.5%

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

   3. Taylor expanded in x around 0 86.2%

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

   4. Taylor expanded in a around 0 83.3%

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

   5. Taylor expanded in b around inf 70.1%

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

   if -1.7499999999999999e205 < (*.f64 b c) < -7.7999999999999996e-87 or 1.5999999999999999e32 < (*.f64 b c) < 7.5000000000000005e181

   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 89.9%

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

   5. Taylor expanded in x around inf 74.1%

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

      1. associate-*r* 74.1%

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

      2. *-commutative 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in y around inf 36.8%

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

      1. *-commutative 36.8%

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

      2. *-commutative 36.8%

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

      3. associate-*l* 36.8%

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

      4. *-commutative 36.8%

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

      5. associate-*l* 38.0%

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

   10. Simplified 38.0%

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

   if -7.7999999999999996e-87 < (*.f64 b c) < 3.19999999999999978e-302

   1. Initial program 87.2%

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

   3. Taylor expanded in x around 0 86.4%

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

   4. Taylor expanded in a around 0 79.6%

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

   5. Taylor expanded in j around inf 46.4%

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

      1. associate-*r* 46.4%

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

   7. Simplified 46.4%

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

   if 3.19999999999999978e-302 < (*.f64 b c) < 3.7999999999999999e-78

   1. Initial program 86.6%

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

   3. Simplified 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. Taylor expanded in x around inf 64.1%

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

   6. Taylor expanded in t around 0 43.6%

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

   if 3.7999999999999999e-78 < (*.f64 b c) < 1.5999999999999999e32

   1. Initial program 75.8%

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

   3. Taylor expanded in x around 0 84.9%

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

   4. Taylor expanded in t around 0 69.4%

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

      1. *-commutative 69.4%

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

      2. *-commutative 69.4%

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

      3. associate-*r* 69.4%

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

      4. *-commutative 69.4%

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

   6. Simplified 69.4%

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

   7. Taylor expanded in a around inf 45.1%

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

      1. associate-*r* 45.1%

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

   9. Simplified 45.1%

      \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.75 \cdot 10^{+205}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -7.8 \cdot 10^{-87}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{-302}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{-78}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{+181}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(t \cdot a\right)\\ t_2 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+28}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot i\right) \cdot -4\right) - t\_1\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-12}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 450000000 \lor \neg \left(x \leq 2.5 \cdot 10^{+162}\right) \land x \leq 1.8 \cdot 10^{+216}:\\ \;\;\;\;\left(b \cdot c - t\_1\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* t a))) (t_2 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<= x -3.8e+103)
     t_2
     (if (<= x -1.8e+28)
       (- (+ (* b c) (* (* x i) -4.0)) t_1)
       (if (<= x -5.1e-12)
         (+ (* j (* k -27.0)) (* x (* (* y t) (* 18.0 z))))
         (if (or (<= x 450000000.0)
                 (and (not (<= x 2.5e+162)) (<= x 1.8e+216)))
           (- (- (* b c) t_1) (* (* j 27.0) k))
           t_2))))))

C

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 = 4.0 * (t * a);
	double t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -3.8e+103) {
		tmp = t_2;
	} else if (x <= -1.8e+28) {
		tmp = ((b * c) + ((x * i) * -4.0)) - t_1;
	} else if (x <= -5.1e-12) {
		tmp = (j * (k * -27.0)) + (x * ((y * t) * (18.0 * z)));
	} else if ((x <= 450000000.0) || (!(x <= 2.5e+162) && (x <= 1.8e+216))) {
		tmp = ((b * c) - t_1) - ((j * 27.0) * k);
	} else {
		tmp = t_2;
	}
	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.
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 = 4.0d0 * (t * a)
    t_2 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (x <= (-3.8d+103)) then
        tmp = t_2
    else if (x <= (-1.8d+28)) then
        tmp = ((b * c) + ((x * i) * (-4.0d0))) - t_1
    else if (x <= (-5.1d-12)) then
        tmp = (j * (k * (-27.0d0))) + (x * ((y * t) * (18.0d0 * z)))
    else if ((x <= 450000000.0d0) .or. (.not. (x <= 2.5d+162)) .and. (x <= 1.8d+216)) then
        tmp = ((b * c) - t_1) - ((j * 27.0d0) * k)
    else
        tmp = t_2
    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;
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 = 4.0 * (t * a);
	double t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -3.8e+103) {
		tmp = t_2;
	} else if (x <= -1.8e+28) {
		tmp = ((b * c) + ((x * i) * -4.0)) - t_1;
	} else if (x <= -5.1e-12) {
		tmp = (j * (k * -27.0)) + (x * ((y * t) * (18.0 * z)));
	} else if ((x <= 450000000.0) || (!(x <= 2.5e+162) && (x <= 1.8e+216))) {
		tmp = ((b * c) - t_1) - ((j * 27.0) * k);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[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 = 4.0 * (t * a)
	t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if x <= -3.8e+103:
		tmp = t_2
	elif x <= -1.8e+28:
		tmp = ((b * c) + ((x * i) * -4.0)) - t_1
	elif x <= -5.1e-12:
		tmp = (j * (k * -27.0)) + (x * ((y * t) * (18.0 * z)))
	elif (x <= 450000000.0) or (not (x <= 2.5e+162) and (x <= 1.8e+216)):
		tmp = ((b * c) - t_1) - ((j * 27.0) * k)
	else:
		tmp = t_2
	return tmp

Julia

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(4.0 * Float64(t * a))
	t_2 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -3.8e+103)
		tmp = t_2;
	elseif (x <= -1.8e+28)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(x * i) * -4.0)) - t_1);
	elseif (x <= -5.1e-12)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(x * Float64(Float64(y * t) * Float64(18.0 * z))));
	elseif ((x <= 450000000.0) || (!(x <= 2.5e+162) && (x <= 1.8e+216)))
		tmp = Float64(Float64(Float64(b * c) - t_1) - Float64(Float64(j * 27.0) * k));
	else
		tmp = t_2;
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (t * a);
	t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (x <= -3.8e+103)
		tmp = t_2;
	elseif (x <= -1.8e+28)
		tmp = ((b * c) + ((x * i) * -4.0)) - t_1;
	elseif (x <= -5.1e-12)
		tmp = (j * (k * -27.0)) + (x * ((y * t) * (18.0 * z)));
	elseif ((x <= 450000000.0) || (~((x <= 2.5e+162)) && (x <= 1.8e+216)))
		tmp = ((b * c) - t_1) - ((j * 27.0) * k);
	else
		tmp = t_2;
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e+103], t$95$2, If[LessEqual[x, -1.8e+28], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, -5.1e-12], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * t), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 450000000.0], And[N[Not[LessEqual[x, 2.5e+162]], $MachinePrecision], LessEqual[x, 1.8e+216]]], N[(N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.7999999999999997e103 or 4.5e8 < x < 2.4999999999999998e162 or 1.8000000000000001e216 < x

   1. Initial program 71.3%

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

   3. Simplified 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 inf 78.7%

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

   if -3.7999999999999997e103 < x < -1.8e28

   1. Initial program 76.9%

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

   3. Taylor expanded in x around 0 76.9%

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

   4. Taylor expanded in t around 0 92.3%

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

      1. *-commutative 92.3%

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

      2. *-commutative 92.3%

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

      3. associate-*r* 92.3%

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

      4. *-commutative 92.3%

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

   6. Simplified 92.3%

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

   7. Taylor expanded in j around 0 84.9%

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

   if -1.8e28 < x < -5.09999999999999968e-12

   1. Initial program 91.2%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in y around inf 83.3%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. *-commutative 83.3%

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

      2. *-commutative 83.3%

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

      3. associate-*l* 83.3%

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

      4. *-commutative 83.3%

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

      5. associate-*r* 83.3%

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

      6. associate-*r* 83.3%

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

      7. associate-*l* 83.3%

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

   7. Simplified 83.3%

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

   if -5.09999999999999968e-12 < x < 4.5e8 or 2.4999999999999998e162 < x < 1.8000000000000001e216

   1. Initial program 92.2%

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

   3. Taylor expanded in x around 0 78.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+28}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot i\right) \cdot -4\right) - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-12}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 450000000 \lor \neg \left(x \leq 2.5 \cdot 10^{+162}\right) \land x \leq 1.8 \cdot 10^{+216}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-189}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+77}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k -27.0)) (* x (* i -4.0))))
        (t_2 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -7e-15)
     t_2
     (if (<= t -5.4e-44)
       t_1
       (if (<= t -2.15e-75)
         t_2
         (if (<= t -8.5e-189)
           (- (* b c) (* 4.0 (* x i)))
           (if (<= t 2.05e-202)
             t_1
             (if (<= t 1.8e+77) (- (* b c) (* (* j 27.0) k)) t_2))))))))

C

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)) + (x * (i * -4.0));
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -7e-15) {
		tmp = t_2;
	} else if (t <= -5.4e-44) {
		tmp = t_1;
	} else if (t <= -2.15e-75) {
		tmp = t_2;
	} else if (t <= -8.5e-189) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 2.05e-202) {
		tmp = t_1;
	} else if (t <= 1.8e+77) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else {
		tmp = t_2;
	}
	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.
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))) + (x * (i * (-4.0d0)))
    t_2 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-7d-15)) then
        tmp = t_2
    else if (t <= (-5.4d-44)) then
        tmp = t_1
    else if (t <= (-2.15d-75)) then
        tmp = t_2
    else if (t <= (-8.5d-189)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t <= 2.05d-202) then
        tmp = t_1
    else if (t <= 1.8d+77) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else
        tmp = t_2
    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;
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)) + (x * (i * -4.0));
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -7e-15) {
		tmp = t_2;
	} else if (t <= -5.4e-44) {
		tmp = t_1;
	} else if (t <= -2.15e-75) {
		tmp = t_2;
	} else if (t <= -8.5e-189) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 2.05e-202) {
		tmp = t_1;
	} else if (t <= 1.8e+77) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[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)) + (x * (i * -4.0))
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -7e-15:
		tmp = t_2
	elif t <= -5.4e-44:
		tmp = t_1
	elif t <= -2.15e-75:
		tmp = t_2
	elif t <= -8.5e-189:
		tmp = (b * c) - (4.0 * (x * i))
	elif t <= 2.05e-202:
		tmp = t_1
	elif t <= 1.8e+77:
		tmp = (b * c) - ((j * 27.0) * k)
	else:
		tmp = t_2
	return tmp

Julia

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 * Float64(k * -27.0)) + Float64(x * Float64(i * -4.0)))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -7e-15)
		tmp = t_2;
	elseif (t <= -5.4e-44)
		tmp = t_1;
	elseif (t <= -2.15e-75)
		tmp = t_2;
	elseif (t <= -8.5e-189)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t <= 2.05e-202)
		tmp = t_1;
	elseif (t <= 1.8e+77)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	else
		tmp = t_2;
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (x * (i * -4.0));
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -7e-15)
		tmp = t_2;
	elseif (t <= -5.4e-44)
		tmp = t_1;
	elseif (t <= -2.15e-75)
		tmp = t_2;
	elseif (t <= -8.5e-189)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t <= 2.05e-202)
		tmp = t_1;
	elseif (t <= 1.8e+77)
		tmp = (b * c) - ((j * 27.0) * k);
	else
		tmp = t_2;
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e-15], t$95$2, If[LessEqual[t, -5.4e-44], t$95$1, If[LessEqual[t, -2.15e-75], t$95$2, If[LessEqual[t, -8.5e-189], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e-202], t$95$1, If[LessEqual[t, 1.8e+77], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.0000000000000001e-15 or -5.3999999999999998e-44 < t < -2.15e-75 or 1.7999999999999999e77 < t

   1. Initial program 77.0%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in x around inf 78.3%

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

      1. associate-*r* 78.3%

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

      2. *-commutative 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in t around inf 67.6%

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

   if -7.0000000000000001e-15 < t < -5.3999999999999998e-44 or -8.50000000000000068e-189 < t < 2.0500000000000002e-202

   1. Initial program 88.5%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in i around inf 78.2%

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

      1. associate-*r* 78.2%

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

      2. *-commutative 78.2%

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

   7. Simplified 78.2%

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

   if -2.15e-75 < t < -8.50000000000000068e-189

   1. Initial program 89.2%

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

   3. Taylor expanded in t around 0 83.0%

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

   4. Taylor expanded in j around 0 71.1%

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

   if 2.0500000000000002e-202 < t < 1.7999999999999999e77

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0 93.9%

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

   4. Taylor expanded in b around inf 73.3%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-189}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+77}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{-14}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-186}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 10^{-201}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+72}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
        (t_2 (+ (* j (* k -27.0)) (* x (* i -4.0)))))
   (if (<= t -2.8e-14)
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
     (if (<= t -2.8e-43)
       t_2
       (if (<= t -1.1e-75)
         t_1
         (if (<= t -1.52e-186)
           (- (* b c) (* 4.0 (* x i)))
           (if (<= t 1e-201)
             t_2
             (if (<= t 1.42e+72) (- (* b c) (* (* j 27.0) k)) t_1))))))))

C

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 * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_2 = (j * (k * -27.0)) + (x * (i * -4.0));
	double tmp;
	if (t <= -2.8e-14) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -2.8e-43) {
		tmp = t_2;
	} else if (t <= -1.1e-75) {
		tmp = t_1;
	} else if (t <= -1.52e-186) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 1e-201) {
		tmp = t_2;
	} else if (t <= 1.42e+72) {
		tmp = (b * c) - ((j * 27.0) * k);
	} 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.
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 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    t_2 = (j * (k * (-27.0d0))) + (x * (i * (-4.0d0)))
    if (t <= (-2.8d-14)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= (-2.8d-43)) then
        tmp = t_2
    else if (t <= (-1.1d-75)) then
        tmp = t_1
    else if (t <= (-1.52d-186)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t <= 1d-201) then
        tmp = t_2
    else if (t <= 1.42d+72) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    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;
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 * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_2 = (j * (k * -27.0)) + (x * (i * -4.0));
	double tmp;
	if (t <= -2.8e-14) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -2.8e-43) {
		tmp = t_2;
	} else if (t <= -1.1e-75) {
		tmp = t_1;
	} else if (t <= -1.52e-186) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 1e-201) {
		tmp = t_2;
	} else if (t <= 1.42e+72) {
		tmp = (b * c) - ((j * 27.0) * k);
	} 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	t_2 = (j * (k * -27.0)) + (x * (i * -4.0))
	tmp = 0
	if t <= -2.8e-14:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= -2.8e-43:
		tmp = t_2
	elif t <= -1.1e-75:
		tmp = t_1
	elif t <= -1.52e-186:
		tmp = (b * c) - (4.0 * (x * i))
	elif t <= 1e-201:
		tmp = t_2
	elif t <= 1.42e+72:
		tmp = (b * c) - ((j * 27.0) * k)
	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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	t_2 = Float64(Float64(j * Float64(k * -27.0)) + Float64(x * Float64(i * -4.0)))
	tmp = 0.0
	if (t <= -2.8e-14)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= -2.8e-43)
		tmp = t_2;
	elseif (t <= -1.1e-75)
		tmp = t_1;
	elseif (t <= -1.52e-186)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t <= 1e-201)
		tmp = t_2;
	elseif (t <= 1.42e+72)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	t_2 = (j * (k * -27.0)) + (x * (i * -4.0));
	tmp = 0.0;
	if (t <= -2.8e-14)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= -2.8e-43)
		tmp = t_2;
	elseif (t <= -1.1e-75)
		tmp = t_1;
	elseif (t <= -1.52e-186)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t <= 1e-201)
		tmp = t_2;
	elseif (t <= 1.42e+72)
		tmp = (b * c) - ((j * 27.0) * k);
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e-14], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.8e-43], t$95$2, If[LessEqual[t, -1.1e-75], t$95$1, If[LessEqual[t, -1.52e-186], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-201], t$95$2, If[LessEqual[t, 1.42e+72], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.8000000000000001e-14

   1. Initial program 85.0%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in x around inf 81.4%

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

      1. associate-*r* 81.4%

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

      2. *-commutative 81.4%

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

   7. Simplified 81.4%

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

   8. Taylor expanded in t around inf 68.3%

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

   if -2.8000000000000001e-14 < t < -2.7999999999999998e-43 or -1.5200000000000001e-186 < t < 9.99999999999999946e-202

   1. Initial program 88.5%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in i around inf 78.2%

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

      1. associate-*r* 78.2%

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

      2. *-commutative 78.2%

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

   7. Simplified 78.2%

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

   if -2.7999999999999998e-43 < t < -1.10000000000000003e-75 or 1.41999999999999997e72 < t

   1. Initial program 67.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in x around inf 71.2%

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

   if -1.10000000000000003e-75 < t < -1.5200000000000001e-186

   1. Initial program 89.2%

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

   3. Taylor expanded in t around 0 83.0%

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

   4. Taylor expanded in j around 0 71.1%

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

   if 9.99999999999999946e-202 < t < 1.41999999999999997e72

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0 93.6%

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

   4. Taylor expanded in b around inf 74.3%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-14}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-43}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-186}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 10^{-201}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+72}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(y \cdot z\right)\\ t_2 := j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-77}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(x \cdot t\_1\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-187}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+72}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot t\_1 - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* y z))) (t_2 (+ (* j (* k -27.0)) (* x (* i -4.0)))))
   (if (<= t -1.75e-15)
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
     (if (<= t -1.02e-42)
       t_2
       (if (<= t -5.2e-77)
         (+ (* b c) (* 18.0 (* x t_1)))
         (if (<= t -2.2e-187)
           (- (* b c) (* 4.0 (* x i)))
           (if (<= t 8e-202)
             t_2
             (if (<= t 9e+72)
               (- (* b c) (* (* j 27.0) k))
               (* x (- (* 18.0 t_1) (* 4.0 i)))))))))))

C

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 = t * (y * z);
	double t_2 = (j * (k * -27.0)) + (x * (i * -4.0));
	double tmp;
	if (t <= -1.75e-15) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -1.02e-42) {
		tmp = t_2;
	} else if (t <= -5.2e-77) {
		tmp = (b * c) + (18.0 * (x * t_1));
	} else if (t <= -2.2e-187) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 8e-202) {
		tmp = t_2;
	} else if (t <= 9e+72) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else {
		tmp = x * ((18.0 * t_1) - (4.0 * 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.
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 = t * (y * z)
    t_2 = (j * (k * (-27.0d0))) + (x * (i * (-4.0d0)))
    if (t <= (-1.75d-15)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= (-1.02d-42)) then
        tmp = t_2
    else if (t <= (-5.2d-77)) then
        tmp = (b * c) + (18.0d0 * (x * t_1))
    else if (t <= (-2.2d-187)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t <= 8d-202) then
        tmp = t_2
    else if (t <= 9d+72) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else
        tmp = x * ((18.0d0 * t_1) - (4.0d0 * 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;
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 = t * (y * z);
	double t_2 = (j * (k * -27.0)) + (x * (i * -4.0));
	double tmp;
	if (t <= -1.75e-15) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -1.02e-42) {
		tmp = t_2;
	} else if (t <= -5.2e-77) {
		tmp = (b * c) + (18.0 * (x * t_1));
	} else if (t <= -2.2e-187) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 8e-202) {
		tmp = t_2;
	} else if (t <= 9e+72) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else {
		tmp = x * ((18.0 * t_1) - (4.0 * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (y * z)
	t_2 = (j * (k * -27.0)) + (x * (i * -4.0))
	tmp = 0
	if t <= -1.75e-15:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= -1.02e-42:
		tmp = t_2
	elif t <= -5.2e-77:
		tmp = (b * c) + (18.0 * (x * t_1))
	elif t <= -2.2e-187:
		tmp = (b * c) - (4.0 * (x * i))
	elif t <= 8e-202:
		tmp = t_2
	elif t <= 9e+72:
		tmp = (b * c) - ((j * 27.0) * k)
	else:
		tmp = x * ((18.0 * t_1) - (4.0 * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(y * z))
	t_2 = Float64(Float64(j * Float64(k * -27.0)) + Float64(x * Float64(i * -4.0)))
	tmp = 0.0
	if (t <= -1.75e-15)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= -1.02e-42)
		tmp = t_2;
	elseif (t <= -5.2e-77)
		tmp = Float64(Float64(b * c) + Float64(18.0 * Float64(x * t_1)));
	elseif (t <= -2.2e-187)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t <= 8e-202)
		tmp = t_2;
	elseif (t <= 9e+72)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(x * Float64(Float64(18.0 * t_1) - Float64(4.0 * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (y * z);
	t_2 = (j * (k * -27.0)) + (x * (i * -4.0));
	tmp = 0.0;
	if (t <= -1.75e-15)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= -1.02e-42)
		tmp = t_2;
	elseif (t <= -5.2e-77)
		tmp = (b * c) + (18.0 * (x * t_1));
	elseif (t <= -2.2e-187)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t <= 8e-202)
		tmp = t_2;
	elseif (t <= 9e+72)
		tmp = (b * c) - ((j * 27.0) * k);
	else
		tmp = x * ((18.0 * t_1) - (4.0 * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.75e-15], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.02e-42], t$95$2, If[LessEqual[t, -5.2e-77], N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.2e-187], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-202], t$95$2, If[LessEqual[t, 9e+72], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * t$95$1), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.75e-15

   1. Initial program 85.0%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in x around inf 81.4%

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

      1. associate-*r* 81.4%

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

      2. *-commutative 81.4%

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

   7. Simplified 81.4%

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

   8. Taylor expanded in t around inf 68.3%

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

   if -1.75e-15 < t < -1.0199999999999999e-42 or -2.20000000000000008e-187 < t < 8.0000000000000003e-202

   1. Initial program 88.5%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in i around inf 78.2%

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

      1. associate-*r* 78.2%

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

      2. *-commutative 78.2%

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

   7. Simplified 78.2%

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

   if -1.0199999999999999e-42 < t < -5.2000000000000002e-77

   1. Initial program 62.7%

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

   3. Taylor expanded in x around 0 99.8%

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

   4. Taylor expanded in a around 0 80.5%

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

   5. Taylor expanded in j around 0 80.5%

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

   6. Taylor expanded in t around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. associate-*r* 70.4%

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

   8. Simplified 70.4%

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

   if -5.2000000000000002e-77 < t < -2.20000000000000008e-187

   1. Initial program 89.2%

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

   3. Taylor expanded in t around 0 83.0%

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

   4. Taylor expanded in j around 0 71.1%

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

   if 8.0000000000000003e-202 < t < 8.9999999999999997e72

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0 93.6%

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

   4. Taylor expanded in b around inf 74.3%

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

   if 8.9999999999999997e72 < t

   1. Initial program 69.0%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in x around inf 71.6%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-42}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-77}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-187}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+72}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-7}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{+67}:\\ \;\;\;\;t\_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+113}:\\ \;\;\;\;t\_1 + x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))))
   (if (<= x -4.2e+62)
     t_2
     (if (<= x 1.95e-7)
       (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))
       (if (<= x 1.06e+46)
         t_2
         (if (<= x 1.26e+67)
           (+ t_1 (* x (* i -4.0)))
           (if (<= x 2.6e+113) (+ t_1 (* x (* (* y t) (* 18.0 z)))) t_2)))))))

C

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) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	double tmp;
	if (x <= -4.2e+62) {
		tmp = t_2;
	} else if (x <= 1.95e-7) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (x <= 1.06e+46) {
		tmp = t_2;
	} else if (x <= 1.26e+67) {
		tmp = t_1 + (x * (i * -4.0));
	} else if (x <= 2.6e+113) {
		tmp = t_1 + (x * ((y * t) * (18.0 * z)));
	} else {
		tmp = t_2;
	}
	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.
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) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))
    if (x <= (-4.2d+62)) then
        tmp = t_2
    else if (x <= 1.95d-7) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    else if (x <= 1.06d+46) then
        tmp = t_2
    else if (x <= 1.26d+67) then
        tmp = t_1 + (x * (i * (-4.0d0)))
    else if (x <= 2.6d+113) then
        tmp = t_1 + (x * ((y * t) * (18.0d0 * z)))
    else
        tmp = t_2
    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;
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) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	double tmp;
	if (x <= -4.2e+62) {
		tmp = t_2;
	} else if (x <= 1.95e-7) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (x <= 1.06e+46) {
		tmp = t_2;
	} else if (x <= 1.26e+67) {
		tmp = t_1 + (x * (i * -4.0));
	} else if (x <= 2.6e+113) {
		tmp = t_1 + (x * ((y * t) * (18.0 * z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[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) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))
	tmp = 0
	if x <= -4.2e+62:
		tmp = t_2
	elif x <= 1.95e-7:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	elif x <= 1.06e+46:
		tmp = t_2
	elif x <= 1.26e+67:
		tmp = t_1 + (x * (i * -4.0))
	elif x <= 2.6e+113:
		tmp = t_1 + (x * ((y * t) * (18.0 * z)))
	else:
		tmp = t_2
	return tmp

Julia

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(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))))
	tmp = 0.0
	if (x <= -4.2e+62)
		tmp = t_2;
	elseif (x <= 1.95e-7)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	elseif (x <= 1.06e+46)
		tmp = t_2;
	elseif (x <= 1.26e+67)
		tmp = Float64(t_1 + Float64(x * Float64(i * -4.0)));
	elseif (x <= 2.6e+113)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * t) * Float64(18.0 * z))));
	else
		tmp = t_2;
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	tmp = 0.0;
	if (x <= -4.2e+62)
		tmp = t_2;
	elseif (x <= 1.95e-7)
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	elseif (x <= 1.06e+46)
		tmp = t_2;
	elseif (x <= 1.26e+67)
		tmp = t_1 + (x * (i * -4.0));
	elseif (x <= 2.6e+113)
		tmp = t_1 + (x * ((y * t) * (18.0 * z)));
	else
		tmp = t_2;
	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.
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[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+62], t$95$2, If[LessEqual[x, 1.95e-7], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.06e+46], t$95$2, If[LessEqual[x, 1.26e+67], N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+113], N[(t$95$1 + N[(x * N[(N[(y * t), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.2e62 or 1.95000000000000012e-7 < x < 1.05999999999999998e46 or 2.5999999999999999e113 < x

   1. Initial program 73.3%

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

   3. Taylor expanded in x around 0 93.6%

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

   4. Taylor expanded in a around 0 91.8%

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

   5. Taylor expanded in j around 0 88.1%

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

   if -4.2e62 < x < 1.95000000000000012e-7

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0 75.8%

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

   if 1.05999999999999998e46 < x < 1.26e67

   1. Initial program 50.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in i around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if 1.26e67 < x < 2.5999999999999999e113

   1. Initial program 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in y around inf 90.1%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. *-commutative 90.1%

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

      2. *-commutative 90.1%

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

      3. associate-*l* 90.0%

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

      4. *-commutative 90.0%

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

      5. associate-*r* 90.1%

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

      6. associate-*r* 81.1%

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

      7. associate-*l* 81.1%

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

   7. Simplified 81.1%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+62}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-7}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{+67}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+113}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+148}:\\ \;\;\;\;b \cdot c - t\_1\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+186}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot i\right) \cdot -4\right) - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+148)
     (- (* b c) t_1)
     (if (<= t_1 -5e-56)
       (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
       (if (<= t_1 2e+186)
         (- (+ (* b c) (* (* x i) -4.0)) (* 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);
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 * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+148) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= -5e-56) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t_1 <= 2e+186) {
		tmp = ((b * c) + ((x * i) * -4.0)) - (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.
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 * 27.0d0) * k
    if (t_1 <= (-2d+148)) then
        tmp = (b * c) - t_1
    else if (t_1 <= (-5d-56)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (t_1 <= 2d+186) then
        tmp = ((b * c) + ((x * i) * (-4.0d0))) - (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;
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 * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+148) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= -5e-56) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t_1 <= 2e+186) {
		tmp = ((b * c) + ((x * i) * -4.0)) - (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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+148:
		tmp = (b * c) - t_1
	elif t_1 <= -5e-56:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif t_1 <= 2e+186:
		tmp = ((b * c) + ((x * i) * -4.0)) - (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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+148)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (t_1 <= -5e-56)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (t_1 <= 2e+186)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(x * i) * -4.0)) - Float64(4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(Float64(t * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+148)
		tmp = (b * c) - t_1;
	elseif (t_1 <= -5e-56)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (t_1 <= 2e+186)
		tmp = ((b * c) + ((x * i) * -4.0)) - (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+148], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, -5e-56], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+186], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j 27) k) < -2.0000000000000001e148

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0 87.4%

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

   4. Taylor expanded in b around inf 81.4%

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

   if -2.0000000000000001e148 < (*.f64 (*.f64 j 27) k) < -4.99999999999999997e-56

   1. Initial program 79.4%

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

   3. Simplified 79.9%

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

   5. Taylor expanded in x around inf 66.9%

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

   if -4.99999999999999997e-56 < (*.f64 (*.f64 j 27) k) < 1.99999999999999996e186

   1. Initial program 85.4%

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

   3. Taylor expanded in x around 0 89.2%

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

   4. Taylor expanded in t around 0 76.6%

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

      1. *-commutative 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*r* 76.6%

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

      4. *-commutative 76.6%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in j around 0 71.7%

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

   if 1.99999999999999996e186 < (*.f64 (*.f64 j 27) k)

   1. Initial program 79.2%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in a around inf 85.5%

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

      1. *-commutative 85.5%

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

   7. Simplified 85.5%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+148}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+186}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot i\right) \cdot -4\right) - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(x \cdot i\right) \cdot -4\\ \mathbf{if}\;b \cdot c \leq -1.35 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 2.15 \cdot 10^{-303}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 3.75 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.85 \cdot 10^{+185}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* x i) -4.0)))
   (if (<= (* b c) -1.35e+153)
     (* b c)
     (if (<= (* b c) 2.15e-303)
       (* k (* j -27.0))
       (if (<= (* b c) 3.75e-78)
         t_1
         (if (<= (* b c) 3.2e+28)
           (* t (* a -4.0))
           (if (<= (* b c) 1.85e+185) t_1 (* b c))))))))

C

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 * i) * -4.0;
	double tmp;
	if ((b * c) <= -1.35e+153) {
		tmp = b * c;
	} else if ((b * c) <= 2.15e-303) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 3.75e-78) {
		tmp = t_1;
	} else if ((b * c) <= 3.2e+28) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 1.85e+185) {
		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.
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 = (x * i) * (-4.0d0)
    if ((b * c) <= (-1.35d+153)) then
        tmp = b * c
    else if ((b * c) <= 2.15d-303) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 3.75d-78) then
        tmp = t_1
    else if ((b * c) <= 3.2d+28) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= 1.85d+185) 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;
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 * i) * -4.0;
	double tmp;
	if ((b * c) <= -1.35e+153) {
		tmp = b * c;
	} else if ((b * c) <= 2.15e-303) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 3.75e-78) {
		tmp = t_1;
	} else if ((b * c) <= 3.2e+28) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 1.85e+185) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * i) * -4.0
	tmp = 0
	if (b * c) <= -1.35e+153:
		tmp = b * c
	elif (b * c) <= 2.15e-303:
		tmp = k * (j * -27.0)
	elif (b * c) <= 3.75e-78:
		tmp = t_1
	elif (b * c) <= 3.2e+28:
		tmp = t * (a * -4.0)
	elif (b * c) <= 1.85e+185:
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * i) * -4.0)
	tmp = 0.0
	if (Float64(b * c) <= -1.35e+153)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 2.15e-303)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 3.75e-78)
		tmp = t_1;
	elseif (Float64(b * c) <= 3.2e+28)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= 1.85e+185)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * i) * -4.0;
	tmp = 0.0;
	if ((b * c) <= -1.35e+153)
		tmp = b * c;
	elseif ((b * c) <= 2.15e-303)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 3.75e-78)
		tmp = t_1;
	elseif ((b * c) <= 3.2e+28)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= 1.85e+185)
		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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.35e+153], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.15e-303], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.75e-78], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 3.2e+28], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.85e+185], t$95$1, N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.35e153 or 1.8499999999999999e185 < (*.f64 b c)

   1. Initial program 81.9%

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

   3. Taylor expanded in x around 0 86.8%

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

   4. Taylor expanded in a around 0 83.0%

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

   5. Taylor expanded in b around inf 64.9%

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

   if -1.35e153 < (*.f64 b c) < 2.14999999999999991e-303

   1. Initial program 88.1%

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

   3. Taylor expanded in x around 0 87.8%

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

   4. Taylor expanded in a around 0 79.6%

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

   5. Taylor expanded in j around inf 38.4%

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

      1. associate-*r* 38.4%

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

   7. Simplified 38.4%

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

   if 2.14999999999999991e-303 < (*.f64 b c) < 3.75000000000000021e-78 or 3.2e28 < (*.f64 b c) < 1.8499999999999999e185

   1. Initial program 80.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in x around inf 63.1%

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

   6. Taylor expanded in t around 0 36.5%

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

   if 3.75000000000000021e-78 < (*.f64 b c) < 3.2e28

   1. Initial program 75.8%

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

   3. Taylor expanded in x around 0 84.9%

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

   4. Taylor expanded in t around 0 69.4%

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

      1. *-commutative 69.4%

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

      2. *-commutative 69.4%

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

      3. associate-*r* 69.4%

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

      4. *-commutative 69.4%

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

   6. Simplified 69.4%

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

   7. Taylor expanded in a around inf 45.1%

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

      1. associate-*r* 45.1%

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

   9. Simplified 45.1%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.35 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 2.15 \cdot 10^{-303}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 3.75 \cdot 10^{-78}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.85 \cdot 10^{+185}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -6 \cdot 10^{+133}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq 3.7 \cdot 10^{-78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 3.6 \cdot 10^{+28}:\\ \;\;\;\;t\_1 + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 6.2 \cdot 10^{+182}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ t_1 (* x (* i -4.0)))))
   (if (<= (* b c) -6e+133)
     (- (* b c) (* (* j 27.0) k))
     (if (<= (* b c) 3.7e-78)
       t_2
       (if (<= (* b c) 3.6e+28)
         (+ t_1 (* (* t a) -4.0))
         (if (<= (* b c) 6.2e+182) t_2 (- (* b c) (* 4.0 (* x i)))))))))

C

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 = t_1 + (x * (i * -4.0));
	double tmp;
	if ((b * c) <= -6e+133) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if ((b * c) <= 3.7e-78) {
		tmp = t_2;
	} else if ((b * c) <= 3.6e+28) {
		tmp = t_1 + ((t * a) * -4.0);
	} else if ((b * c) <= 6.2e+182) {
		tmp = t_2;
	} else {
		tmp = (b * c) - (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.
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 = t_1 + (x * (i * (-4.0d0)))
    if ((b * c) <= (-6d+133)) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else if ((b * c) <= 3.7d-78) then
        tmp = t_2
    else if ((b * c) <= 3.6d+28) then
        tmp = t_1 + ((t * a) * (-4.0d0))
    else if ((b * c) <= 6.2d+182) then
        tmp = t_2
    else
        tmp = (b * c) - (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;
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 = t_1 + (x * (i * -4.0));
	double tmp;
	if ((b * c) <= -6e+133) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if ((b * c) <= 3.7e-78) {
		tmp = t_2;
	} else if ((b * c) <= 3.6e+28) {
		tmp = t_1 + ((t * a) * -4.0);
	} else if ((b * c) <= 6.2e+182) {
		tmp = t_2;
	} else {
		tmp = (b * c) - (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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (x * (i * -4.0))
	tmp = 0
	if (b * c) <= -6e+133:
		tmp = (b * c) - ((j * 27.0) * k)
	elif (b * c) <= 3.7e-78:
		tmp = t_2
	elif (b * c) <= 3.6e+28:
		tmp = t_1 + ((t * a) * -4.0)
	elif (b * c) <= 6.2e+182:
		tmp = t_2
	else:
		tmp = (b * c) - (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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(x * Float64(i * -4.0)))
	tmp = 0.0
	if (Float64(b * c) <= -6e+133)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (Float64(b * c) <= 3.7e-78)
		tmp = t_2;
	elseif (Float64(b * c) <= 3.6e+28)
		tmp = Float64(t_1 + Float64(Float64(t * a) * -4.0));
	elseif (Float64(b * c) <= 6.2e+182)
		tmp = t_2;
	else
		tmp = Float64(Float64(b * c) - 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (x * (i * -4.0));
	tmp = 0.0;
	if ((b * c) <= -6e+133)
		tmp = (b * c) - ((j * 27.0) * k);
	elseif ((b * c) <= 3.7e-78)
		tmp = t_2;
	elseif ((b * c) <= 3.6e+28)
		tmp = t_1 + ((t * a) * -4.0);
	elseif ((b * c) <= 6.2e+182)
		tmp = t_2;
	else
		tmp = (b * c) - (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.
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[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -6e+133], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.7e-78], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 3.6e+28], N[(t$95$1 + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6.2e+182], t$95$2, N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -6.00000000000000013e133

   1. Initial program 86.8%

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

   3. Taylor expanded in x around 0 91.0%

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

   4. Taylor expanded in b around inf 71.8%

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

   if -6.00000000000000013e133 < (*.f64 b c) < 3.70000000000000006e-78 or 3.5999999999999999e28 < (*.f64 b c) < 6.19999999999999993e182

   1. Initial program 84.8%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in i around inf 57.6%

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

      1. associate-*r* 57.6%

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

      2. *-commutative 57.6%

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

   7. Simplified 57.6%

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

   if 3.70000000000000006e-78 < (*.f64 b c) < 3.5999999999999999e28

   1. Initial program 75.8%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in a around inf 50.1%

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

      1. *-commutative 50.1%

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

   7. Simplified 50.1%

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

   if 6.19999999999999993e182 < (*.f64 b c)

   1. Initial program 76.2%

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

   3. Taylor expanded in t around 0 82.0%

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

   4. Taylor expanded in j around 0 82.0%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6 \cdot 10^{+133}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq 3.7 \cdot 10^{-78}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 3.6 \cdot 10^{+28}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 6.2 \cdot 10^{+182}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 89.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+111} \lor \neg \left(x \leq 2 \cdot 10^{+35}\right):\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -2e+111) (not (<= x 2e+35)))
   (-
    (- (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))) (* 4.0 (* t a)))
    (* (* j 27.0) k))
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* 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);
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 <= -2e+111) || !(x <= 2e+35)) {
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (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.
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 <= (-2d+111)) .or. (.not. (x <= 2d+35))) then
        tmp = (((b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    else
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (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;
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 <= -2e+111) || !(x <= 2e+35)) {
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -2e+111) or not (x <= 2e+35):
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - ((j * 27.0) * k)
	else:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -2e+111) || !(x <= 2e+35))
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	else
		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))));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -2e+111) || ~((x <= 2e+35)))
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - ((j * 27.0) * k);
	else
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -2e+111], N[Not[LessEqual[x, 2e+35]], $MachinePrecision]], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if x < -1.99999999999999991e111 or 1.9999999999999999e35 < x

   1. Initial program 71.6%

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

   3. Taylor expanded in x around 0 93.1%

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

   if -1.99999999999999991e111 < x < 1.9999999999999999e35

   1. Initial program 91.2%

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

   3. Simplified 92.4%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+111} \lor \neg \left(x \leq 2 \cdot 10^{+35}\right):\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 88.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+195}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))))
   (if (<= x -1e+124)
     t_1
     (if (<= x 1.02e+195)
       (-
        (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
        (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
       (- t_1 (* (* j 27.0) k))))))

C

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) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	double tmp;
	if (x <= -1e+124) {
		tmp = t_1;
	} else if (x <= 1.02e+195) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = t_1 - ((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.
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 = (b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))
    if (x <= (-1d+124)) then
        tmp = t_1
    else if (x <= 1.02d+195) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = t_1 - ((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;
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) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	double tmp;
	if (x <= -1e+124) {
		tmp = t_1;
	} else if (x <= 1.02e+195) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = t_1 - ((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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))
	tmp = 0
	if x <= -1e+124:
		tmp = t_1
	elif x <= 1.02e+195:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = t_1 - ((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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))))
	tmp = 0.0
	if (x <= -1e+124)
		tmp = t_1;
	elseif (x <= 1.02e+195)
		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(t_1 - 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	tmp = 0.0;
	if (x <= -1e+124)
		tmp = t_1;
	elseif (x <= 1.02e+195)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = t_1 - ((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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+124], t$95$1, If[LessEqual[x, 1.02e+195], 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[(t$95$1 - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.99999999999999948e123

   1. Initial program 64.6%

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

   3. Taylor expanded in x around 0 95.4%

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

   4. Taylor expanded in a around 0 93.2%

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

   5. Taylor expanded in j around 0 93.4%

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

   if -9.99999999999999948e123 < x < 1.02e195

   1. Initial program 91.0%

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

   3. Simplified 92.0%

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

   if 1.02e195 < x

   1. Initial program 65.2%

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

   3. Taylor expanded in x around 0 90.3%

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

   4. Taylor expanded in a around 0 90.3%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+124}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+195}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-51}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 1.24 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+175}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))))
   (if (<= x -4.2e+62)
     t_2
     (if (<= x 2.15e-51)
       (- (- (* b c) (* 4.0 (* t a))) t_1)
       (if (<= x 1.24e+107)
         (+ (* t (+ (* a -4.0) (* 18.0 (* x (* y z))))) (* j (* k -27.0)))
         (if (<= x 2.9e+175) (- (- (* b c) (* 4.0 (* x i))) t_1) t_2))))))

C

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 * 27.0) * k;
	double t_2 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	double tmp;
	if (x <= -4.2e+62) {
		tmp = t_2;
	} else if (x <= 2.15e-51) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 1.24e+107) {
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (j * (k * -27.0));
	} else if (x <= 2.9e+175) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	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.
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 * 27.0d0) * k
    t_2 = (b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))
    if (x <= (-4.2d+62)) then
        tmp = t_2
    else if (x <= 2.15d-51) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (x <= 1.24d+107) then
        tmp = (t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z))))) + (j * (k * (-27.0d0)))
    else if (x <= 2.9d+175) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else
        tmp = t_2
    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;
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 * 27.0) * k;
	double t_2 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	double tmp;
	if (x <= -4.2e+62) {
		tmp = t_2;
	} else if (x <= 2.15e-51) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 1.24e+107) {
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (j * (k * -27.0));
	} else if (x <= 2.9e+175) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[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 * 27.0) * k
	t_2 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))
	tmp = 0
	if x <= -4.2e+62:
		tmp = t_2
	elif x <= 2.15e-51:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif x <= 1.24e+107:
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (j * (k * -27.0))
	elif x <= 2.9e+175:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	else:
		tmp = t_2
	return tmp

Julia

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 * 27.0) * k)
	t_2 = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))))
	tmp = 0.0
	if (x <= -4.2e+62)
		tmp = t_2;
	elseif (x <= 2.15e-51)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (x <= 1.24e+107)
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z))))) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 2.9e+175)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	else
		tmp = t_2;
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	tmp = 0.0;
	if (x <= -4.2e+62)
		tmp = t_2;
	elseif (x <= 2.15e-51)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (x <= 1.24e+107)
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + (j * (k * -27.0));
	elseif (x <= 2.9e+175)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	else
		tmp = t_2;
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+62], t$95$2, If[LessEqual[x, 2.15e-51], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 1.24e+107], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e+175], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.2e62 or 2.9e175 < x

   1. Initial program 68.6%

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

   3. Taylor expanded in x around 0 94.2%

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

   4. Taylor expanded in a around 0 90.8%

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

   5. Taylor expanded in j around 0 89.4%

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

   if -4.2e62 < x < 2.1499999999999999e-51

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 76.2%

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

   if 2.1499999999999999e-51 < x < 1.24e107

   1. Initial program 79.9%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in t around inf 72.5%

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

   if 1.24e107 < x < 2.9e175

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 94.1%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+62}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-51}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.24 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+175}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-44}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+107}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+175}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))))
   (if (<= x -4.2e+62)
     t_2
     (if (<= x 2.55e-44)
       (- (- (* b c) (* 4.0 (* t a))) t_1)
       (if (<= x 1.42e+107)
         (- (+ (* b c) (* 18.0 (* t (* x (* y z))))) t_1)
         (if (<= x 2.9e+175) (- (- (* b c) (* 4.0 (* x i))) t_1) t_2))))))

C

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 * 27.0) * k;
	double t_2 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	double tmp;
	if (x <= -4.2e+62) {
		tmp = t_2;
	} else if (x <= 2.55e-44) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 1.42e+107) {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - t_1;
	} else if (x <= 2.9e+175) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	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.
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 * 27.0d0) * k
    t_2 = (b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))
    if (x <= (-4.2d+62)) then
        tmp = t_2
    else if (x <= 2.55d-44) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (x <= 1.42d+107) then
        tmp = ((b * c) + (18.0d0 * (t * (x * (y * z))))) - t_1
    else if (x <= 2.9d+175) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else
        tmp = t_2
    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;
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 * 27.0) * k;
	double t_2 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	double tmp;
	if (x <= -4.2e+62) {
		tmp = t_2;
	} else if (x <= 2.55e-44) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 1.42e+107) {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - t_1;
	} else if (x <= 2.9e+175) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[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 * 27.0) * k
	t_2 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))
	tmp = 0
	if x <= -4.2e+62:
		tmp = t_2
	elif x <= 2.55e-44:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif x <= 1.42e+107:
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - t_1
	elif x <= 2.9e+175:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	else:
		tmp = t_2
	return tmp

Julia

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 * 27.0) * k)
	t_2 = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))))
	tmp = 0.0
	if (x <= -4.2e+62)
		tmp = t_2;
	elseif (x <= 2.55e-44)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (x <= 1.42e+107)
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))) - t_1);
	elseif (x <= 2.9e+175)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	else
		tmp = t_2;
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	tmp = 0.0;
	if (x <= -4.2e+62)
		tmp = t_2;
	elseif (x <= 2.55e-44)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (x <= 1.42e+107)
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - t_1;
	elseif (x <= 2.9e+175)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	else
		tmp = t_2;
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+62], t$95$2, If[LessEqual[x, 2.55e-44], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 1.42e+107], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 2.9e+175], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.2e62 or 2.9e175 < x

   1. Initial program 68.6%

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

   3. Taylor expanded in x around 0 94.2%

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

   4. Taylor expanded in a around 0 90.8%

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

   5. Taylor expanded in j around 0 89.4%

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

   if -4.2e62 < x < 2.5500000000000002e-44

   1. Initial program 92.0%

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

   3. Taylor expanded in x around 0 76.3%

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

   if 2.5500000000000002e-44 < x < 1.42000000000000006e107

   1. Initial program 79.0%

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

   3. Taylor expanded in i around 0 75.0%

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

   4. Taylor expanded in a around 0 83.0%

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

   if 1.42000000000000006e107 < x < 2.9e175

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 94.1%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+62}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-44}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+107}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+175}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;a \cdot 4 \leq -5 \cdot 10^{+204} \lor \neg \left(a \cdot 4 \leq 10^{+36}\right):\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= (* a 4.0) -5e+204) (not (<= (* a 4.0) 1e+36)))
     (- (- (* b c) (+ (* 4.0 (* t a)) (* 4.0 (* x i)))) t_1)
     (- (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))) t_1))))

C

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 * 27.0) * k;
	double tmp;
	if (((a * 4.0) <= -5e+204) || !((a * 4.0) <= 1e+36)) {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1;
	} else {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - 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.
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 * 27.0d0) * k
    if (((a * 4.0d0) <= (-5d+204)) .or. (.not. ((a * 4.0d0) <= 1d+36))) then
        tmp = ((b * c) - ((4.0d0 * (t * a)) + (4.0d0 * (x * i)))) - t_1
    else
        tmp = ((b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))) - 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;
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 * 27.0) * k;
	double tmp;
	if (((a * 4.0) <= -5e+204) || !((a * 4.0) <= 1e+36)) {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1;
	} else {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if ((a * 4.0) <= -5e+204) or not ((a * 4.0) <= 1e+36):
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1
	else:
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((Float64(a * 4.0) <= -5e+204) || !(Float64(a * 4.0) <= 1e+36))
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + Float64(4.0 * Float64(x * i)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))) - 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (((a * 4.0) <= -5e+204) || ~(((a * 4.0) <= 1e+36)))
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1;
	else
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[N[(a * 4.0), $MachinePrecision], -5e+204], N[Not[LessEqual[N[(a * 4.0), $MachinePrecision], 1e+36]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 4) < -5.00000000000000008e204 or 1.00000000000000004e36 < (*.f64 a 4)

   1. Initial program 81.3%

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

   3. Taylor expanded in y around 0 90.5%

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

   if -5.00000000000000008e204 < (*.f64 a 4) < 1.00000000000000004e36

   1. Initial program 84.2%

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

   3. Taylor expanded in x around 0 89.5%

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

   4. Taylor expanded in a around 0 88.3%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 4 \leq -5 \cdot 10^{+204} \lor \neg \left(a \cdot 4 \leq 10^{+36}\right):\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 77.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{+117}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-34} \lor \neg \left(x \leq 1.95 \cdot 10^{+107}\right):\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= x -9.2e+117)
     (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
     (if (or (<= x 6.2e-34) (not (<= x 1.95e+107)))
       (- (- (* b c) (+ (* 4.0 (* t a)) (* 4.0 (* x i)))) t_1)
       (- (+ (* b c) (* 18.0 (* t (* x (* y z))))) t_1)))))

C

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 * 27.0) * k;
	double tmp;
	if (x <= -9.2e+117) {
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	} else if ((x <= 6.2e-34) || !(x <= 1.95e+107)) {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1;
	} else {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - 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.
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 * 27.0d0) * k
    if (x <= (-9.2d+117)) then
        tmp = (b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))
    else if ((x <= 6.2d-34) .or. (.not. (x <= 1.95d+107))) then
        tmp = ((b * c) - ((4.0d0 * (t * a)) + (4.0d0 * (x * i)))) - t_1
    else
        tmp = ((b * c) + (18.0d0 * (t * (x * (y * z))))) - 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;
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 * 27.0) * k;
	double tmp;
	if (x <= -9.2e+117) {
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	} else if ((x <= 6.2e-34) || !(x <= 1.95e+107)) {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1;
	} else {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if x <= -9.2e+117:
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))
	elif (x <= 6.2e-34) or not (x <= 1.95e+107):
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1
	else:
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -9.2e+117)
		tmp = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))));
	elseif ((x <= 6.2e-34) || !(x <= 1.95e+107))
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + Float64(4.0 * Float64(x * i)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))) - 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (x <= -9.2e+117)
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	elseif ((x <= 6.2e-34) || ~((x <= 1.95e+107)))
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - t_1;
	else
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -9.2e+117], N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 6.2e-34], N[Not[LessEqual[x, 1.95e+107]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.19999999999999951e117

   1. Initial program 64.6%

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

   3. Taylor expanded in x around 0 95.4%

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

   4. Taylor expanded in a around 0 93.2%

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

   5. Taylor expanded in j around 0 93.4%

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

   if -9.19999999999999951e117 < x < 6.1999999999999996e-34 or 1.9499999999999999e107 < x

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0 84.0%

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

   if 6.1999999999999996e-34 < x < 1.9499999999999999e107

   1. Initial program 79.0%

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

   3. Taylor expanded in i around 0 75.0%

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

   4. Taylor expanded in a around 0 83.0%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+117}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-34} \lor \neg \left(x \leq 1.95 \cdot 10^{+107}\right):\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 69.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+34}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+106}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= x -3.3e+161)
     (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
     (if (<= x 2.3e+34)
       (- (- (* b c) (* 4.0 (* t a))) t_1)
       (if (<= x 5.6e+106)
         (+ (* j (* k -27.0)) (* x (* (* y t) (* 18.0 z))))
         (- (- (* b c) (* 4.0 (* x i))) t_1))))))

C

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 * 27.0) * k;
	double tmp;
	if (x <= -3.3e+161) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (x <= 2.3e+34) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 5.6e+106) {
		tmp = (j * (k * -27.0)) + (x * ((y * t) * (18.0 * z)));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - 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.
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 * 27.0d0) * k
    if (x <= (-3.3d+161)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (x <= 2.3d+34) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (x <= 5.6d+106) then
        tmp = (j * (k * (-27.0d0))) + (x * ((y * t) * (18.0d0 * z)))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - 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;
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 * 27.0) * k;
	double tmp;
	if (x <= -3.3e+161) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (x <= 2.3e+34) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 5.6e+106) {
		tmp = (j * (k * -27.0)) + (x * ((y * t) * (18.0 * z)));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if x <= -3.3e+161:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif x <= 2.3e+34:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif x <= 5.6e+106:
		tmp = (j * (k * -27.0)) + (x * ((y * t) * (18.0 * z)))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -3.3e+161)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (x <= 2.3e+34)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (x <= 5.6e+106)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(x * Float64(Float64(y * t) * Float64(18.0 * z))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (x <= -3.3e+161)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (x <= 2.3e+34)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (x <= 5.6e+106)
		tmp = (j * (k * -27.0)) + (x * ((y * t) * (18.0 * z)));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -3.3e+161], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+34], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 5.6e+106], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * t), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.29999999999999997e161

   1. Initial program 66.9%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in x around inf 82.0%

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

   if -3.29999999999999997e161 < x < 2.2999999999999998e34

   1. Initial program 90.7%

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

   3. Taylor expanded in x around 0 73.5%

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

   if 2.2999999999999998e34 < x < 5.59999999999999986e106

   1. Initial program 72.7%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around inf 81.9%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   6. Step-by-step derivation

      1. *-commutative 81.9%

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

      2. *-commutative 81.9%

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

      3. associate-*l* 81.7%

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

      4. *-commutative 81.7%

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

      5. associate-*r* 81.9%

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

      6. associate-*r* 73.6%

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

      7. associate-*l* 73.6%

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

   7. Simplified 73.6%

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

   if 5.59999999999999986e106 < x

   1. Initial program 76.1%

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

   3. Taylor expanded in t around 0 81.3%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+34}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+106}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 35.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.3 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.85 \cdot 10^{-302}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.02 \cdot 10^{+183}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1.3e+153)
   (* b c)
   (if (<= (* b c) 1.85e-302)
     (* -27.0 (* j k))
     (if (<= (* b c) 1.02e+183) (* (* x i) -4.0) (* b c)))))

C

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) <= -1.3e+153) {
		tmp = b * c;
	} else if ((b * c) <= 1.85e-302) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 1.02e+183) {
		tmp = (x * i) * -4.0;
	} 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.
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) <= (-1.3d+153)) then
        tmp = b * c
    else if ((b * c) <= 1.85d-302) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 1.02d+183) then
        tmp = (x * i) * (-4.0d0)
    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;
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) <= -1.3e+153) {
		tmp = b * c;
	} else if ((b * c) <= 1.85e-302) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 1.02e+183) {
		tmp = (x * i) * -4.0;
	} 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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.3e+153:
		tmp = b * c
	elif (b * c) <= 1.85e-302:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 1.02e+183:
		tmp = (x * i) * -4.0
	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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1.3e+153)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 1.85e-302)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 1.02e+183)
		tmp = Float64(Float64(x * i) * -4.0);
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1.3e+153)
		tmp = b * c;
	elseif ((b * c) <= 1.85e-302)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 1.02e+183)
		tmp = (x * i) * -4.0;
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1.3e+153], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.85e-302], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.02e+183], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.2999999999999999e153 or 1.02000000000000002e183 < (*.f64 b c)

   1. Initial program 81.9%

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

   3. Taylor expanded in x around 0 86.8%

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

   4. Taylor expanded in a around 0 83.0%

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

   5. Taylor expanded in b around inf 64.9%

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

   if -1.2999999999999999e153 < (*.f64 b c) < 1.85e-302

   1. Initial program 88.1%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in j around inf 38.4%

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

   if 1.85e-302 < (*.f64 b c) < 1.02000000000000002e183

   1. Initial program 79.4%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in x around inf 60.1%

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

   6. Taylor expanded in t around 0 33.2%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.3 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.85 \cdot 10^{-302}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.02 \cdot 10^{+183}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 35.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.02 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 2.8 \cdot 10^{-303}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.45 \cdot 10^{+181}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1.02e+153)
   (* b c)
   (if (<= (* b c) 2.8e-303)
     (* k (* j -27.0))
     (if (<= (* b c) 1.45e+181) (* (* x i) -4.0) (* b c)))))

C

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) <= -1.02e+153) {
		tmp = b * c;
	} else if ((b * c) <= 2.8e-303) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 1.45e+181) {
		tmp = (x * i) * -4.0;
	} 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.
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) <= (-1.02d+153)) then
        tmp = b * c
    else if ((b * c) <= 2.8d-303) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 1.45d+181) then
        tmp = (x * i) * (-4.0d0)
    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;
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) <= -1.02e+153) {
		tmp = b * c;
	} else if ((b * c) <= 2.8e-303) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 1.45e+181) {
		tmp = (x * i) * -4.0;
	} 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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.02e+153:
		tmp = b * c
	elif (b * c) <= 2.8e-303:
		tmp = k * (j * -27.0)
	elif (b * c) <= 1.45e+181:
		tmp = (x * i) * -4.0
	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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1.02e+153)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 2.8e-303)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 1.45e+181)
		tmp = Float64(Float64(x * i) * -4.0);
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1.02e+153)
		tmp = b * c;
	elseif ((b * c) <= 2.8e-303)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 1.45e+181)
		tmp = (x * i) * -4.0;
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1.02e+153], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.8e-303], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.45e+181], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.0199999999999999e153 or 1.45e181 < (*.f64 b c)

   1. Initial program 81.9%

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

   3. Taylor expanded in x around 0 86.8%

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

   4. Taylor expanded in a around 0 83.0%

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

   5. Taylor expanded in b around inf 64.9%

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

   if -1.0199999999999999e153 < (*.f64 b c) < 2.8e-303

   1. Initial program 88.1%

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

   3. Taylor expanded in x around 0 87.8%

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

   4. Taylor expanded in a around 0 79.6%

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

   5. Taylor expanded in j around inf 38.4%

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

      1. associate-*r* 38.4%

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

   7. Simplified 38.4%

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

   if 2.8e-303 < (*.f64 b c) < 1.45e181

   1. Initial program 79.4%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in x around inf 60.1%

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

   6. Taylor expanded in t around 0 33.2%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.02 \cdot 10^{+153}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 2.8 \cdot 10^{-303}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.45 \cdot 10^{+181}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 37.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.1 \cdot 10^{+153} \lor \neg \left(b \cdot c \leq 1.8 \cdot 10^{+146}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -1.1e+153) (not (<= (* b c) 1.8e+146)))
   (* b c)
   (* -27.0 (* j k))))

C

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) <= -1.1e+153) || !((b * c) <= 1.8e+146)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * 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.
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) <= (-1.1d+153)) .or. (.not. ((b * c) <= 1.8d+146))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * 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;
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) <= -1.1e+153) || !((b * c) <= 1.8e+146)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * 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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -1.1e+153) or not ((b * c) <= 1.8e+146):
		tmp = b * c
	else:
		tmp = -27.0 * (j * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -1.1e+153) || !(Float64(b * c) <= 1.8e+146))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -1.1e+153) || ~(((b * c) <= 1.8e+146)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -1.1e+153], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.8e+146]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.1e153 or 1.7999999999999999e146 < (*.f64 b c)

   1. Initial program 82.8%

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

   3. Taylor expanded in x around 0 87.5%

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

   4. Taylor expanded in a around 0 82.6%

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

   5. Taylor expanded in b around inf 61.8%

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

   if -1.1e153 < (*.f64 b c) < 1.7999999999999999e146

   1. Initial program 83.6%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in j around inf 32.1%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.1 \cdot 10^{+153} \lor \neg \left(b \cdot c \leq 1.8 \cdot 10^{+146}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 47.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -3 \cdot 10^{+108} \lor \neg \left(i \leq 1.05 \cdot 10^{+109}\right):\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= i -3e+108) (not (<= i 1.05e+109)))
   (* (* x i) -4.0)
   (+ (* 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);
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 ((i <= -3e+108) || !(i <= 1.05e+109)) {
		tmp = (x * i) * -4.0;
	} else {
		tmp = (b * c) + (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.
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 ((i <= (-3d+108)) .or. (.not. (i <= 1.05d+109))) then
        tmp = (x * i) * (-4.0d0)
    else
        tmp = (b * c) + (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;
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 ((i <= -3e+108) || !(i <= 1.05e+109)) {
		tmp = (x * i) * -4.0;
	} else {
		tmp = (b * c) + (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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (i <= -3e+108) or not (i <= 1.05e+109):
		tmp = (x * i) * -4.0
	else:
		tmp = (b * c) + (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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((i <= -3e+108) || !(i <= 1.05e+109))
		tmp = Float64(Float64(x * i) * -4.0);
	else
		tmp = Float64(Float64(b * c) + 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((i <= -3e+108) || ~((i <= 1.05e+109)))
		tmp = (x * i) * -4.0;
	else
		tmp = (b * c) + (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[i, -3e+108], N[Not[LessEqual[i, 1.05e+109]], $MachinePrecision]], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.99999999999999984e108 or 1.0500000000000001e109 < i

   1. Initial program 77.6%

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

   3. Simplified 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 inf 65.1%

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

   6. Taylor expanded in t around 0 51.4%

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

   if -2.99999999999999984e108 < i < 1.0500000000000001e109

   1. Initial program 86.7%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in b around inf 56.2%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3 \cdot 10^{+108} \lor \neg \left(i \leq 1.05 \cdot 10^{+109}\right):\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 51.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+108} \lor \neg \left(i \leq 310000000\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= i -1.4e+108) (not (<= i 310000000.0)))
   (- (* b c) (* 4.0 (* x i)))
   (+ (* 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);
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 ((i <= -1.4e+108) || !(i <= 310000000.0)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) + (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.
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 ((i <= (-1.4d+108)) .or. (.not. (i <= 310000000.0d0))) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = (b * c) + (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;
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 ((i <= -1.4e+108) || !(i <= 310000000.0)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) + (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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (i <= -1.4e+108) or not (i <= 310000000.0):
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = (b * c) + (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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((i <= -1.4e+108) || !(i <= 310000000.0))
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(b * c) + 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((i <= -1.4e+108) || ~((i <= 310000000.0)))
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = (b * c) + (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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[i, -1.4e+108], N[Not[LessEqual[i, 310000000.0]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.3999999999999999e108 or 3.1e8 < i

   1. Initial program 78.8%

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

   3. Taylor expanded in t around 0 65.8%

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

   4. Taylor expanded in j around 0 57.0%

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

   if -1.3999999999999999e108 < i < 3.1e8

   1. Initial program 87.2%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in b around inf 57.0%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+108} \lor \neg \left(i \leq 310000000\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 23.6% accurate, 10.3× speedup

Math

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

FPCore

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

Derivation

1. Initial program 83.3%

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

3. Taylor expanded in x around 0 88.0%

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

4. Taylor expanded in a around 0 79.7%

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

5. Taylor expanded in b around inf 21.9%

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

6. Final simplification 21.9%

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

Developer target: 89.2% 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 2024026 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (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)))