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

Percentage Accurate: 84.8% → 91.5%

Time: 27.3s

Alternatives: 24

Speedup: 0.7×

• 50.3% 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: 84.8% 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: 91.5% accurate, 0.5× speedup

Math

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

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
         (-
          (-
           (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
           (* (* x 4.0) i))
          (* (* j 27.0) k))))
   (if (<= t_1 INFINITY) t_1 (* x (- (* 18.0 (* t (* y z))) (* 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 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	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 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (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 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (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(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)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - 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 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (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[(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] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 96.3%

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

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) 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 10.7%

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

   5. Taylor expanded in x around inf 65.0%

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

4. Final simplification 92.8%

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

Alternative 2: 70.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_2 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_3 := b \cdot c + t \cdot \left(t\_2 - a \cdot 4\right)\\ t_4 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_4 \leq -4 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + t\_2\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t\_4 \leq -1 \cdot 10^{-120}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq -4 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_4 \leq -1 \cdot 10^{-317}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_4 \leq 1.22 \cdot 10^{+107}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (+ (* t a) (* x i)))))
        (t_2 (* 18.0 (* x (* y z))))
        (t_3 (+ (* b c) (* t (- t_2 (* a 4.0)))))
        (t_4 (* (* j 27.0) k)))
   (if (<= t_4 -4e+50)
     (+ (* t (+ (* a -4.0) t_2)) (* j (* k -27.0)))
     (if (<= t_4 -1e-120)
       t_3
       (if (<= t_4 -4e-220)
         t_1
         (if (<= t_4 -1e-317)
           t_3
           (if (<= t_4 1e-110)
             t_1
             (if (<= t_4 1.22e+107)
               t_3
               (- (- (* b c) (* 4.0 (* x i))) t_4)))))))))

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 * ((t * a) + (x * i)));
	double t_2 = 18.0 * (x * (y * z));
	double t_3 = (b * c) + (t * (t_2 - (a * 4.0)));
	double t_4 = (j * 27.0) * k;
	double tmp;
	if (t_4 <= -4e+50) {
		tmp = (t * ((a * -4.0) + t_2)) + (j * (k * -27.0));
	} else if (t_4 <= -1e-120) {
		tmp = t_3;
	} else if (t_4 <= -4e-220) {
		tmp = t_1;
	} else if (t_4 <= -1e-317) {
		tmp = t_3;
	} else if (t_4 <= 1e-110) {
		tmp = t_1;
	} else if (t_4 <= 1.22e+107) {
		tmp = t_3;
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - t_4;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * ((t * a) + (x * i)))
    t_2 = 18.0d0 * (x * (y * z))
    t_3 = (b * c) + (t * (t_2 - (a * 4.0d0)))
    t_4 = (j * 27.0d0) * k
    if (t_4 <= (-4d+50)) then
        tmp = (t * ((a * (-4.0d0)) + t_2)) + (j * (k * (-27.0d0)))
    else if (t_4 <= (-1d-120)) then
        tmp = t_3
    else if (t_4 <= (-4d-220)) then
        tmp = t_1
    else if (t_4 <= (-1d-317)) then
        tmp = t_3
    else if (t_4 <= 1d-110) then
        tmp = t_1
    else if (t_4 <= 1.22d+107) then
        tmp = t_3
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_4
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * ((t * a) + (x * i)));
	double t_2 = 18.0 * (x * (y * z));
	double t_3 = (b * c) + (t * (t_2 - (a * 4.0)));
	double t_4 = (j * 27.0) * k;
	double tmp;
	if (t_4 <= -4e+50) {
		tmp = (t * ((a * -4.0) + t_2)) + (j * (k * -27.0));
	} else if (t_4 <= -1e-120) {
		tmp = t_3;
	} else if (t_4 <= -4e-220) {
		tmp = t_1;
	} else if (t_4 <= -1e-317) {
		tmp = t_3;
	} else if (t_4 <= 1e-110) {
		tmp = t_1;
	} else if (t_4 <= 1.22e+107) {
		tmp = t_3;
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - t_4;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * ((t * a) + (x * i)))
	t_2 = 18.0 * (x * (y * z))
	t_3 = (b * c) + (t * (t_2 - (a * 4.0)))
	t_4 = (j * 27.0) * k
	tmp = 0
	if t_4 <= -4e+50:
		tmp = (t * ((a * -4.0) + t_2)) + (j * (k * -27.0))
	elif t_4 <= -1e-120:
		tmp = t_3
	elif t_4 <= -4e-220:
		tmp = t_1
	elif t_4 <= -1e-317:
		tmp = t_3
	elif t_4 <= 1e-110:
		tmp = t_1
	elif t_4 <= 1.22e+107:
		tmp = t_3
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - t_4
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))))
	t_2 = Float64(18.0 * Float64(x * Float64(y * z)))
	t_3 = Float64(Float64(b * c) + Float64(t * Float64(t_2 - Float64(a * 4.0))))
	t_4 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_4 <= -4e+50)
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) + t_2)) + Float64(j * Float64(k * -27.0)));
	elseif (t_4 <= -1e-120)
		tmp = t_3;
	elseif (t_4 <= -4e-220)
		tmp = t_1;
	elseif (t_4 <= -1e-317)
		tmp = t_3;
	elseif (t_4 <= 1e-110)
		tmp = t_1;
	elseif (t_4 <= 1.22e+107)
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_4);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * ((t * a) + (x * i)));
	t_2 = 18.0 * (x * (y * z));
	t_3 = (b * c) + (t * (t_2 - (a * 4.0)));
	t_4 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_4 <= -4e+50)
		tmp = (t * ((a * -4.0) + t_2)) + (j * (k * -27.0));
	elseif (t_4 <= -1e-120)
		tmp = t_3;
	elseif (t_4 <= -4e-220)
		tmp = t_1;
	elseif (t_4 <= -1e-317)
		tmp = t_3;
	elseif (t_4 <= 1e-110)
		tmp = t_1;
	elseif (t_4 <= 1.22e+107)
		tmp = t_3;
	else
		tmp = ((b * c) - (4.0 * (x * i))) - t_4;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$2 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$4, -4e+50], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, -1e-120], t$95$3, If[LessEqual[t$95$4, -4e-220], t$95$1, If[LessEqual[t$95$4, -1e-317], t$95$3, If[LessEqual[t$95$4, 1e-110], t$95$1, If[LessEqual[t$95$4, 1.22e+107], t$95$3, N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.0000000000000003e50

   1. Initial program 79.8%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in t around inf 77.9%

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

   if -4.0000000000000003e50 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.99999999999999979e-121 or -3.99999999999999997e-220 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000023e-317 or 1.0000000000000001e-110 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.22e107

   1. Initial program 88.0%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in x around inf 89.4%

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

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in i around 0 84.0%

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

   if -9.99999999999999979e-121 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -3.99999999999999997e-220 or -1.00000023e-317 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.0000000000000001e-110

   1. Initial program 91.1%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in x around inf 89.7%

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

      1. associate-*r* 89.7%

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

      2. *-commutative 89.7%

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

   7. Simplified 89.7%

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

   8. Taylor expanded in y around 0 80.9%

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

      1. *-commutative 80.9%

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

      2. sub-neg 80.9%

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

      3. +-commutative 80.9%

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

      4. associate-+l+ 80.9%

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

      5. distribute-lft-neg-in 80.9%

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

      6. *-commutative 80.9%

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

      7. metadata-eval 80.9%

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

      8. distribute-lft-out 80.9%

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

      9. *-commutative 80.9%

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

   10. Simplified 80.9%

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

   if 1.22e107 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 80.8%

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

   3. Taylor expanded in t around 0 79.0%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{-120}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{-220}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{-317}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-110}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 1.22 \cdot 10^{+107}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ t_4 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_4 \leq -5 \cdot 10^{+66}:\\ \;\;\;\;t\_2 + 18 \cdot \left(t \cdot t\_3\right)\\ \mathbf{elif}\;t\_4 \leq -4 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_4 \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t \cdot \left(18 \cdot t\_3 - a \cdot 4\right)\\ \mathbf{elif}\;t\_4 \leq 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + -4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

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 (+ (* t a) (* x i)))))
        (t_2 (* j (* k -27.0)))
        (t_3 (* x (* y z)))
        (t_4 (* (* j 27.0) k)))
   (if (<= t_4 -5e+66)
     (+ t_2 (* 18.0 (* t t_3)))
     (if (<= t_4 -4e-220)
       t_1
       (if (<= t_4 -5e-287)
         (* t (- (* 18.0 t_3) (* a 4.0)))
         (if (<= t_4 1e+164) t_1 (+ t_2 (* -4.0 (* t a)))))))))

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 * ((t * a) + (x * i)));
	double t_2 = j * (k * -27.0);
	double t_3 = x * (y * z);
	double t_4 = (j * 27.0) * k;
	double tmp;
	if (t_4 <= -5e+66) {
		tmp = t_2 + (18.0 * (t * t_3));
	} else if (t_4 <= -4e-220) {
		tmp = t_1;
	} else if (t_4 <= -5e-287) {
		tmp = t * ((18.0 * t_3) - (a * 4.0));
	} else if (t_4 <= 1e+164) {
		tmp = t_1;
	} else {
		tmp = t_2 + (-4.0 * (t * a));
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * ((t * a) + (x * i)))
    t_2 = j * (k * (-27.0d0))
    t_3 = x * (y * z)
    t_4 = (j * 27.0d0) * k
    if (t_4 <= (-5d+66)) then
        tmp = t_2 + (18.0d0 * (t * t_3))
    else if (t_4 <= (-4d-220)) then
        tmp = t_1
    else if (t_4 <= (-5d-287)) then
        tmp = t * ((18.0d0 * t_3) - (a * 4.0d0))
    else if (t_4 <= 1d+164) then
        tmp = t_1
    else
        tmp = t_2 + ((-4.0d0) * (t * a))
    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 * ((t * a) + (x * i)));
	double t_2 = j * (k * -27.0);
	double t_3 = x * (y * z);
	double t_4 = (j * 27.0) * k;
	double tmp;
	if (t_4 <= -5e+66) {
		tmp = t_2 + (18.0 * (t * t_3));
	} else if (t_4 <= -4e-220) {
		tmp = t_1;
	} else if (t_4 <= -5e-287) {
		tmp = t * ((18.0 * t_3) - (a * 4.0));
	} else if (t_4 <= 1e+164) {
		tmp = t_1;
	} else {
		tmp = t_2 + (-4.0 * (t * a));
	}
	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 * ((t * a) + (x * i)))
	t_2 = j * (k * -27.0)
	t_3 = x * (y * z)
	t_4 = (j * 27.0) * k
	tmp = 0
	if t_4 <= -5e+66:
		tmp = t_2 + (18.0 * (t * t_3))
	elif t_4 <= -4e-220:
		tmp = t_1
	elif t_4 <= -5e-287:
		tmp = t * ((18.0 * t_3) - (a * 4.0))
	elif t_4 <= 1e+164:
		tmp = t_1
	else:
		tmp = t_2 + (-4.0 * (t * a))
	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(Float64(t * a) + Float64(x * i))))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(x * Float64(y * z))
	t_4 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_4 <= -5e+66)
		tmp = Float64(t_2 + Float64(18.0 * Float64(t * t_3)));
	elseif (t_4 <= -4e-220)
		tmp = t_1;
	elseif (t_4 <= -5e-287)
		tmp = Float64(t * Float64(Float64(18.0 * t_3) - Float64(a * 4.0)));
	elseif (t_4 <= 1e+164)
		tmp = t_1;
	else
		tmp = Float64(t_2 + Float64(-4.0 * Float64(t * a)));
	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 * ((t * a) + (x * i)));
	t_2 = j * (k * -27.0);
	t_3 = x * (y * z);
	t_4 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_4 <= -5e+66)
		tmp = t_2 + (18.0 * (t * t_3));
	elseif (t_4 <= -4e-220)
		tmp = t_1;
	elseif (t_4 <= -5e-287)
		tmp = t * ((18.0 * t_3) - (a * 4.0));
	elseif (t_4 <= 1e+164)
		tmp = t_1;
	else
		tmp = t_2 + (-4.0 * (t * a));
	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[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$4, -5e+66], N[(t$95$2 + N[(18.0 * N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, -4e-220], t$95$1, If[LessEqual[t$95$4, -5e-287], N[(t * N[(N[(18.0 * t$95$3), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 1e+164], t$95$1, N[(t$95$2 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999991e66

   1. Initial program 78.7%

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

   3. Simplified 80.3%

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

   5. Taylor expanded in y around inf 73.9%

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

      1. *-commutative 73.9%

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

   7. Simplified 73.9%

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

   if -4.99999999999999991e66 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -3.99999999999999997e-220 or -5.00000000000000025e-287 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e164

   1. Initial program 89.1%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in x around inf 86.9%

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

      1. associate-*r* 86.9%

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

      2. *-commutative 86.9%

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

   7. Simplified 86.9%

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

   8. Taylor expanded in y around 0 71.9%

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

      1. *-commutative 71.9%

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

      2. sub-neg 71.9%

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

      3. +-commutative 71.9%

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

      4. associate-+l+ 71.9%

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

      5. distribute-lft-neg-in 71.9%

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

      6. *-commutative 71.9%

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

      7. metadata-eval 71.9%

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

      8. distribute-lft-out 71.9%

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

      9. *-commutative 71.9%

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

   10. Simplified 71.9%

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

   if -3.99999999999999997e-220 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.00000000000000025e-287

   1. Initial program 94.1%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 99.9%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around inf 84.0%

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

   if 1e164 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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 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 a around inf 88.5%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{-220}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+164}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+77} \lor \neg \left(t \leq 4.1 \cdot 10^{-51}\right) \land \left(t \leq 16500000000000 \lor \neg \left(t \leq 1.1 \cdot 10^{+56}\right)\right):\\ \;\;\;\;t \cdot \left(\left(a \cdot -4 + \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right)\right) - 27 \cdot \frac{j \cdot k}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -2.8e+77)
         (and (not (<= t 4.1e-51))
              (or (<= t 16500000000000.0) (not (<= t 1.1e+56)))))
   (*
    t
    (-
     (+ (* a -4.0) (+ (* 18.0 (* x (* y z))) (/ (* b c) t)))
     (* 27.0 (/ (* j k) t))))
   (- (- (* b c) (* 4.0 (+ (* t a) (* x 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 ((t <= -2.8e+77) || (!(t <= 4.1e-51) && ((t <= 16500000000000.0) || !(t <= 1.1e+56)))) {
		tmp = t * (((a * -4.0) + ((18.0 * (x * (y * z))) + ((b * c) / t))) - (27.0 * ((j * k) / t)));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * 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 ((t <= (-2.8d+77)) .or. (.not. (t <= 4.1d-51)) .and. (t <= 16500000000000.0d0) .or. (.not. (t <= 1.1d+56))) then
        tmp = t * (((a * (-4.0d0)) + ((18.0d0 * (x * (y * z))) + ((b * c) / t))) - (27.0d0 * ((j * k) / t)))
    else
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * 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 ((t <= -2.8e+77) || (!(t <= 4.1e-51) && ((t <= 16500000000000.0) || !(t <= 1.1e+56)))) {
		tmp = t * (((a * -4.0) + ((18.0 * (x * (y * z))) + ((b * c) / t))) - (27.0 * ((j * k) / t)));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * 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 (t <= -2.8e+77) or (not (t <= 4.1e-51) and ((t <= 16500000000000.0) or not (t <= 1.1e+56))):
		tmp = t * (((a * -4.0) + ((18.0 * (x * (y * z))) + ((b * c) / t))) - (27.0 * ((j * k) / t)))
	else:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * 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 ((t <= -2.8e+77) || (!(t <= 4.1e-51) && ((t <= 16500000000000.0) || !(t <= 1.1e+56))))
		tmp = Float64(t * Float64(Float64(Float64(a * -4.0) + Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(Float64(b * c) / t))) - Float64(27.0 * Float64(Float64(j * k) / t))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -2.8e+77) || (~((t <= 4.1e-51)) && ((t <= 16500000000000.0) || ~((t <= 1.1e+56)))))
		tmp = t * (((a * -4.0) + ((18.0 * (x * (y * z))) + ((b * c) / t))) - (27.0 * ((j * k) / t)));
	else
		tmp = ((b * c) - (4.0 * ((t * a) + (x * 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[t, -2.8e+77], And[N[Not[LessEqual[t, 4.1e-51]], $MachinePrecision], Or[LessEqual[t, 16500000000000.0], N[Not[LessEqual[t, 1.1e+56]], $MachinePrecision]]]], N[(t * N[(N[(N[(a * -4.0), $MachinePrecision] + N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(N[(j * k), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8e77 or 4.09999999999999973e-51 < t < 1.65e13 or 1.10000000000000008e56 < t

   1. Initial program 85.4%

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

   3. Simplified 86.7%

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

      1. associate-*r* 86.2%

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

      2. distribute-rgt-out-- 85.4%

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

      3. associate-*l* 78.5%

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

      4. fmm-def 78.5%

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

      5. associate-*l* 78.6%

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

      6. associate-*l* 77.8%

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

   6. Applied egg-rr 77.8%

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

      1. fmm-undef 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-*l* 78.6%

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

      4. *-commutative 78.6%

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

      5. cancel-sign-sub-inv 78.6%

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

      6. metadata-eval 78.6%

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

      7. fma-undefine 78.6%

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

      8. associate-*r* 78.5%

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

      9. *-commutative 78.5%

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

      10. associate-*r* 78.6%

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

   8. Simplified 78.6%

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

   9. Taylor expanded in x around 0 77.8%

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

       1. associate-*r* 77.9%

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

       2. *-commutative 77.9%

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

   11. Simplified 77.9%

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

   12. Taylor expanded in t around inf 89.9%

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

   if -2.8e77 < t < 4.09999999999999973e-51 or 1.65e13 < t < 1.10000000000000008e56

   1. Initial program 86.0%

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

   3. Taylor expanded in y around 0 85.2%

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

      1. distribute-lft-out 85.2%

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

      2. *-commutative 85.2%

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

   5. Simplified 85.2%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+77} \lor \neg \left(t \leq 4.1 \cdot 10^{-51}\right) \land \left(t \leq 16500000000000 \lor \neg \left(t \leq 1.1 \cdot 10^{+56}\right)\right):\\ \;\;\;\;t \cdot \left(\left(a \cdot -4 + \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right)\right) - 27 \cdot \frac{j \cdot k}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+237}:\\ \;\;\;\;k \cdot \left(j \cdot -27 + -4 \cdot \frac{x \cdot i}{k}\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+269}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -1e+237)
     (* k (+ (* j -27.0) (* -4.0 (/ (* x i) k))))
     (if (<= t_1 2e+269)
       (-
        (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
        (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
       (* -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 t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+237) {
		tmp = k * ((j * -27.0) + (-4.0 * ((x * i) / k)));
	} else if (t_1 <= 2e+269) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-1d+237)) then
        tmp = k * ((j * (-27.0d0)) + ((-4.0d0) * ((x * i) / k)))
    else if (t_1 <= 2d+269) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    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 t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+237) {
		tmp = k * ((j * -27.0) + (-4.0 * ((x * i) / k)));
	} else if (t_1 <= 2e+269) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} 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):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -1e+237:
		tmp = k * ((j * -27.0) + (-4.0 * ((x * i) / k)))
	elif t_1 <= 2e+269:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	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)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -1e+237)
		tmp = Float64(k * Float64(Float64(j * -27.0) + Float64(-4.0 * Float64(Float64(x * i) / k))));
	elseif (t_1 <= 2e+269)
		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(-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)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -1e+237)
		tmp = k * ((j * -27.0) + (-4.0 * ((x * i) / k)));
	elseif (t_1 <= 2e+269)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	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_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+237], N[(k * N[(N[(j * -27.0), $MachinePrecision] + N[(-4.0 * N[(N[(x * i), $MachinePrecision] / k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+269], 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[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.9999999999999994e236

   1. Initial program 65.5%

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

   3. Simplified 73.0%

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

   5. Taylor expanded in i around inf 80.6%

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

      1. *-commutative 80.6%

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

      2. *-commutative 80.6%

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

      3. associate-*l* 80.6%

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

      4. *-commutative 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in k around inf 84.8%

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

   if -9.9999999999999994e236 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000000000000001e269

   1. Initial program 89.7%

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

   3. Simplified 89.6%

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

   if 2.0000000000000001e269 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 71.4%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in j around inf 95.2%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+237}:\\ \;\;\;\;k \cdot \left(j \cdot -27 + -4 \cdot \frac{x \cdot i}{k}\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+269}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27 + -4 \cdot \frac{x \cdot i}{k}\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.08 \cdot 10^{+198}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+150}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \left(z \cdot \left(18 \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-228}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-274}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* k (+ (* j -27.0) (* -4.0 (/ (* x i) k)))))
        (t_2 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -1.08e+198)
     t_2
     (if (<= t -8.2e+150)
       (+ (* j (* k -27.0)) (* -4.0 (* t a)))
       (if (<= t -2.65e-64)
         (* t (- (* z (* 18.0 (* x y))) (* a 4.0)))
         (if (<= t -2.6e-228)
           t_1
           (if (<= t -1.9e-274)
             (- (* b c) (* 4.0 (* x i)))
             (if (<= t 1.1e+56) 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 = k * ((j * -27.0) + (-4.0 * ((x * i) / k)));
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.08e+198) {
		tmp = t_2;
	} else if (t <= -8.2e+150) {
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a));
	} else if (t <= -2.65e-64) {
		tmp = t * ((z * (18.0 * (x * y))) - (a * 4.0));
	} else if (t <= -2.6e-228) {
		tmp = t_1;
	} else if (t <= -1.9e-274) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 1.1e+56) {
		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 = k * ((j * (-27.0d0)) + ((-4.0d0) * ((x * i) / k)))
    t_2 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-1.08d+198)) then
        tmp = t_2
    else if (t <= (-8.2d+150)) then
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * (t * a))
    else if (t <= (-2.65d-64)) then
        tmp = t * ((z * (18.0d0 * (x * y))) - (a * 4.0d0))
    else if (t <= (-2.6d-228)) then
        tmp = t_1
    else if (t <= (-1.9d-274)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t <= 1.1d+56) 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 = k * ((j * -27.0) + (-4.0 * ((x * i) / k)));
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.08e+198) {
		tmp = t_2;
	} else if (t <= -8.2e+150) {
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a));
	} else if (t <= -2.65e-64) {
		tmp = t * ((z * (18.0 * (x * y))) - (a * 4.0));
	} else if (t <= -2.6e-228) {
		tmp = t_1;
	} else if (t <= -1.9e-274) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 1.1e+56) {
		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 = k * ((j * -27.0) + (-4.0 * ((x * i) / k)))
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -1.08e+198:
		tmp = t_2
	elif t <= -8.2e+150:
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a))
	elif t <= -2.65e-64:
		tmp = t * ((z * (18.0 * (x * y))) - (a * 4.0))
	elif t <= -2.6e-228:
		tmp = t_1
	elif t <= -1.9e-274:
		tmp = (b * c) - (4.0 * (x * i))
	elif t <= 1.1e+56:
		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(k * Float64(Float64(j * -27.0) + Float64(-4.0 * Float64(Float64(x * i) / k))))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -1.08e+198)
		tmp = t_2;
	elseif (t <= -8.2e+150)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(t * a)));
	elseif (t <= -2.65e-64)
		tmp = Float64(t * Float64(Float64(z * Float64(18.0 * Float64(x * y))) - Float64(a * 4.0)));
	elseif (t <= -2.6e-228)
		tmp = t_1;
	elseif (t <= -1.9e-274)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t <= 1.1e+56)
		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 = k * ((j * -27.0) + (-4.0 * ((x * i) / k)));
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -1.08e+198)
		tmp = t_2;
	elseif (t <= -8.2e+150)
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a));
	elseif (t <= -2.65e-64)
		tmp = t * ((z * (18.0 * (x * y))) - (a * 4.0));
	elseif (t <= -2.6e-228)
		tmp = t_1;
	elseif (t <= -1.9e-274)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t <= 1.1e+56)
		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[(k * N[(N[(j * -27.0), $MachinePrecision] + N[(-4.0 * N[(N[(x * i), $MachinePrecision] / k), $MachinePrecision]), $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, -1.08e+198], t$95$2, If[LessEqual[t, -8.2e+150], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.65e-64], N[(t * N[(N[(z * N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.6e-228], t$95$1, If[LessEqual[t, -1.9e-274], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+56], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.08e198 or 1.10000000000000008e56 < t

   1. Initial program 85.5%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in x around inf 81.0%

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

      1. associate-*r* 81.0%

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

      2. *-commutative 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in t around inf 68.9%

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

   if -1.08e198 < t < -8.19999999999999988e150

   1. Initial program 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in a around inf 82.5%

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

   if -8.19999999999999988e150 < t < -2.6500000000000001e-64

   1. Initial program 83.9%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in x around inf 79.2%

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

      1. associate-*r* 79.2%

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

      2. *-commutative 79.2%

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

   7. Simplified 79.2%

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

   8. Taylor expanded in t around inf 55.6%

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

      1. pow1 55.6%

         \[\leadsto t \cdot \left(\color{blue}{{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}^{1}} - 4 \cdot a\right) \]

      2. associate-*r* 60.5%

         \[\leadsto t \cdot \left({\left(18 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right)}^{1} - 4 \cdot a\right) \]

      3. associate-*r* 60.5%

         \[\leadsto t \cdot \left({\color{blue}{\left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot z\right)}}^{1} - 4 \cdot a\right) \]

      4. *-commutative 60.5%

         \[\leadsto t \cdot \left({\left(\left(18 \cdot \color{blue}{\left(y \cdot x\right)}\right) \cdot z\right)}^{1} - 4 \cdot a\right) \]

      5. associate-*r* 60.6%

         \[\leadsto t \cdot \left({\left(\color{blue}{\left(\left(18 \cdot y\right) \cdot x\right)} \cdot z\right)}^{1} - 4 \cdot a\right) \]

   10. Applied egg-rr 60.6%

       \[\leadsto t \cdot \left(\color{blue}{{\left(\left(\left(18 \cdot y\right) \cdot x\right) \cdot z\right)}^{1}} - 4 \cdot a\right) \]
   11. Step-by-step derivation

       1. unpow1 60.6%

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

       2. *-commutative 60.6%

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

       3. associate-*l* 60.5%

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

       4. *-commutative 60.5%

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

   12. Simplified 60.5%

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

   if -2.6500000000000001e-64 < t < -2.6e-228 or -1.89999999999999992e-274 < t < 1.10000000000000008e56

   1. Initial program 85.8%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in i around inf 64.0%

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

      1. *-commutative 64.0%

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

      2. *-commutative 64.0%

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

      3. associate-*l* 64.0%

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

      4. *-commutative 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in k around inf 63.1%

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

   if -2.6e-228 < t < -1.89999999999999992e-274

   1. Initial program 89.4%

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

   3. Taylor expanded in t around 0 89.0%

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

   4. Taylor expanded in j around 0 89.0%

      \[\leadsto \color{blue}{b \cdot c - 4 \cdot \left(i \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{+198}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+150}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \left(z \cdot \left(18 \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-228}:\\ \;\;\;\;k \cdot \left(j \cdot -27 + -4 \cdot \frac{x \cdot i}{k}\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-274}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+56}:\\ \;\;\;\;k \cdot \left(j \cdot -27 + -4 \cdot \frac{x \cdot i}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+164}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + -4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

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 (* (* j 27.0) k)))
   (if (<= t_2 -4e+50)
     (+ (* t (+ (* a -4.0) (* 18.0 (* x (* y z))))) t_1)
     (if (<= t_2 1e+164)
       (-
        (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
        (* x (* 4.0 i)))
       (+ t_1 (* -4.0 (* t a)))))))

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 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -4e+50) {
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + t_1;
	} else if (t_2 <= 1e+164) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i));
	} else {
		tmp = t_1 + (-4.0 * (t * a));
	}
	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 = (j * 27.0d0) * k
    if (t_2 <= (-4d+50)) then
        tmp = (t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z))))) + t_1
    else if (t_2 <= 1d+164) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - (x * (4.0d0 * i))
    else
        tmp = t_1 + ((-4.0d0) * (t * a))
    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 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -4e+50) {
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + t_1;
	} else if (t_2 <= 1e+164) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i));
	} else {
		tmp = t_1 + (-4.0 * (t * a));
	}
	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 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -4e+50:
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + t_1
	elif t_2 <= 1e+164:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i))
	else:
		tmp = t_1 + (-4.0 * (t * a))
	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(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -4e+50)
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z))))) + t_1);
	elseif (t_2 <= 1e+164)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(x * Float64(4.0 * i)));
	else
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	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 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -4e+50)
		tmp = (t * ((a * -4.0) + (18.0 * (x * (y * z))))) + t_1;
	elseif (t_2 <= 1e+164)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i));
	else
		tmp = t_1 + (-4.0 * (t * a));
	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[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+50], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 1e+164], 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[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.0000000000000003e50

   1. Initial program 79.8%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in t around inf 77.9%

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

   if -4.0000000000000003e50 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e164

   1. Initial program 89.2%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in x around inf 88.2%

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

      1. associate-*r* 88.2%

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

      2. *-commutative 88.2%

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

   7. Simplified 88.2%

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

   if 1e164 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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 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 a around inf 88.5%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+164}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-244}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+133}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(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 (* k -27.0)) (* -4.0 (* t a)))))
   (if (<= x -1.2e+21)
     (* y (* (* x z) (* 18.0 t)))
     (if (<= x -1.7e-244)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= x 2.7e-5)
         t_2
         (if (<= x 1.45e+96)
           t_1
           (if (<= x 8.6e+133)
             t_2
             (if (<= x 1.82e+165) (* t (* 18.0 (* z (* x y)))) 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 = (b * c) - (4.0 * (x * i));
	double t_2 = (j * (k * -27.0)) + (-4.0 * (t * a));
	double tmp;
	if (x <= -1.2e+21) {
		tmp = y * ((x * z) * (18.0 * t));
	} else if (x <= -1.7e-244) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 2.7e-5) {
		tmp = t_2;
	} else if (x <= 1.45e+96) {
		tmp = t_1;
	} else if (x <= 8.6e+133) {
		tmp = t_2;
	} else if (x <= 1.82e+165) {
		tmp = t * (18.0 * (z * (x * y)));
	} 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 = (b * c) - (4.0d0 * (x * i))
    t_2 = (j * (k * (-27.0d0))) + ((-4.0d0) * (t * a))
    if (x <= (-1.2d+21)) then
        tmp = y * ((x * z) * (18.0d0 * t))
    else if (x <= (-1.7d-244)) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (x <= 2.7d-5) then
        tmp = t_2
    else if (x <= 1.45d+96) then
        tmp = t_1
    else if (x <= 8.6d+133) then
        tmp = t_2
    else if (x <= 1.82d+165) then
        tmp = t * (18.0d0 * (z * (x * y)))
    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 = (b * c) - (4.0 * (x * i));
	double t_2 = (j * (k * -27.0)) + (-4.0 * (t * a));
	double tmp;
	if (x <= -1.2e+21) {
		tmp = y * ((x * z) * (18.0 * t));
	} else if (x <= -1.7e-244) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 2.7e-5) {
		tmp = t_2;
	} else if (x <= 1.45e+96) {
		tmp = t_1;
	} else if (x <= 8.6e+133) {
		tmp = t_2;
	} else if (x <= 1.82e+165) {
		tmp = t * (18.0 * (z * (x * y)));
	} 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 = (b * c) - (4.0 * (x * i))
	t_2 = (j * (k * -27.0)) + (-4.0 * (t * a))
	tmp = 0
	if x <= -1.2e+21:
		tmp = y * ((x * z) * (18.0 * t))
	elif x <= -1.7e-244:
		tmp = (b * c) - (27.0 * (j * k))
	elif x <= 2.7e-5:
		tmp = t_2
	elif x <= 1.45e+96:
		tmp = t_1
	elif x <= 8.6e+133:
		tmp = t_2
	elif x <= 1.82e+165:
		tmp = t * (18.0 * (z * (x * y)))
	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(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	t_2 = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (x <= -1.2e+21)
		tmp = Float64(y * Float64(Float64(x * z) * Float64(18.0 * t)));
	elseif (x <= -1.7e-244)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (x <= 2.7e-5)
		tmp = t_2;
	elseif (x <= 1.45e+96)
		tmp = t_1;
	elseif (x <= 8.6e+133)
		tmp = t_2;
	elseif (x <= 1.82e+165)
		tmp = Float64(t * Float64(18.0 * Float64(z * Float64(x * y))));
	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 = (b * c) - (4.0 * (x * i));
	t_2 = (j * (k * -27.0)) + (-4.0 * (t * a));
	tmp = 0.0;
	if (x <= -1.2e+21)
		tmp = y * ((x * z) * (18.0 * t));
	elseif (x <= -1.7e-244)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (x <= 2.7e-5)
		tmp = t_2;
	elseif (x <= 1.45e+96)
		tmp = t_1;
	elseif (x <= 8.6e+133)
		tmp = t_2;
	elseif (x <= 1.82e+165)
		tmp = t * (18.0 * (z * (x * y)));
	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[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+21], N[(y * N[(N[(x * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.7e-244], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e-5], t$95$2, If[LessEqual[x, 1.45e+96], t$95$1, If[LessEqual[x, 8.6e+133], t$95$2, If[LessEqual[x, 1.82e+165], N[(t * N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.2e21

   1. Initial program 75.7%

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

   3. Simplified 80.3%

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

      1. associate-*r* 77.3%

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

      2. distribute-rgt-out-- 75.7%

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

      3. associate-*l* 77.3%

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

      4. fmm-def 77.3%

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

      5. associate-*l* 77.3%

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

      6. associate-*l* 78.6%

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

   6. Applied egg-rr 78.6%

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

      1. fmm-undef 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*l* 78.6%

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

      4. *-commutative 78.6%

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

      5. cancel-sign-sub-inv 78.6%

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

      6. metadata-eval 78.6%

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

      7. fma-undefine 78.6%

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

      8. associate-*r* 78.6%

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

      9. *-commutative 78.6%

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

      10. associate-*r* 78.6%

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

   8. Simplified 78.6%

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

   9. Taylor expanded in x around 0 72.4%

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

       1. associate-*r* 72.4%

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

       2. *-commutative 72.4%

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

   11. Simplified 72.4%

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

   12. Taylor expanded in t around inf 66.4%

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

   13. Taylor expanded in x around inf 50.0%

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

       1. associate-*r* 49.9%

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

       2. *-commutative 49.9%

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

       3. associate-*r* 50.0%

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

       4. associate-*l* 53.0%

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

       5. associate-*r* 52.9%

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

       6. *-commutative 52.9%

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

       7. *-commutative 52.9%

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

       8. *-commutative 52.9%

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

       9. associate-*l* 53.0%

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

   15. Simplified 53.0%

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

   if -1.2e21 < x < -1.70000000000000004e-244

   1. Initial program 90.0%

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

   3. Taylor expanded in t around 0 73.2%

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

   4. Taylor expanded in i around 0 60.8%

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

   if -1.70000000000000004e-244 < x < 2.6999999999999999e-5 or 1.44999999999999989e96 < x < 8.59999999999999989e133

   1. Initial program 96.5%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in a around inf 66.7%

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

   if 2.6999999999999999e-5 < x < 1.44999999999999989e96 or 1.82000000000000003e165 < x

   1. Initial program 72.8%

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

   3. Taylor expanded in t around 0 60.5%

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

   4. Taylor expanded in j around 0 62.8%

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

   if 8.59999999999999989e133 < x < 1.82000000000000003e165

   1. Initial program 90.7%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around inf 80.7%

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

   9. Taylor expanded in x around inf 71.0%

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

       1. associate-*r* 61.7%

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

       2. *-commutative 61.7%

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

   11. Simplified 61.7%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-244}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+96}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+133}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+197}:\\ \;\;\;\;b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-40} \lor \neg \left(t \leq 5800000000000\right) \land t \leq 6 \cdot 10^{+56}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + t\_1\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z)))))
   (if (<= t -3.3e+197)
     (+ (* b c) (* t (- t_1 (* a 4.0))))
     (if (or (<= t 2.2e-40) (and (not (<= t 5800000000000.0)) (<= t 6e+56)))
       (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) (* (* j 27.0) k))
       (+ (* t (+ (* a -4.0) t_1)) (* 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 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -3.3e+197) {
		tmp = (b * c) + (t * (t_1 - (a * 4.0)));
	} else if ((t <= 2.2e-40) || (!(t <= 5800000000000.0) && (t <= 6e+56))) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	} else {
		tmp = (t * ((a * -4.0) + t_1)) + (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) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    if (t <= (-3.3d+197)) then
        tmp = (b * c) + (t * (t_1 - (a * 4.0d0)))
    else if ((t <= 2.2d-40) .or. (.not. (t <= 5800000000000.0d0)) .and. (t <= 6d+56)) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - ((j * 27.0d0) * k)
    else
        tmp = (t * ((a * (-4.0d0)) + t_1)) + (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 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -3.3e+197) {
		tmp = (b * c) + (t * (t_1 - (a * 4.0)));
	} else if ((t <= 2.2e-40) || (!(t <= 5800000000000.0) && (t <= 6e+56))) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	} else {
		tmp = (t * ((a * -4.0) + t_1)) + (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 = 18.0 * (x * (y * z))
	tmp = 0
	if t <= -3.3e+197:
		tmp = (b * c) + (t * (t_1 - (a * 4.0)))
	elif (t <= 2.2e-40) or (not (t <= 5800000000000.0) and (t <= 6e+56)):
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k)
	else:
		tmp = (t * ((a * -4.0) + t_1)) + (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(18.0 * Float64(x * Float64(y * z)))
	tmp = 0.0
	if (t <= -3.3e+197)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(t_1 - Float64(a * 4.0))));
	elseif ((t <= 2.2e-40) || (!(t <= 5800000000000.0) && (t <= 6e+56)))
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) + t_1)) + 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 = 18.0 * (x * (y * z));
	tmp = 0.0;
	if (t <= -3.3e+197)
		tmp = (b * c) + (t * (t_1 - (a * 4.0)));
	elseif ((t <= 2.2e-40) || (~((t <= 5800000000000.0)) && (t <= 6e+56)))
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	else
		tmp = (t * ((a * -4.0) + t_1)) + (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[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e+197], N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 2.2e-40], And[N[Not[LessEqual[t, 5800000000000.0]], $MachinePrecision], LessEqual[t, 6e+56]]], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2999999999999997e197

   1. Initial program 74.1%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in x around inf 78.0%

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

      1. associate-*r* 78.0%

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

      2. *-commutative 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in i around 0 82.0%

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

   if -3.2999999999999997e197 < t < 2.20000000000000009e-40 or 5.8e12 < t < 6.00000000000000012e56

   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 y around 0 84.2%

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

      1. distribute-lft-out 84.2%

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

      2. *-commutative 84.2%

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

   5. Simplified 84.2%

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

   if 2.20000000000000009e-40 < t < 5.8e12 or 6.00000000000000012e56 < t

   1. Initial program 86.8%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in t around inf 77.7%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+197}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-40} \lor \neg \left(t \leq 5800000000000\right) \land t \leq 6 \cdot 10^{+56}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6000000000000:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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) (* 4.0 (* x i))) (* (* j 27.0) k)))
        (t_2 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))))
   (if (<= t -1.55e+81)
     t_2
     (if (<= t 1.75e-128)
       t_1
       (if (<= t 6000000000000.0)
         (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
         (if (<= t 3.5e+56) 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) - (4.0 * (x * i))) - ((j * 27.0) * k);
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -1.55e+81) {
		tmp = t_2;
	} else if (t <= 1.75e-128) {
		tmp = t_1;
	} else if (t <= 6000000000000.0) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= 3.5e+56) {
		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) - (4.0d0 * (x * i))) - ((j * 27.0d0) * k)
    t_2 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    if (t <= (-1.55d+81)) then
        tmp = t_2
    else if (t <= 1.75d-128) then
        tmp = t_1
    else if (t <= 6000000000000.0d0) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (t <= 3.5d+56) 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) - (4.0 * (x * i))) - ((j * 27.0) * k);
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -1.55e+81) {
		tmp = t_2;
	} else if (t <= 1.75e-128) {
		tmp = t_1;
	} else if (t <= 6000000000000.0) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= 3.5e+56) {
		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) - (4.0 * (x * i))) - ((j * 27.0) * k)
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	tmp = 0
	if t <= -1.55e+81:
		tmp = t_2
	elif t <= 1.75e-128:
		tmp = t_1
	elif t <= 6000000000000.0:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif t <= 3.5e+56:
		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(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(Float64(j * 27.0) * k))
	t_2 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))))
	tmp = 0.0
	if (t <= -1.55e+81)
		tmp = t_2;
	elseif (t <= 1.75e-128)
		tmp = t_1;
	elseif (t <= 6000000000000.0)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (t <= 3.5e+56)
		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) - (4.0 * (x * i))) - ((j * 27.0) * k);
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	tmp = 0.0;
	if (t <= -1.55e+81)
		tmp = t_2;
	elseif (t <= 1.75e-128)
		tmp = t_1;
	elseif (t <= 6000000000000.0)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (t <= 3.5e+56)
		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[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e+81], t$95$2, If[LessEqual[t, 1.75e-128], t$95$1, If[LessEqual[t, 6000000000000.0], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+56], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55e81 or 3.49999999999999999e56 < t

   1. Initial program 86.3%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in x around inf 78.8%

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

      1. associate-*r* 78.8%

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

      2. *-commutative 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in i around 0 78.0%

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

   if -1.55e81 < t < 1.75e-128 or 6e12 < t < 3.49999999999999999e56

   1. Initial program 89.8%

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

   3. Taylor expanded in t around 0 79.6%

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

   if 1.75e-128 < t < 6e12

   1. Initial program 63.0%

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

   3. Simplified 70.9%

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

   5. Taylor expanded in x around inf 69.5%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+81}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-128}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 6000000000000:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+56}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -4.7 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-244}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+28}:\\ \;\;\;\;t\_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+136}:\\ \;\;\;\;t\_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

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))))
   (if (<= x -4.7e+24)
     (* y (* (* x z) (* 18.0 t)))
     (if (<= x -3.4e-244)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= x 1.6e+28)
         (+ t_1 (* -4.0 (* t a)))
         (if (<= x 2.7e+136)
           (+ t_1 (* x (* i -4.0)))
           (if (<= x 1.7e+165)
             (* t (* 18.0 (* z (* x y))))
             (- (* 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 tmp;
	if (x <= -4.7e+24) {
		tmp = y * ((x * z) * (18.0 * t));
	} else if (x <= -3.4e-244) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 1.6e+28) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (x <= 2.7e+136) {
		tmp = t_1 + (x * (i * -4.0));
	} else if (x <= 1.7e+165) {
		tmp = t * (18.0 * (z * (x * y)));
	} 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) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (x <= (-4.7d+24)) then
        tmp = y * ((x * z) * (18.0d0 * t))
    else if (x <= (-3.4d-244)) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (x <= 1.6d+28) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else if (x <= 2.7d+136) then
        tmp = t_1 + (x * (i * (-4.0d0)))
    else if (x <= 1.7d+165) then
        tmp = t * (18.0d0 * (z * (x * y)))
    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 tmp;
	if (x <= -4.7e+24) {
		tmp = y * ((x * z) * (18.0 * t));
	} else if (x <= -3.4e-244) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 1.6e+28) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if (x <= 2.7e+136) {
		tmp = t_1 + (x * (i * -4.0));
	} else if (x <= 1.7e+165) {
		tmp = t * (18.0 * (z * (x * y)));
	} 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)
	tmp = 0
	if x <= -4.7e+24:
		tmp = y * ((x * z) * (18.0 * t))
	elif x <= -3.4e-244:
		tmp = (b * c) - (27.0 * (j * k))
	elif x <= 1.6e+28:
		tmp = t_1 + (-4.0 * (t * a))
	elif x <= 2.7e+136:
		tmp = t_1 + (x * (i * -4.0))
	elif x <= 1.7e+165:
		tmp = t * (18.0 * (z * (x * y)))
	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))
	tmp = 0.0
	if (x <= -4.7e+24)
		tmp = Float64(y * Float64(Float64(x * z) * Float64(18.0 * t)));
	elseif (x <= -3.4e-244)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (x <= 1.6e+28)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 2.7e+136)
		tmp = Float64(t_1 + Float64(x * Float64(i * -4.0)));
	elseif (x <= 1.7e+165)
		tmp = Float64(t * Float64(18.0 * Float64(z * Float64(x * y))));
	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);
	tmp = 0.0;
	if (x <= -4.7e+24)
		tmp = y * ((x * z) * (18.0 * t));
	elseif (x <= -3.4e-244)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (x <= 1.6e+28)
		tmp = t_1 + (-4.0 * (t * a));
	elseif (x <= 2.7e+136)
		tmp = t_1 + (x * (i * -4.0));
	elseif (x <= 1.7e+165)
		tmp = t * (18.0 * (z * (x * y)));
	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]}, If[LessEqual[x, -4.7e+24], N[(y * N[(N[(x * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.4e-244], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+28], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+136], N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+165], N[(t * N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -4.7e24

   1. Initial program 75.7%

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

   3. Simplified 80.3%

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

      1. associate-*r* 77.3%

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

      2. distribute-rgt-out-- 75.7%

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

      3. associate-*l* 77.3%

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

      4. fmm-def 77.3%

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

      5. associate-*l* 77.3%

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

      6. associate-*l* 78.6%

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

   6. Applied egg-rr 78.6%

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

      1. fmm-undef 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*l* 78.6%

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

      4. *-commutative 78.6%

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

      5. cancel-sign-sub-inv 78.6%

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

      6. metadata-eval 78.6%

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

      7. fma-undefine 78.6%

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

      8. associate-*r* 78.6%

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

      9. *-commutative 78.6%

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

      10. associate-*r* 78.6%

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

   8. Simplified 78.6%

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

   9. Taylor expanded in x around 0 72.4%

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

       1. associate-*r* 72.4%

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

       2. *-commutative 72.4%

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

   11. Simplified 72.4%

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

   12. Taylor expanded in t around inf 66.4%

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

   13. Taylor expanded in x around inf 50.0%

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

       1. associate-*r* 49.9%

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

       2. *-commutative 49.9%

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

       3. associate-*r* 50.0%

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

       4. associate-*l* 53.0%

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

       5. associate-*r* 52.9%

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

       6. *-commutative 52.9%

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

       7. *-commutative 52.9%

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

       8. *-commutative 52.9%

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

       9. associate-*l* 53.0%

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

   15. Simplified 53.0%

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

   if -4.7e24 < x < -3.40000000000000009e-244

   1. Initial program 90.0%

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

   3. Taylor expanded in t around 0 73.2%

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

   4. Taylor expanded in i around 0 60.8%

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

   if -3.40000000000000009e-244 < x < 1.6e28

   1. Initial program 96.4%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in a around inf 64.3%

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

   if 1.6e28 < x < 2.7000000000000002e136

   1. Initial program 89.4%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in i around inf 69.6%

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

      1. *-commutative 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-*l* 69.6%

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

      4. *-commutative 69.6%

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

   7. Simplified 69.6%

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

   if 2.7000000000000002e136 < x < 1.70000000000000005e165

   1. Initial program 90.7%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around inf 80.7%

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

   9. Taylor expanded in x around inf 71.0%

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

       1. associate-*r* 61.7%

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

       2. *-commutative 61.7%

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

   11. Simplified 61.7%

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

   if 1.70000000000000005e165 < x

   1. Initial program 64.4%

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

   3. Taylor expanded in t around 0 58.7%

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

   4. Taylor expanded in j around 0 65.8%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-244}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+28}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+136}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -1.5 \cdot 10^{+129}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -2.15 \cdot 10^{-80}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq 9 \cdot 10^{+82}:\\ \;\;\;\;t\_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t\_1\\ \end{array} \end{array} \]

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 (* k -27.0))))
   (if (<= (* b c) -1.5e+129)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= (* b c) -2.15e-80)
       (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
       (if (<= (* b c) 9e+82) (+ t_1 (* x (* i -4.0))) (+ (* b c) 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 * (k * -27.0);
	double tmp;
	if ((b * c) <= -1.5e+129) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -2.15e-80) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if ((b * c) <= 9e+82) {
		tmp = t_1 + (x * (i * -4.0));
	} else {
		tmp = (b * c) + 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 * (k * (-27.0d0))
    if ((b * c) <= (-1.5d+129)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if ((b * c) <= (-2.15d-80)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if ((b * c) <= 9d+82) then
        tmp = t_1 + (x * (i * (-4.0d0)))
    else
        tmp = (b * c) + 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 * (k * -27.0);
	double tmp;
	if ((b * c) <= -1.5e+129) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -2.15e-80) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if ((b * c) <= 9e+82) {
		tmp = t_1 + (x * (i * -4.0));
	} else {
		tmp = (b * c) + 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 * (k * -27.0)
	tmp = 0
	if (b * c) <= -1.5e+129:
		tmp = (b * c) - (4.0 * (x * i))
	elif (b * c) <= -2.15e-80:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif (b * c) <= 9e+82:
		tmp = t_1 + (x * (i * -4.0))
	else:
		tmp = (b * c) + 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(j * Float64(k * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -1.5e+129)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= -2.15e-80)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (Float64(b * c) <= 9e+82)
		tmp = Float64(t_1 + Float64(x * Float64(i * -4.0)));
	else
		tmp = Float64(Float64(b * c) + 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 * (k * -27.0);
	tmp = 0.0;
	if ((b * c) <= -1.5e+129)
		tmp = (b * c) - (4.0 * (x * i));
	elseif ((b * c) <= -2.15e-80)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif ((b * c) <= 9e+82)
		tmp = t_1 + (x * (i * -4.0));
	else
		tmp = (b * c) + 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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.5e+129], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.15e-80], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 9e+82], N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.50000000000000015e129

   1. Initial program 86.9%

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

   3. Taylor expanded in t around 0 70.9%

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

   4. Taylor expanded in j around 0 66.7%

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

   if -1.50000000000000015e129 < (*.f64 b c) < -2.1500000000000001e-80

   1. Initial program 84.0%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around inf 83.5%

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

      1. associate-*r* 83.5%

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

      2. *-commutative 83.5%

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

   7. Simplified 83.5%

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

   8. Taylor expanded in t around inf 70.9%

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

   if -2.1500000000000001e-80 < (*.f64 b c) < 8.9999999999999993e82

   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 86.5%

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

   5. Taylor expanded in i around inf 56.9%

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

      1. *-commutative 56.9%

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

      2. *-commutative 56.9%

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

      3. associate-*l* 56.9%

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

      4. *-commutative 56.9%

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

   7. Simplified 56.9%

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

   if 8.9999999999999993e82 < (*.f64 b c)

   1. Initial program 80.9%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in b around inf 57.1%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.5 \cdot 10^{+129}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -2.15 \cdot 10^{-80}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;b \cdot c \leq 9 \cdot 10^{+82}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.95 \cdot 10^{-57}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{+143} \lor \neg \left(k \leq 1.22 \cdot 10^{+238}\right) \land k \leq 2 \cdot 10^{+268}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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 (<= k -1.95e-57)
   (* k (* j -27.0))
   (if (or (<= k 2.2e+143) (and (not (<= k 1.22e+238)) (<= k 2e+268)))
     (* 18.0 (* t (* x (* y z))))
     (* -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 (k <= -1.95e-57) {
		tmp = k * (j * -27.0);
	} else if ((k <= 2.2e+143) || (!(k <= 1.22e+238) && (k <= 2e+268))) {
		tmp = 18.0 * (t * (x * (y * z)));
	} 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 (k <= (-1.95d-57)) then
        tmp = k * (j * (-27.0d0))
    else if ((k <= 2.2d+143) .or. (.not. (k <= 1.22d+238)) .and. (k <= 2d+268)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    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 (k <= -1.95e-57) {
		tmp = k * (j * -27.0);
	} else if ((k <= 2.2e+143) || (!(k <= 1.22e+238) && (k <= 2e+268))) {
		tmp = 18.0 * (t * (x * (y * z)));
	} 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 k <= -1.95e-57:
		tmp = k * (j * -27.0)
	elif (k <= 2.2e+143) or (not (k <= 1.22e+238) and (k <= 2e+268)):
		tmp = 18.0 * (t * (x * (y * z)))
	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 (k <= -1.95e-57)
		tmp = Float64(k * Float64(j * -27.0));
	elseif ((k <= 2.2e+143) || (!(k <= 1.22e+238) && (k <= 2e+268)))
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	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 (k <= -1.95e-57)
		tmp = k * (j * -27.0);
	elseif ((k <= 2.2e+143) || (~((k <= 1.22e+238)) && (k <= 2e+268)))
		tmp = 18.0 * (t * (x * (y * z)));
	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[LessEqual[k, -1.95e-57], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[k, 2.2e+143], And[N[Not[LessEqual[k, 1.22e+238]], $MachinePrecision], LessEqual[k, 2e+268]]], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -1.95000000000000003e-57

   1. Initial program 74.6%

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

   3. Simplified 78.2%

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

      1. associate-*r* 77.0%

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

      2. distribute-rgt-out-- 75.7%

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

      3. associate-*l* 72.0%

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

      4. fmm-def 72.0%

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

      5. associate-*l* 72.1%

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

      6. associate-*l* 73.3%

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

   6. Applied egg-rr 73.3%

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

      1. fmm-undef 73.3%

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

      2. *-commutative 73.3%

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

      3. associate-*l* 73.3%

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

      4. *-commutative 73.3%

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

      5. cancel-sign-sub-inv 73.3%

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

      6. metadata-eval 73.3%

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

      7. fma-undefine 73.3%

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

      8. associate-*r* 73.3%

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

      9. *-commutative 73.3%

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

      10. associate-*r* 73.3%

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

   8. Simplified 73.3%

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

   9. Taylor expanded in x around 0 68.4%

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

       1. associate-*r* 67.2%

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

       2. *-commutative 67.2%

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

   11. Simplified 67.2%

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

   12. Taylor expanded in j around inf 33.5%

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

       1. associate-*r* 32.4%

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

       2. *-commutative 32.4%

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

       3. *-commutative 32.4%

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

   14. Simplified 32.4%

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

   if -1.95000000000000003e-57 < k < 2.20000000000000014e143 or 1.2200000000000001e238 < k < 1.9999999999999999e268

   1. Initial program 91.4%

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

   3. Simplified 90.0%

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

      1. associate-*r* 91.4%

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

      2. distribute-rgt-out-- 91.4%

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

      3. associate-*l* 90.7%

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

      4. fmm-def 90.7%

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

      5. associate-*l* 90.0%

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

      6. associate-*l* 90.6%

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

   6. Applied egg-rr 90.6%

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

      1. fmm-undef 90.6%

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

      2. *-commutative 90.6%

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

      3. associate-*l* 90.6%

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

      4. *-commutative 90.6%

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

      5. cancel-sign-sub-inv 90.6%

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

      6. metadata-eval 90.6%

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

      7. fma-undefine 90.6%

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

      8. associate-*r* 91.2%

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

      9. *-commutative 91.2%

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

      10. associate-*r* 91.3%

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

   8. Simplified 91.3%

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

   9. Taylor expanded in x around 0 73.4%

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

       1. associate-*r* 73.4%

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

       2. *-commutative 73.4%

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

   11. Simplified 73.4%

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

   12. Taylor expanded in x around inf 33.4%

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

   if 2.20000000000000014e143 < k < 1.2200000000000001e238 or 1.9999999999999999e268 < k

   1. Initial program 87.0%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in j around inf 68.2%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.95 \cdot 10^{-57}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{+143} \lor \neg \left(k \leq 1.22 \cdot 10^{+238}\right) \land k \leq 2 \cdot 10^{+268}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 33.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.95 \cdot 10^{-57}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.75 \cdot 10^{+143} \lor \neg \left(k \leq 2.9 \cdot 10^{+238}\right) \land k \leq 6.5 \cdot 10^{+266}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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 (<= k -1.95e-57)
   (* k (* j -27.0))
   (if (or (<= k 1.75e+143) (and (not (<= k 2.9e+238)) (<= k 6.5e+266)))
     (* 18.0 (* t (* y (* x z))))
     (* -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 (k <= -1.95e-57) {
		tmp = k * (j * -27.0);
	} else if ((k <= 1.75e+143) || (!(k <= 2.9e+238) && (k <= 6.5e+266))) {
		tmp = 18.0 * (t * (y * (x * z)));
	} 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 (k <= (-1.95d-57)) then
        tmp = k * (j * (-27.0d0))
    else if ((k <= 1.75d+143) .or. (.not. (k <= 2.9d+238)) .and. (k <= 6.5d+266)) then
        tmp = 18.0d0 * (t * (y * (x * z)))
    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 (k <= -1.95e-57) {
		tmp = k * (j * -27.0);
	} else if ((k <= 1.75e+143) || (!(k <= 2.9e+238) && (k <= 6.5e+266))) {
		tmp = 18.0 * (t * (y * (x * z)));
	} 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 k <= -1.95e-57:
		tmp = k * (j * -27.0)
	elif (k <= 1.75e+143) or (not (k <= 2.9e+238) and (k <= 6.5e+266)):
		tmp = 18.0 * (t * (y * (x * z)))
	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 (k <= -1.95e-57)
		tmp = Float64(k * Float64(j * -27.0));
	elseif ((k <= 1.75e+143) || (!(k <= 2.9e+238) && (k <= 6.5e+266)))
		tmp = Float64(18.0 * Float64(t * Float64(y * Float64(x * z))));
	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 (k <= -1.95e-57)
		tmp = k * (j * -27.0);
	elseif ((k <= 1.75e+143) || (~((k <= 2.9e+238)) && (k <= 6.5e+266)))
		tmp = 18.0 * (t * (y * (x * z)));
	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[LessEqual[k, -1.95e-57], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[k, 1.75e+143], And[N[Not[LessEqual[k, 2.9e+238]], $MachinePrecision], LessEqual[k, 6.5e+266]]], N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -1.95000000000000003e-57

   1. Initial program 74.6%

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

   3. Simplified 78.2%

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

      1. associate-*r* 77.0%

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

      2. distribute-rgt-out-- 75.7%

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

      3. associate-*l* 72.0%

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

      4. fmm-def 72.0%

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

      5. associate-*l* 72.1%

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

      6. associate-*l* 73.3%

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

   6. Applied egg-rr 73.3%

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

      1. fmm-undef 73.3%

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

      2. *-commutative 73.3%

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

      3. associate-*l* 73.3%

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

      4. *-commutative 73.3%

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

      5. cancel-sign-sub-inv 73.3%

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

      6. metadata-eval 73.3%

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

      7. fma-undefine 73.3%

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

      8. associate-*r* 73.3%

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

      9. *-commutative 73.3%

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

      10. associate-*r* 73.3%

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

   8. Simplified 73.3%

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

   9. Taylor expanded in x around 0 68.4%

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

       1. associate-*r* 67.2%

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

       2. *-commutative 67.2%

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

   11. Simplified 67.2%

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

   12. Taylor expanded in j around inf 33.5%

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

       1. associate-*r* 32.4%

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

       2. *-commutative 32.4%

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

       3. *-commutative 32.4%

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

   14. Simplified 32.4%

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

   if -1.95000000000000003e-57 < k < 1.75000000000000004e143 or 2.9000000000000002e238 < k < 6.50000000000000006e266

   1. Initial program 91.4%

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

   3. Simplified 90.0%

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

      1. associate-*r* 91.4%

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

      2. distribute-rgt-out-- 91.4%

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

      3. associate-*l* 90.7%

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

      4. fmm-def 90.7%

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

      5. associate-*l* 90.0%

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

      6. associate-*l* 90.6%

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

   6. Applied egg-rr 90.6%

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

      1. fmm-undef 90.6%

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

      2. *-commutative 90.6%

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

      3. associate-*l* 90.6%

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

      4. *-commutative 90.6%

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

      5. cancel-sign-sub-inv 90.6%

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

      6. metadata-eval 90.6%

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

      7. fma-undefine 90.6%

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

      8. associate-*r* 91.2%

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

      9. *-commutative 91.2%

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

      10. associate-*r* 91.3%

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

   8. Simplified 91.3%

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

   9. Taylor expanded in x around 0 73.4%

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

       1. associate-*r* 73.4%

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

       2. *-commutative 73.4%

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

   11. Simplified 73.4%

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

   12. Taylor expanded in x around inf 33.4%

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

       1. pow1 33.4%

          \[\leadsto 18 \cdot \color{blue}{{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}^{1}} \]

       2. associate-*r* 31.4%

          \[\leadsto 18 \cdot {\color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)}}^{1} \]

   14. Applied egg-rr 31.4%

       \[\leadsto 18 \cdot \color{blue}{{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)}^{1}} \]
   15. Step-by-step derivation

       1. unpow1 31.4%

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

       2. associate-*r* 33.4%

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

       3. *-commutative 33.4%

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

       4. associate-*l* 36.5%

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

       5. *-commutative 36.5%

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

   16. Simplified 36.5%

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

   if 1.75000000000000004e143 < k < 2.9000000000000002e238 or 6.50000000000000006e266 < k

   1. Initial program 87.0%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in j around inf 68.2%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.95 \cdot 10^{-57}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.75 \cdot 10^{+143} \lor \neg \left(k \leq 2.9 \cdot 10^{+238}\right) \land k \leq 6.5 \cdot 10^{+266}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 33.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.85 \cdot 10^{-57}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.2 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{+235} \lor \neg \left(k \leq 6.5 \cdot 10^{+266}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= k -1.85e-57)
   (* k (* j -27.0))
   (if (<= k 1.2e+143)
     (* t (* 18.0 (* z (* x y))))
     (if (or (<= k 9.5e+235) (not (<= k 6.5e+266)))
       (* -27.0 (* j k))
       (* 18.0 (* t (* y (* x z))))))))

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 (k <= -1.85e-57) {
		tmp = k * (j * -27.0);
	} else if (k <= 1.2e+143) {
		tmp = t * (18.0 * (z * (x * y)));
	} else if ((k <= 9.5e+235) || !(k <= 6.5e+266)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = 18.0 * (t * (y * (x * z)));
	}
	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 (k <= (-1.85d-57)) then
        tmp = k * (j * (-27.0d0))
    else if (k <= 1.2d+143) then
        tmp = t * (18.0d0 * (z * (x * y)))
    else if ((k <= 9.5d+235) .or. (.not. (k <= 6.5d+266))) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = 18.0d0 * (t * (y * (x * z)))
    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 (k <= -1.85e-57) {
		tmp = k * (j * -27.0);
	} else if (k <= 1.2e+143) {
		tmp = t * (18.0 * (z * (x * y)));
	} else if ((k <= 9.5e+235) || !(k <= 6.5e+266)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = 18.0 * (t * (y * (x * z)));
	}
	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 k <= -1.85e-57:
		tmp = k * (j * -27.0)
	elif k <= 1.2e+143:
		tmp = t * (18.0 * (z * (x * y)))
	elif (k <= 9.5e+235) or not (k <= 6.5e+266):
		tmp = -27.0 * (j * k)
	else:
		tmp = 18.0 * (t * (y * (x * z)))
	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 (k <= -1.85e-57)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (k <= 1.2e+143)
		tmp = Float64(t * Float64(18.0 * Float64(z * Float64(x * y))));
	elseif ((k <= 9.5e+235) || !(k <= 6.5e+266))
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(18.0 * Float64(t * Float64(y * Float64(x * z))));
	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 (k <= -1.85e-57)
		tmp = k * (j * -27.0);
	elseif (k <= 1.2e+143)
		tmp = t * (18.0 * (z * (x * y)));
	elseif ((k <= 9.5e+235) || ~((k <= 6.5e+266)))
		tmp = -27.0 * (j * k);
	else
		tmp = 18.0 * (t * (y * (x * z)));
	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[k, -1.85e-57], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.2e+143], N[(t * N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[k, 9.5e+235], N[Not[LessEqual[k, 6.5e+266]], $MachinePrecision]], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -1.85e-57

   1. Initial program 74.6%

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

   3. Simplified 78.2%

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

      1. associate-*r* 77.0%

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

      2. distribute-rgt-out-- 75.7%

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

      3. associate-*l* 72.0%

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

      4. fmm-def 72.0%

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

      5. associate-*l* 72.1%

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

      6. associate-*l* 73.3%

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

   6. Applied egg-rr 73.3%

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

      1. fmm-undef 73.3%

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

      2. *-commutative 73.3%

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

      3. associate-*l* 73.3%

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

      4. *-commutative 73.3%

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

      5. cancel-sign-sub-inv 73.3%

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

      6. metadata-eval 73.3%

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

      7. fma-undefine 73.3%

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

      8. associate-*r* 73.3%

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

      9. *-commutative 73.3%

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

      10. associate-*r* 73.3%

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

   8. Simplified 73.3%

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

   9. Taylor expanded in x around 0 68.4%

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

       1. associate-*r* 67.2%

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

       2. *-commutative 67.2%

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

   11. Simplified 67.2%

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

   12. Taylor expanded in j around inf 33.5%

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

       1. associate-*r* 32.4%

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

       2. *-commutative 32.4%

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

       3. *-commutative 32.4%

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

   14. Simplified 32.4%

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

   if -1.85e-57 < k < 1.1999999999999999e143

   1. Initial program 91.7%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in x around inf 81.8%

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

      1. associate-*r* 81.8%

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

      2. *-commutative 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in t around inf 50.0%

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

   9. Taylor expanded in x around inf 32.2%

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

       1. associate-*r* 33.6%

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

       2. *-commutative 33.6%

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

   11. Simplified 33.6%

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

   if 1.1999999999999999e143 < k < 9.49999999999999966e235 or 6.50000000000000006e266 < k

   1. Initial program 87.0%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in j around inf 68.2%

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

   if 9.49999999999999966e235 < k < 6.50000000000000006e266

   1. Initial program 85.7%

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

   3. Simplified 85.7%

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

      1. associate-*r* 85.7%

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

      2. distribute-rgt-out-- 85.7%

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

      3. associate-*l* 85.7%

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

      4. fmm-def 85.7%

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

      5. associate-*l* 85.7%

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

      6. associate-*l* 85.7%

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

   6. Applied egg-rr 85.7%

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

      1. fmm-undef 85.7%

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

      2. *-commutative 85.7%

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

      3. associate-*l* 85.7%

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

      4. *-commutative 85.7%

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

      5. cancel-sign-sub-inv 85.7%

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

      6. metadata-eval 85.7%

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

      7. fma-undefine 85.7%

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

      8. associate-*r* 85.7%

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

      9. *-commutative 85.7%

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

      10. associate-*r* 85.7%

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

   8. Simplified 85.7%

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

   9. Taylor expanded in x around 0 85.7%

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

       1. associate-*r* 85.7%

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

       2. *-commutative 85.7%

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

   11. Simplified 85.7%

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

   12. Taylor expanded in x around inf 58.1%

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

       1. pow1 58.1%

          \[\leadsto 18 \cdot \color{blue}{{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}^{1}} \]

       2. associate-*r* 43.8%

          \[\leadsto 18 \cdot {\color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)}}^{1} \]

   14. Applied egg-rr 43.8%

       \[\leadsto 18 \cdot \color{blue}{{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)}^{1}} \]
   15. Step-by-step derivation

       1. unpow1 43.8%

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

       2. associate-*r* 58.1%

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

       3. *-commutative 58.1%

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

       4. associate-*l* 71.9%

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

       5. *-commutative 71.9%

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

   16. Simplified 71.9%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.85 \cdot 10^{-57}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.2 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{+235} \lor \neg \left(k \leq 6.5 \cdot 10^{+266}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-42}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a)))))
   (if (<= z -9.2e-119)
     (* t (* 18.0 (* z (* x y))))
     (if (<= z 1.25e-100)
       t_1
       (if (<= z 1e-42)
         (* k (* j -27.0))
         (if (<= z 4.5e+85) t_1 (* y (* (* x z) (* 18.0 t)))))))))

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 * (t * a));
	double tmp;
	if (z <= -9.2e-119) {
		tmp = t * (18.0 * (z * (x * y)));
	} else if (z <= 1.25e-100) {
		tmp = t_1;
	} else if (z <= 1e-42) {
		tmp = k * (j * -27.0);
	} else if (z <= 4.5e+85) {
		tmp = t_1;
	} else {
		tmp = y * ((x * z) * (18.0 * t));
	}
	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) + ((-4.0d0) * (t * a))
    if (z <= (-9.2d-119)) then
        tmp = t * (18.0d0 * (z * (x * y)))
    else if (z <= 1.25d-100) then
        tmp = t_1
    else if (z <= 1d-42) then
        tmp = k * (j * (-27.0d0))
    else if (z <= 4.5d+85) then
        tmp = t_1
    else
        tmp = y * ((x * z) * (18.0d0 * t))
    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 * (t * a));
	double tmp;
	if (z <= -9.2e-119) {
		tmp = t * (18.0 * (z * (x * y)));
	} else if (z <= 1.25e-100) {
		tmp = t_1;
	} else if (z <= 1e-42) {
		tmp = k * (j * -27.0);
	} else if (z <= 4.5e+85) {
		tmp = t_1;
	} else {
		tmp = y * ((x * z) * (18.0 * t));
	}
	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 * (t * a))
	tmp = 0
	if z <= -9.2e-119:
		tmp = t * (18.0 * (z * (x * y)))
	elif z <= 1.25e-100:
		tmp = t_1
	elif z <= 1e-42:
		tmp = k * (j * -27.0)
	elif z <= 4.5e+85:
		tmp = t_1
	else:
		tmp = y * ((x * z) * (18.0 * t))
	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(t * a)))
	tmp = 0.0
	if (z <= -9.2e-119)
		tmp = Float64(t * Float64(18.0 * Float64(z * Float64(x * y))));
	elseif (z <= 1.25e-100)
		tmp = t_1;
	elseif (z <= 1e-42)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (z <= 4.5e+85)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(x * z) * Float64(18.0 * t)));
	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 * (t * a));
	tmp = 0.0;
	if (z <= -9.2e-119)
		tmp = t * (18.0 * (z * (x * y)));
	elseif (z <= 1.25e-100)
		tmp = t_1;
	elseif (z <= 1e-42)
		tmp = k * (j * -27.0);
	elseif (z <= 4.5e+85)
		tmp = t_1;
	else
		tmp = y * ((x * z) * (18.0 * t));
	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[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e-119], N[(t * N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-100], t$95$1, If[LessEqual[z, 1e-42], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+85], t$95$1, N[(y * N[(N[(x * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.19999999999999973e-119

   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 87.4%

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

   5. Taylor expanded in x around inf 69.1%

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

      1. associate-*r* 69.1%

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

      2. *-commutative 69.1%

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

   7. Simplified 69.1%

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

   8. Taylor expanded in t around inf 47.6%

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

   9. Taylor expanded in x around inf 33.5%

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

       1. associate-*r* 34.4%

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

       2. *-commutative 34.4%

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

   11. Simplified 34.4%

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

   if -9.19999999999999973e-119 < z < 1.25e-100 or 1.00000000000000004e-42 < z < 4.50000000000000007e85

   1. Initial program 83.3%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in x around inf 70.7%

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

      1. associate-*r* 70.7%

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

      2. *-commutative 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in x around 0 43.6%

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

   if 1.25e-100 < z < 1.00000000000000004e-42

   1. Initial program 92.1%

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

   3. Simplified 92.3%

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

      1. associate-*r* 92.2%

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

      2. distribute-rgt-out-- 92.1%

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

      3. associate-*l* 92.2%

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

      4. fmm-def 92.2%

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

      5. associate-*l* 92.2%

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

      6. associate-*l* 92.2%

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

   6. Applied egg-rr 92.2%

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

      1. fmm-undef 92.2%

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

      2. *-commutative 92.2%

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

      3. associate-*l* 92.2%

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

      4. *-commutative 92.2%

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

      5. cancel-sign-sub-inv 92.2%

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

      6. metadata-eval 92.2%

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

      7. fma-undefine 92.2%

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

      8. associate-*r* 92.2%

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

      9. *-commutative 92.2%

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

      10. associate-*r* 92.3%

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

   8. Simplified 92.3%

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

   9. Taylor expanded in x around 0 84.5%

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

       1. associate-*r* 84.6%

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

       2. *-commutative 84.6%

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

   11. Simplified 84.6%

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

   12. Taylor expanded in j around inf 40.0%

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

       1. associate-*r* 40.1%

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

       2. *-commutative 40.1%

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

       3. *-commutative 40.1%

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

   14. Simplified 40.1%

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

   if 4.50000000000000007e85 < z

   1. Initial program 77.1%

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

   3. Simplified 76.6%

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

      1. associate-*r* 77.1%

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

      2. distribute-rgt-out-- 77.1%

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

      3. associate-*l* 76.8%

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

      4. fmm-def 76.8%

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

      5. associate-*l* 76.8%

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

      6. associate-*l* 74.7%

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

   6. Applied egg-rr 74.7%

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

      1. fmm-undef 74.7%

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

      2. *-commutative 74.7%

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

      3. associate-*l* 76.8%

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

      4. *-commutative 76.8%

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

      5. cancel-sign-sub-inv 76.8%

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

      6. metadata-eval 76.8%

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

      7. fma-undefine 76.8%

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

      8. associate-*r* 76.8%

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

      9. *-commutative 76.8%

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

      10. associate-*r* 76.8%

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

   8. Simplified 76.8%

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

   9. Taylor expanded in x around 0 72.2%

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

       1. associate-*r* 72.2%

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

       2. *-commutative 72.2%

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

   11. Simplified 72.2%

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

   12. Taylor expanded in t around inf 69.9%

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

   13. Taylor expanded in x around inf 52.2%

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

       1. associate-*r* 54.2%

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

       2. *-commutative 54.2%

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

       3. associate-*r* 58.3%

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

       4. associate-*l* 57.6%

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

       5. associate-*r* 57.6%

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

       6. *-commutative 57.6%

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

       7. *-commutative 57.6%

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

       8. *-commutative 57.6%

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

       9. associate-*l* 57.6%

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

   15. Simplified 57.6%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-100}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 10^{-42}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+85}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 46.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-268}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

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 (+ (* b c) (* j (* k -27.0)))))
   (if (<= x -2.8e+24)
     (* y (* (* x z) (* 18.0 t)))
     (if (<= x -3.5e-291)
       t_1
       (if (<= x 4.7e-268)
         (+ (* b c) (* -4.0 (* t a)))
         (if (<= x 2.8e+15) t_1 (* -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 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (x <= -2.8e+24) {
		tmp = y * ((x * z) * (18.0 * t));
	} else if (x <= -3.5e-291) {
		tmp = t_1;
	} else if (x <= 4.7e-268) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 2.8e+15) {
		tmp = t_1;
	} else {
		tmp = -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) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    if (x <= (-2.8d+24)) then
        tmp = y * ((x * z) * (18.0d0 * t))
    else if (x <= (-3.5d-291)) then
        tmp = t_1
    else if (x <= 4.7d-268) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (x <= 2.8d+15) then
        tmp = t_1
    else
        tmp = (-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 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (x <= -2.8e+24) {
		tmp = y * ((x * z) * (18.0 * t));
	} else if (x <= -3.5e-291) {
		tmp = t_1;
	} else if (x <= 4.7e-268) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 2.8e+15) {
		tmp = t_1;
	} else {
		tmp = -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 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if x <= -2.8e+24:
		tmp = y * ((x * z) * (18.0 * t))
	elif x <= -3.5e-291:
		tmp = t_1
	elif x <= 4.7e-268:
		tmp = (b * c) + (-4.0 * (t * a))
	elif x <= 2.8e+15:
		tmp = t_1
	else:
		tmp = -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(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (x <= -2.8e+24)
		tmp = Float64(y * Float64(Float64(x * z) * Float64(18.0 * t)));
	elseif (x <= -3.5e-291)
		tmp = t_1;
	elseif (x <= 4.7e-268)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 2.8e+15)
		tmp = t_1;
	else
		tmp = 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 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (x <= -2.8e+24)
		tmp = y * ((x * z) * (18.0 * t));
	elseif (x <= -3.5e-291)
		tmp = t_1;
	elseif (x <= 4.7e-268)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (x <= 2.8e+15)
		tmp = t_1;
	else
		tmp = -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[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+24], N[(y * N[(N[(x * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.5e-291], t$95$1, If[LessEqual[x, 4.7e-268], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+15], t$95$1, N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.8000000000000002e24

   1. Initial program 75.7%

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

   3. Simplified 80.3%

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

      1. associate-*r* 77.3%

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

      2. distribute-rgt-out-- 75.7%

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

      3. associate-*l* 77.3%

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

      4. fmm-def 77.3%

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

      5. associate-*l* 77.3%

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

      6. associate-*l* 78.6%

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

   6. Applied egg-rr 78.6%

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

      1. fmm-undef 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*l* 78.6%

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

      4. *-commutative 78.6%

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

      5. cancel-sign-sub-inv 78.6%

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

      6. metadata-eval 78.6%

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

      7. fma-undefine 78.6%

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

      8. associate-*r* 78.6%

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

      9. *-commutative 78.6%

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

      10. associate-*r* 78.6%

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

   8. Simplified 78.6%

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

   9. Taylor expanded in x around 0 72.4%

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

       1. associate-*r* 72.4%

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

       2. *-commutative 72.4%

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

   11. Simplified 72.4%

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

   12. Taylor expanded in t around inf 66.4%

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

   13. Taylor expanded in x around inf 50.0%

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

       1. associate-*r* 49.9%

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

       2. *-commutative 49.9%

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

       3. associate-*r* 50.0%

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

       4. associate-*l* 53.0%

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

       5. associate-*r* 52.9%

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

       6. *-commutative 52.9%

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

       7. *-commutative 52.9%

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

       8. *-commutative 52.9%

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

       9. associate-*l* 53.0%

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

   15. Simplified 53.0%

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

   if -2.8000000000000002e24 < x < -3.49999999999999996e-291 or 4.69999999999999973e-268 < x < 2.8e15

   1. Initial program 94.1%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in b around inf 56.9%

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

   if -3.49999999999999996e-291 < x < 4.69999999999999973e-268

   1. Initial program 94.0%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in x around inf 82.4%

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

      1. associate-*r* 82.4%

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

      2. *-commutative 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in x around 0 71.6%

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

   if 2.8e15 < x

   1. Initial program 78.1%

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

   3. Simplified 83.0%

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

      1. associate-*r* 78.1%

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

      2. distribute-rgt-out-- 78.1%

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

      3. associate-*l* 78.2%

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

      4. fmm-def 78.2%

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

      5. associate-*l* 78.2%

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

      6. associate-*l* 79.9%

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

   6. Applied egg-rr 79.9%

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

      1. fmm-undef 79.9%

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

      2. *-commutative 79.9%

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

      3. associate-*l* 79.9%

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

      4. *-commutative 79.9%

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

      5. cancel-sign-sub-inv 79.9%

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

      6. metadata-eval 79.9%

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

      7. fma-undefine 79.9%

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

      8. associate-*r* 79.9%

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

      9. *-commutative 79.9%

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

      10. associate-*r* 79.9%

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

   8. Simplified 79.9%

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

   9. Taylor expanded in i around inf 47.2%

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

       1. *-commutative 47.2%

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

   11. Simplified 47.2%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-291}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-268}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+15}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-267}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

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 (+ (* b c) (* j (* k -27.0)))))
   (if (<= x -2e+24)
     (* y (* (* x z) (* 18.0 t)))
     (if (<= x -2e-293)
       t_1
       (if (<= x 3.3e-267)
         (+ (* b c) (* -4.0 (* t a)))
         (if (<= x 1.55e-9) t_1 (- (* 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 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (x <= -2e+24) {
		tmp = y * ((x * z) * (18.0 * t));
	} else if (x <= -2e-293) {
		tmp = t_1;
	} else if (x <= 3.3e-267) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 1.55e-9) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    if (x <= (-2d+24)) then
        tmp = y * ((x * z) * (18.0d0 * t))
    else if (x <= (-2d-293)) then
        tmp = t_1
    else if (x <= 3.3d-267) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (x <= 1.55d-9) then
        tmp = t_1
    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 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (x <= -2e+24) {
		tmp = y * ((x * z) * (18.0 * t));
	} else if (x <= -2e-293) {
		tmp = t_1;
	} else if (x <= 3.3e-267) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 1.55e-9) {
		tmp = t_1;
	} 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 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if x <= -2e+24:
		tmp = y * ((x * z) * (18.0 * t))
	elif x <= -2e-293:
		tmp = t_1
	elif x <= 3.3e-267:
		tmp = (b * c) + (-4.0 * (t * a))
	elif x <= 1.55e-9:
		tmp = t_1
	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(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (x <= -2e+24)
		tmp = Float64(y * Float64(Float64(x * z) * Float64(18.0 * t)));
	elseif (x <= -2e-293)
		tmp = t_1;
	elseif (x <= 3.3e-267)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 1.55e-9)
		tmp = t_1;
	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 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (x <= -2e+24)
		tmp = y * ((x * z) * (18.0 * t));
	elseif (x <= -2e-293)
		tmp = t_1;
	elseif (x <= 3.3e-267)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (x <= 1.55e-9)
		tmp = t_1;
	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[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+24], N[(y * N[(N[(x * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2e-293], t$95$1, If[LessEqual[x, 3.3e-267], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e-9], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2e24

   1. Initial program 75.7%

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

   3. Simplified 80.3%

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

      1. associate-*r* 77.3%

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

      2. distribute-rgt-out-- 75.7%

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

      3. associate-*l* 77.3%

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

      4. fmm-def 77.3%

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

      5. associate-*l* 77.3%

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

      6. associate-*l* 78.6%

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

   6. Applied egg-rr 78.6%

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

      1. fmm-undef 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*l* 78.6%

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

      4. *-commutative 78.6%

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

      5. cancel-sign-sub-inv 78.6%

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

      6. metadata-eval 78.6%

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

      7. fma-undefine 78.6%

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

      8. associate-*r* 78.6%

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

      9. *-commutative 78.6%

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

      10. associate-*r* 78.6%

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

   8. Simplified 78.6%

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

   9. Taylor expanded in x around 0 72.4%

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

       1. associate-*r* 72.4%

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

       2. *-commutative 72.4%

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

   11. Simplified 72.4%

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

   12. Taylor expanded in t around inf 66.4%

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

   13. Taylor expanded in x around inf 50.0%

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

       1. associate-*r* 49.9%

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

       2. *-commutative 49.9%

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

       3. associate-*r* 50.0%

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

       4. associate-*l* 53.0%

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

       5. associate-*r* 52.9%

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

       6. *-commutative 52.9%

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

       7. *-commutative 52.9%

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

       8. *-commutative 52.9%

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

       9. associate-*l* 53.0%

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

   15. Simplified 53.0%

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

   if -2e24 < x < -2.0000000000000001e-293 or 3.30000000000000004e-267 < x < 1.55000000000000002e-9

   1. Initial program 93.9%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in b around inf 58.0%

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

   if -2.0000000000000001e-293 < x < 3.30000000000000004e-267

   1. Initial program 94.0%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in x around inf 82.4%

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

      1. associate-*r* 82.4%

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

      2. *-commutative 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in x around 0 71.6%

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

   if 1.55000000000000002e-9 < x

   1. Initial program 79.5%

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

   3. Taylor expanded in t around 0 57.1%

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

   4. Taylor expanded in j around 0 52.5%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-293}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-267}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-9}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 49.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-268}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

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 (- (* b c) (* 27.0 (* j k)))))
   (if (<= x -9.5e+22)
     (* y (* (* x z) (* 18.0 t)))
     (if (<= x -1.3e-292)
       t_1
       (if (<= x 5e-268)
         (+ (* b c) (* -4.0 (* t a)))
         (if (<= x 1.02e-9) t_1 (- (* 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 = (b * c) - (27.0 * (j * k));
	double tmp;
	if (x <= -9.5e+22) {
		tmp = y * ((x * z) * (18.0 * t));
	} else if (x <= -1.3e-292) {
		tmp = t_1;
	} else if (x <= 5e-268) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 1.02e-9) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = (b * c) - (27.0d0 * (j * k))
    if (x <= (-9.5d+22)) then
        tmp = y * ((x * z) * (18.0d0 * t))
    else if (x <= (-1.3d-292)) then
        tmp = t_1
    else if (x <= 5d-268) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (x <= 1.02d-9) then
        tmp = t_1
    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 = (b * c) - (27.0 * (j * k));
	double tmp;
	if (x <= -9.5e+22) {
		tmp = y * ((x * z) * (18.0 * t));
	} else if (x <= -1.3e-292) {
		tmp = t_1;
	} else if (x <= 5e-268) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 1.02e-9) {
		tmp = t_1;
	} 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 = (b * c) - (27.0 * (j * k))
	tmp = 0
	if x <= -9.5e+22:
		tmp = y * ((x * z) * (18.0 * t))
	elif x <= -1.3e-292:
		tmp = t_1
	elif x <= 5e-268:
		tmp = (b * c) + (-4.0 * (t * a))
	elif x <= 1.02e-9:
		tmp = t_1
	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(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	tmp = 0.0
	if (x <= -9.5e+22)
		tmp = Float64(y * Float64(Float64(x * z) * Float64(18.0 * t)));
	elseif (x <= -1.3e-292)
		tmp = t_1;
	elseif (x <= 5e-268)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 1.02e-9)
		tmp = t_1;
	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 = (b * c) - (27.0 * (j * k));
	tmp = 0.0;
	if (x <= -9.5e+22)
		tmp = y * ((x * z) * (18.0 * t));
	elseif (x <= -1.3e-292)
		tmp = t_1;
	elseif (x <= 5e-268)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (x <= 1.02e-9)
		tmp = t_1;
	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[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.5e+22], N[(y * N[(N[(x * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.3e-292], t$95$1, If[LessEqual[x, 5e-268], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e-9], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.49999999999999937e22

   1. Initial program 75.7%

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

   3. Simplified 80.3%

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

      1. associate-*r* 77.3%

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

      2. distribute-rgt-out-- 75.7%

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

      3. associate-*l* 77.3%

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

      4. fmm-def 77.3%

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

      5. associate-*l* 77.3%

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

      6. associate-*l* 78.6%

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

   6. Applied egg-rr 78.6%

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

      1. fmm-undef 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*l* 78.6%

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

      4. *-commutative 78.6%

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

      5. cancel-sign-sub-inv 78.6%

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

      6. metadata-eval 78.6%

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

      7. fma-undefine 78.6%

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

      8. associate-*r* 78.6%

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

      9. *-commutative 78.6%

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

      10. associate-*r* 78.6%

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

   8. Simplified 78.6%

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

   9. Taylor expanded in x around 0 72.4%

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

       1. associate-*r* 72.4%

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

       2. *-commutative 72.4%

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

   11. Simplified 72.4%

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

   12. Taylor expanded in t around inf 66.4%

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

   13. Taylor expanded in x around inf 50.0%

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

       1. associate-*r* 49.9%

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

       2. *-commutative 49.9%

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

       3. associate-*r* 50.0%

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

       4. associate-*l* 53.0%

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

       5. associate-*r* 52.9%

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

       6. *-commutative 52.9%

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

       7. *-commutative 52.9%

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

       8. *-commutative 52.9%

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

       9. associate-*l* 53.0%

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

   15. Simplified 53.0%

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

   if -9.49999999999999937e22 < x < -1.30000000000000007e-292 or 4.9999999999999999e-268 < x < 1.01999999999999999e-9

   1. Initial program 93.9%

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

   3. Taylor expanded in t around 0 66.4%

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

   4. Taylor expanded in i around 0 58.0%

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

   if -1.30000000000000007e-292 < x < 4.9999999999999999e-268

   1. Initial program 94.0%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in x around inf 82.4%

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

      1. associate-*r* 82.4%

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

      2. *-commutative 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in x around 0 71.6%

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

   if 1.01999999999999999e-9 < x

   1. Initial program 79.5%

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

   3. Taylor expanded in t around 0 57.1%

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

   4. Taylor expanded in j around 0 52.5%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-292}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-268}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-9}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 56.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-243}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-100}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(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)))))
   (if (<= x -1.65e+14)
     t_1
     (if (<= x -3.2e-243)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= x 3.9e-100) (+ (* j (* k -27.0)) (* -4.0 (* t a))) 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 tmp;
	if (x <= -1.65e+14) {
		tmp = t_1;
	} else if (x <= -3.2e-243) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 3.9e-100) {
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a));
	} 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) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (x <= (-1.65d+14)) then
        tmp = t_1
    else if (x <= (-3.2d-243)) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (x <= 3.9d-100) then
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * (t * a))
    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 tmp;
	if (x <= -1.65e+14) {
		tmp = t_1;
	} else if (x <= -3.2e-243) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 3.9e-100) {
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a));
	} 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))
	tmp = 0
	if x <= -1.65e+14:
		tmp = t_1
	elif x <= -3.2e-243:
		tmp = (b * c) - (27.0 * (j * k))
	elif x <= 3.9e-100:
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a))
	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)))
	tmp = 0.0
	if (x <= -1.65e+14)
		tmp = t_1;
	elseif (x <= -3.2e-243)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (x <= 3.9e-100)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(t * a)));
	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));
	tmp = 0.0;
	if (x <= -1.65e+14)
		tmp = t_1;
	elseif (x <= -3.2e-243)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (x <= 3.9e-100)
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a));
	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]}, If[LessEqual[x, -1.65e+14], t$95$1, If[LessEqual[x, -3.2e-243], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.9e-100], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65e14 or 3.89999999999999977e-100 < x

   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 84.7%

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

   5. Taylor expanded in x around inf 67.9%

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

   if -1.65e14 < x < -3.1999999999999998e-243

   1. Initial program 89.4%

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

   3. Taylor expanded in t around 0 73.6%

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

   4. Taylor expanded in i around 0 64.7%

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

   if -3.1999999999999998e-243 < x < 3.89999999999999977e-100

   1. Initial program 95.0%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in a around inf 72.2%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-243}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-100}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -3.5 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3 \cdot 10^{+75}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-53}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))))
   (if (<= j -3.5e+204)
     t_1
     (if (<= j -3e+75) (* b c) (if (<= j 4.6e-53) (* -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 = -27.0 * (j * k);
	double tmp;
	if (j <= -3.5e+204) {
		tmp = t_1;
	} else if (j <= -3e+75) {
		tmp = b * c;
	} else if (j <= 4.6e-53) {
		tmp = -4.0 * (x * i);
	} 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) :: tmp
    t_1 = (-27.0d0) * (j * k)
    if (j <= (-3.5d+204)) then
        tmp = t_1
    else if (j <= (-3d+75)) then
        tmp = b * c
    else if (j <= 4.6d-53) then
        tmp = (-4.0d0) * (x * i)
    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 = -27.0 * (j * k);
	double tmp;
	if (j <= -3.5e+204) {
		tmp = t_1;
	} else if (j <= -3e+75) {
		tmp = b * c;
	} else if (j <= 4.6e-53) {
		tmp = -4.0 * (x * i);
	} 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 = -27.0 * (j * k)
	tmp = 0
	if j <= -3.5e+204:
		tmp = t_1
	elif j <= -3e+75:
		tmp = b * c
	elif j <= 4.6e-53:
		tmp = -4.0 * (x * i)
	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(-27.0 * Float64(j * k))
	tmp = 0.0
	if (j <= -3.5e+204)
		tmp = t_1;
	elseif (j <= -3e+75)
		tmp = Float64(b * c);
	elseif (j <= 4.6e-53)
		tmp = Float64(-4.0 * Float64(x * i));
	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 = -27.0 * (j * k);
	tmp = 0.0;
	if (j <= -3.5e+204)
		tmp = t_1;
	elseif (j <= -3e+75)
		tmp = b * c;
	elseif (j <= 4.6e-53)
		tmp = -4.0 * (x * i);
	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[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.5e+204], t$95$1, If[LessEqual[j, -3e+75], N[(b * c), $MachinePrecision], If[LessEqual[j, 4.6e-53], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.49999999999999989e204 or 4.6000000000000003e-53 < j

   1. Initial program 83.8%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in j around inf 42.9%

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

   if -3.49999999999999989e204 < j < -3e75

   1. Initial program 85.7%

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

   3. Simplified 85.7%

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

      1. associate-*r* 85.7%

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

      2. distribute-rgt-out-- 85.7%

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

      3. associate-*l* 81.2%

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

      4. fmm-def 81.2%

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

      5. associate-*l* 81.2%

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

      6. associate-*l* 81.2%

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

   6. Applied egg-rr 81.2%

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

      1. fmm-undef 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-*l* 81.2%

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

      4. *-commutative 81.2%

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

      5. cancel-sign-sub-inv 81.2%

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

      6. metadata-eval 81.2%

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

      7. fma-undefine 81.2%

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

      8. associate-*r* 81.2%

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

      9. *-commutative 81.2%

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

      10. associate-*r* 81.2%

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

   8. Simplified 81.2%

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

   9. Taylor expanded in b around inf 46.0%

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

   if -3e75 < j < 4.6000000000000003e-53

   1. Initial program 87.6%

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

   3. Simplified 87.5%

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

      1. associate-*r* 88.5%

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

      2. distribute-rgt-out-- 87.6%

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

      3. associate-*l* 86.6%

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

      4. fmm-def 86.6%

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

      5. associate-*l* 85.8%

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

      6. associate-*l* 87.4%

         \[\leadsto \left(\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\color{blue}{a \cdot \left(4 \cdot t\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 87.4%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -a \cdot \left(4 \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. fmm-undef 87.4%

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - a \cdot \left(4 \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 87.4%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot t\right) \cdot a}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 87.4%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{4 \cdot \left(t \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 87.4%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - 4 \cdot \color{blue}{\left(a \cdot t\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. cancel-sign-sub-inv 87.4%

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(-4\right) \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. metadata-eval 87.4%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. fma-undefine 87.4%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. associate-*r* 88.2%

         \[\leadsto \left(\mathsf{fma}\left(\color{blue}{\left(x \cdot 18\right) \cdot y}, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 88.2%

         \[\leadsto \left(\mathsf{fma}\left(\color{blue}{\left(18 \cdot x\right)} \cdot y, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. associate-*r* 88.2%

          \[\leadsto \left(\mathsf{fma}\left(\color{blue}{18 \cdot \left(x \cdot y\right)}, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 88.2%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(18 \cdot \left(x \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in i around inf 28.9%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 28.9%

          \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} \]

   11. Simplified 28.9%

       \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.5 \cdot 10^{+204}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -3 \cdot 10^{+75}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{-53}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -4.8 \cdot 10^{+204}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{+77}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-53}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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 (<= j -4.8e+204)
   (* k (* j -27.0))
   (if (<= j -6.6e+77)
     (* b c)
     (if (<= j 2.5e-53) (* -4.0 (* x i)) (* -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 (j <= -4.8e+204) {
		tmp = k * (j * -27.0);
	} else if (j <= -6.6e+77) {
		tmp = b * c;
	} else if (j <= 2.5e-53) {
		tmp = -4.0 * (x * i);
	} 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 (j <= (-4.8d+204)) then
        tmp = k * (j * (-27.0d0))
    else if (j <= (-6.6d+77)) then
        tmp = b * c
    else if (j <= 2.5d-53) then
        tmp = (-4.0d0) * (x * i)
    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 (j <= -4.8e+204) {
		tmp = k * (j * -27.0);
	} else if (j <= -6.6e+77) {
		tmp = b * c;
	} else if (j <= 2.5e-53) {
		tmp = -4.0 * (x * i);
	} 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 j <= -4.8e+204:
		tmp = k * (j * -27.0)
	elif j <= -6.6e+77:
		tmp = b * c
	elif j <= 2.5e-53:
		tmp = -4.0 * (x * i)
	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 (j <= -4.8e+204)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (j <= -6.6e+77)
		tmp = Float64(b * c);
	elseif (j <= 2.5e-53)
		tmp = Float64(-4.0 * Float64(x * i));
	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 (j <= -4.8e+204)
		tmp = k * (j * -27.0);
	elseif (j <= -6.6e+77)
		tmp = b * c;
	elseif (j <= 2.5e-53)
		tmp = -4.0 * (x * i);
	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[LessEqual[j, -4.8e+204], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.6e+77], N[(b * c), $MachinePrecision], If[LessEqual[j, 2.5e-53], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.7999999999999999e204

   1. Initial program 88.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 88.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 88.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 85.1%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. fmm-def 85.1%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 18\right) \cdot y, z \cdot t, -\left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*l* 85.1%

         \[\leadsto \left(\mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot y\right)}, z \cdot t, -\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. associate-*l* 85.1%

         \[\leadsto \left(\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\color{blue}{a \cdot \left(4 \cdot t\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 85.1%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -a \cdot \left(4 \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. fmm-undef 85.1%

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - a \cdot \left(4 \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 85.1%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot t\right) \cdot a}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 85.1%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{4 \cdot \left(t \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 85.1%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - 4 \cdot \color{blue}{\left(a \cdot t\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. cancel-sign-sub-inv 85.1%

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(-4\right) \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. metadata-eval 85.1%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. fma-undefine 85.1%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. associate-*r* 85.1%

         \[\leadsto \left(\mathsf{fma}\left(\color{blue}{\left(x \cdot 18\right) \cdot y}, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 85.1%

         \[\leadsto \left(\mathsf{fma}\left(\color{blue}{\left(18 \cdot x\right)} \cdot y, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. associate-*r* 85.2%

          \[\leadsto \left(\mathsf{fma}\left(\color{blue}{18 \cdot \left(x \cdot y\right)}, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 85.2%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(18 \cdot \left(x \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in x around 0 81.7%

      \[\leadsto \left(\mathsf{fma}\left(18 \cdot \left(x \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 81.7%

          \[\leadsto \left(\mathsf{fma}\left(18 \cdot \left(x \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \color{blue}{\left(27 \cdot j\right) \cdot k} \]

       2. *-commutative 81.7%

          \[\leadsto \left(\mathsf{fma}\left(18 \cdot \left(x \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

   11. Simplified 81.7%

       \[\leadsto \left(\mathsf{fma}\left(18 \cdot \left(x \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \color{blue}{\left(j \cdot 27\right) \cdot k} \]

   12. Taylor expanded in j around inf 45.9%

       \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   13. Step-by-step derivation

       1. associate-*r* 46.0%

          \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

       2. *-commutative 46.0%

          \[\leadsto \color{blue}{\left(j \cdot -27\right)} \cdot k \]

       3. *-commutative 46.0%

          \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   14. Simplified 46.0%

       \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   if -4.7999999999999999e204 < j < -6.5999999999999996e77

   1. Initial program 85.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 85.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 85.7%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 81.2%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. fmm-def 81.2%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 18\right) \cdot y, z \cdot t, -\left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*l* 81.2%

         \[\leadsto \left(\mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot y\right)}, z \cdot t, -\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. associate-*l* 81.2%

         \[\leadsto \left(\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\color{blue}{a \cdot \left(4 \cdot t\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 81.2%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -a \cdot \left(4 \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. fmm-undef 81.2%

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - a \cdot \left(4 \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 81.2%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot t\right) \cdot a}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 81.2%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{4 \cdot \left(t \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 81.2%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - 4 \cdot \color{blue}{\left(a \cdot t\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. cancel-sign-sub-inv 81.2%

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(-4\right) \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. metadata-eval 81.2%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. fma-undefine 81.2%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. associate-*r* 81.2%

         \[\leadsto \left(\mathsf{fma}\left(\color{blue}{\left(x \cdot 18\right) \cdot y}, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 81.2%

         \[\leadsto \left(\mathsf{fma}\left(\color{blue}{\left(18 \cdot x\right)} \cdot y, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. associate-*r* 81.2%

          \[\leadsto \left(\mathsf{fma}\left(\color{blue}{18 \cdot \left(x \cdot y\right)}, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 81.2%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(18 \cdot \left(x \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in b around inf 46.0%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -6.5999999999999996e77 < j < 2.5e-53

   1. Initial program 87.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 88.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 87.6%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 86.6%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. fmm-def 86.6%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 18\right) \cdot y, z \cdot t, -\left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*l* 85.8%

         \[\leadsto \left(\mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot y\right)}, z \cdot t, -\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. associate-*l* 87.4%

         \[\leadsto \left(\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\color{blue}{a \cdot \left(4 \cdot t\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 87.4%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -a \cdot \left(4 \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. fmm-undef 87.4%

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - a \cdot \left(4 \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 87.4%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot t\right) \cdot a}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 87.4%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{4 \cdot \left(t \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 87.4%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - 4 \cdot \color{blue}{\left(a \cdot t\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. cancel-sign-sub-inv 87.4%

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(-4\right) \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. metadata-eval 87.4%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. fma-undefine 87.4%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. associate-*r* 88.2%

         \[\leadsto \left(\mathsf{fma}\left(\color{blue}{\left(x \cdot 18\right) \cdot y}, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 88.2%

         \[\leadsto \left(\mathsf{fma}\left(\color{blue}{\left(18 \cdot x\right)} \cdot y, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. associate-*r* 88.2%

          \[\leadsto \left(\mathsf{fma}\left(\color{blue}{18 \cdot \left(x \cdot y\right)}, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 88.2%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(18 \cdot \left(x \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in i around inf 28.9%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 28.9%

          \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} \]

   11. Simplified 28.9%

       \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right)} \]

   if 2.5e-53 < j

   1. Initial program 82.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 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 41.9%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.8 \cdot 10^{+204}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{+77}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-53}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 38.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.45 \cdot 10^{+65} \lor \neg \left(b \cdot c \leq 2.8 \cdot 10^{+41}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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) -1.45e+65) (not (<= (* b c) 2.8e+41)))
   (* 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) <= -1.45e+65) || !((b * c) <= 2.8e+41)) {
		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) <= (-1.45d+65)) .or. (.not. ((b * c) <= 2.8d+41))) 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) <= -1.45e+65) || !((b * c) <= 2.8e+41)) {
		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) <= -1.45e+65) or not ((b * c) <= 2.8e+41):
		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) <= -1.45e+65) || !(Float64(b * c) <= 2.8e+41))
		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) <= -1.45e+65) || ~(((b * c) <= 2.8e+41)))
		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], -1.45e+65], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2.8e+41]], $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) < -1.45e65 or 2.7999999999999999e41 < (*.f64 b c)

   1. Initial program 85.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 85.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. distribute-rgt-out-- 85.2%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 85.2%

         \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. fmm-def 85.2%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 18\right) \cdot y, z \cdot t, -\left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*l* 84.3%

         \[\leadsto \left(\mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot y\right)}, z \cdot t, -\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. associate-*l* 85.1%

         \[\leadsto \left(\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\color{blue}{a \cdot \left(4 \cdot t\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Applied egg-rr 85.1%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -a \cdot \left(4 \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. fmm-undef 85.1%

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - a \cdot \left(4 \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 85.1%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot t\right) \cdot a}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 85.1%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{4 \cdot \left(t \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 85.1%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - 4 \cdot \color{blue}{\left(a \cdot t\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. cancel-sign-sub-inv 85.1%

         \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(-4\right) \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. metadata-eval 85.1%

         \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. fma-undefine 85.1%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. associate-*r* 86.0%

         \[\leadsto \left(\mathsf{fma}\left(\color{blue}{\left(x \cdot 18\right) \cdot y}, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 86.0%

         \[\leadsto \left(\mathsf{fma}\left(\color{blue}{\left(18 \cdot x\right)} \cdot y, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. associate-*r* 86.1%

          \[\leadsto \left(\mathsf{fma}\left(\color{blue}{18 \cdot \left(x \cdot y\right)}, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Simplified 86.1%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(18 \cdot \left(x \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in b around inf 43.1%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -1.45e65 < (*.f64 b c) < 2.7999999999999999e41

   1. Initial program 86.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 31.4%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.45 \cdot 10^{+65} \lor \neg \left(b \cdot c \leq 2.8 \cdot 10^{+41}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 24.8% 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 85.7%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

3. Simplified 86.0%

   \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. associate-*r* 86.5%

      \[\leadsto \left(t \cdot \left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   2. distribute-rgt-out-- 86.1%

      \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   3. associate-*l* 83.7%

      \[\leadsto \left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   4. fmm-def 83.7%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(\left(x \cdot 18\right) \cdot y, z \cdot t, -\left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. associate-*l* 83.4%

      \[\leadsto \left(\mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot y\right)}, z \cdot t, -\left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. associate-*l* 83.7%

      \[\leadsto \left(\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -\color{blue}{a \cdot \left(4 \cdot t\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

6. Applied egg-rr 83.7%

   \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -a \cdot \left(4 \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
7. Step-by-step derivation

   1. fmm-undef 83.7%

      \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - a \cdot \left(4 \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   2. *-commutative 83.7%

      \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{\left(4 \cdot t\right) \cdot a}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   3. associate-*l* 84.1%

      \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \color{blue}{4 \cdot \left(t \cdot a\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   4. *-commutative 84.1%

      \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - 4 \cdot \color{blue}{\left(a \cdot t\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. cancel-sign-sub-inv 84.1%

      \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \left(-4\right) \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. metadata-eval 84.1%

      \[\leadsto \left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. fma-undefine 84.1%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. associate-*r* 84.5%

      \[\leadsto \left(\mathsf{fma}\left(\color{blue}{\left(x \cdot 18\right) \cdot y}, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. *-commutative 84.5%

      \[\leadsto \left(\mathsf{fma}\left(\color{blue}{\left(18 \cdot x\right)} \cdot y, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   10. associate-*r* 84.5%

       \[\leadsto \left(\mathsf{fma}\left(\color{blue}{18 \cdot \left(x \cdot y\right)}, z \cdot t, -4 \cdot \left(a \cdot t\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

8. Simplified 84.5%

   \[\leadsto \left(\color{blue}{\mathsf{fma}\left(18 \cdot \left(x \cdot y\right), z \cdot t, -4 \cdot \left(a \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

9. Taylor expanded in b around inf 19.8%

   \[\leadsto \color{blue}{b \cdot c} \]

10. Final simplification 19.8%

    \[\leadsto b \cdot c \]
11. Add Preprocessing

Developer target: 88.9% 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 2024076 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))