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

Percentage Accurate: 84.8% → 91.6%

Time: 21.3s

Alternatives: 14

Speedup: 1.0×

• 50.0% 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: 91.6% accurate, 0.5× speedup

Math

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

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

   1. Initial program 96.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 20.0%

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

   5. Taylor expanded in x around inf 73.5%

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

4. Final simplification 93.7%

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

Alternative 2: 86.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 6.1 \cdot 10^{+178}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x 6.1e+178)
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= 6.1e+178) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= 6.1d+178) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= 6.1e+178) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= 6.1e+178:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= 6.1e+178)
		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(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= 6.1e+178)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 6.1e+178], 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[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.1000000000000001e178

   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 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

   if 6.1000000000000001e178 < x

   1. Initial program 51.8%

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

   3. Simplified 58.3%

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

      1. associate-*r* 55.1%

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

      2. distribute-rgt-out-- 51.8%

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

      3. associate-*l* 54.8%

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

      4. *-commutative 54.8%

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

      5. *-commutative 54.8%

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

   6. Applied egg-rr 54.8%

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

   7. Taylor expanded in x around inf 78.1%

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

      1. cancel-sign-sub-inv 78.1%

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

      2. associate-*r* 78.1%

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

      3. metadata-eval 78.1%

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

      4. *-commutative 78.1%

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

   9. Simplified 78.1%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.1 \cdot 10^{+178}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t_1\\ t_3 := t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;x \leq -2.65 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + z \cdot \left(t \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -122000000:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-134}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-267}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-249}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+65}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

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 (* j (* k -27.0)))
        (t_2 (+ (* b c) t_1))
        (t_3 (+ t_1 (* -4.0 (* t a)))))
   (if (<= x -2.65e+51)
     (* x (+ (* i -4.0) (* z (* t (* 18.0 y)))))
     (if (<= x -7.5e+19)
       t_2
       (if (<= x -122000000.0)
         (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))
         (if (<= x -8.5e-134)
           t_3
           (if (<= x -3e-267)
             t_2
             (if (<= x 3.4e-249)
               t_3
               (if (<= x 8.5e+65)
                 (- (* b c) (* 27.0 (* j k)))
                 (* 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 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = t_1 + (-4.0 * (t * a));
	double tmp;
	if (x <= -2.65e+51) {
		tmp = x * ((i * -4.0) + (z * (t * (18.0 * y))));
	} else if (x <= -7.5e+19) {
		tmp = t_2;
	} else if (x <= -122000000.0) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (x <= -8.5e-134) {
		tmp = t_3;
	} else if (x <= -3e-267) {
		tmp = t_2;
	} else if (x <= 3.4e-249) {
		tmp = t_3;
	} else if (x <= 8.5e+65) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    t_3 = t_1 + ((-4.0d0) * (t * a))
    if (x <= (-2.65d+51)) then
        tmp = x * ((i * (-4.0d0)) + (z * (t * (18.0d0 * y))))
    else if (x <= (-7.5d+19)) then
        tmp = t_2
    else if (x <= (-122000000.0d0)) then
        tmp = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    else if (x <= (-8.5d-134)) then
        tmp = t_3
    else if (x <= (-3d-267)) then
        tmp = t_2
    else if (x <= 3.4d-249) then
        tmp = t_3
    else if (x <= 8.5d+65) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = t_1 + (-4.0 * (t * a));
	double tmp;
	if (x <= -2.65e+51) {
		tmp = x * ((i * -4.0) + (z * (t * (18.0 * y))));
	} else if (x <= -7.5e+19) {
		tmp = t_2;
	} else if (x <= -122000000.0) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (x <= -8.5e-134) {
		tmp = t_3;
	} else if (x <= -3e-267) {
		tmp = t_2;
	} else if (x <= 3.4e-249) {
		tmp = t_3;
	} else if (x <= 8.5e+65) {
		tmp = (b * c) - (27.0 * (j * k));
	} 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 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	t_3 = t_1 + (-4.0 * (t * a))
	tmp = 0
	if x <= -2.65e+51:
		tmp = x * ((i * -4.0) + (z * (t * (18.0 * y))))
	elif x <= -7.5e+19:
		tmp = t_2
	elif x <= -122000000.0:
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	elif x <= -8.5e-134:
		tmp = t_3
	elif x <= -3e-267:
		tmp = t_2
	elif x <= 3.4e-249:
		tmp = t_3
	elif x <= 8.5e+65:
		tmp = (b * c) - (27.0 * (j * k))
	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(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(t_1 + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (x <= -2.65e+51)
		tmp = Float64(x * Float64(Float64(i * -4.0) + Float64(z * Float64(t * Float64(18.0 * y)))));
	elseif (x <= -7.5e+19)
		tmp = t_2;
	elseif (x <= -122000000.0)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	elseif (x <= -8.5e-134)
		tmp = t_3;
	elseif (x <= -3e-267)
		tmp = t_2;
	elseif (x <= 3.4e-249)
		tmp = t_3;
	elseif (x <= 8.5e+65)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	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 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	t_3 = t_1 + (-4.0 * (t * a));
	tmp = 0.0;
	if (x <= -2.65e+51)
		tmp = x * ((i * -4.0) + (z * (t * (18.0 * y))));
	elseif (x <= -7.5e+19)
		tmp = t_2;
	elseif (x <= -122000000.0)
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	elseif (x <= -8.5e-134)
		tmp = t_3;
	elseif (x <= -3e-267)
		tmp = t_2;
	elseif (x <= 3.4e-249)
		tmp = t_3;
	elseif (x <= 8.5e+65)
		tmp = (b * c) - (27.0 * (j * k));
	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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.65e+51], N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(z * N[(t * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.5e+19], t$95$2, If[LessEqual[x, -122000000.0], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.5e-134], t$95$3, If[LessEqual[x, -3e-267], t$95$2, If[LessEqual[x, 3.4e-249], t$95$3, If[LessEqual[x, 8.5e+65], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 6 regimes

2. if x < -2.6499999999999998e51

   1. Initial program 75.3%

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

   3. Simplified 79.0%

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

      1. associate-*r* 75.2%

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

      2. distribute-rgt-out-- 75.2%

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

      3. associate-*l* 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. *-commutative 77.3%

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

      5. *-commutative 77.3%

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

   6. Applied egg-rr 77.3%

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

   7. Taylor expanded in x around inf 67.4%

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

      1. cancel-sign-sub-inv 67.4%

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

      2. associate-*r* 65.8%

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

      3. metadata-eval 65.8%

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

      4. *-commutative 65.8%

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

   9. Simplified 65.8%

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

   10. Taylor expanded in t around 0 67.4%

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

       1. associate-*r* 65.8%

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

       2. associate-*r* 65.7%

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

       3. *-commutative 65.7%

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

       4. *-commutative 65.7%

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

       5. associate-*r* 65.7%

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

   12. Simplified 65.7%

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

   if -2.6499999999999998e51 < x < -7.5e19 or -8.50000000000000015e-134 < x < -3e-267

   1. Initial program 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in b around inf 72.0%

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

   if -7.5e19 < x < -1.22e8

   1. Initial program 52.6%

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

   3. Simplified 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. Step-by-step derivation

      1. associate-*r* 52.6%

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

      2. distribute-rgt-out-- 52.6%

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

      3. associate-*l* 52.6%

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

      4. *-commutative 52.6%

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

      5. *-commutative 52.6%

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

   6. Applied egg-rr 52.6%

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

   7. Taylor expanded in x around inf 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. associate-*r* 100.0%

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

      3. metadata-eval 100.0%

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

      4. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if -1.22e8 < x < -8.50000000000000015e-134 or -3e-267 < x < 3.3999999999999998e-249

   1. Initial program 97.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in a around inf 65.3%

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

      1. *-commutative 65.3%

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

   7. Simplified 65.3%

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

   if 3.3999999999999998e-249 < x < 8.50000000000000075e65

   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 91.4%

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

   5. Taylor expanded in i around 0 87.0%

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

   6. Taylor expanded in b around inf 66.9%

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

   if 8.50000000000000075e65 < x

   1. Initial program 68.1%

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

   3. Simplified 73.7%

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

   5. Taylor expanded in x around inf 76.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + z \cdot \left(t \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+19}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -122000000:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-134}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-267}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-249}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+65}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -4.2 \cdot 10^{+119}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;b \cdot c \leq 1.52 \cdot 10^{-298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 1.4 \cdot 10^{+47}:\\ \;\;\;\;t_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.95 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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 (* k -27.0))) (t_2 (+ t_1 (* -4.0 (* t a)))))
   (if (<= (* b c) -4.2e+119)
     (+ (* b c) t_1)
     (if (<= (* b c) 1.52e-298)
       t_2
       (if (<= (* b c) 1.4e+47)
         (+ t_1 (* -4.0 (* x i)))
         (if (<= (* b c) 1.95e+80) t_2 (- (* 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 t_1 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (t * a));
	double tmp;
	if ((b * c) <= -4.2e+119) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= 1.52e-298) {
		tmp = t_2;
	} else if ((b * c) <= 1.4e+47) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if ((b * c) <= 1.95e+80) {
		tmp = t_2;
	} else {
		tmp = (b * c) - (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) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + ((-4.0d0) * (t * a))
    if ((b * c) <= (-4.2d+119)) then
        tmp = (b * c) + t_1
    else if ((b * c) <= 1.52d-298) then
        tmp = t_2
    else if ((b * c) <= 1.4d+47) then
        tmp = t_1 + ((-4.0d0) * (x * i))
    else if ((b * c) <= 1.95d+80) then
        tmp = t_2
    else
        tmp = (b * c) - (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 * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (t * a));
	double tmp;
	if ((b * c) <= -4.2e+119) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= 1.52e-298) {
		tmp = t_2;
	} else if ((b * c) <= 1.4e+47) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if ((b * c) <= 1.95e+80) {
		tmp = t_2;
	} else {
		tmp = (b * c) - (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 * (k * -27.0)
	t_2 = t_1 + (-4.0 * (t * a))
	tmp = 0
	if (b * c) <= -4.2e+119:
		tmp = (b * c) + t_1
	elif (b * c) <= 1.52e-298:
		tmp = t_2
	elif (b * c) <= 1.4e+47:
		tmp = t_1 + (-4.0 * (x * i))
	elif (b * c) <= 1.95e+80:
		tmp = t_2
	else:
		tmp = (b * c) - (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(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (Float64(b * c) <= -4.2e+119)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (Float64(b * c) <= 1.52e-298)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.4e+47)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= 1.95e+80)
		tmp = t_2;
	else
		tmp = Float64(Float64(b * c) - 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 * (k * -27.0);
	t_2 = t_1 + (-4.0 * (t * a));
	tmp = 0.0;
	if ((b * c) <= -4.2e+119)
		tmp = (b * c) + t_1;
	elseif ((b * c) <= 1.52e-298)
		tmp = t_2;
	elseif ((b * c) <= 1.4e+47)
		tmp = t_1 + (-4.0 * (x * i));
	elseif ((b * c) <= 1.95e+80)
		tmp = t_2;
	else
		tmp = (b * c) - (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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -4.2e+119], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.52e-298], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.4e+47], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.95e+80], t$95$2, N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -4.19999999999999966e119

   1. Initial program 80.5%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in b around inf 74.0%

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

   if -4.19999999999999966e119 < (*.f64 b c) < 1.5200000000000001e-298 or 1.39999999999999994e47 < (*.f64 b c) < 1.94999999999999999e80

   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 90.6%

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

   5. Taylor expanded in a around inf 56.2%

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

      1. *-commutative 56.2%

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

   7. Simplified 56.2%

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

   if 1.5200000000000001e-298 < (*.f64 b c) < 1.39999999999999994e47

   1. Initial program 86.0%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in i around inf 56.9%

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

   if 1.94999999999999999e80 < (*.f64 b c)

   1. Initial program 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in i around 0 79.4%

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

   6. Taylor expanded in b around inf 62.5%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.2 \cdot 10^{+119}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.52 \cdot 10^{-298}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.4 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.95 \cdot 10^{+80}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + z \cdot \left(t \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+126}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (<= x -1.9e+167)
   (* x (+ (* i -4.0) (* z (* t (* 18.0 y)))))
   (if (<= x 4.4e+126)
     (-
      (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
      (* 27.0 (* j k)))
     (* 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 tmp;
	if (x <= -1.9e+167) {
		tmp = x * ((i * -4.0) + (z * (t * (18.0 * y))));
	} else if (x <= 4.4e+126) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-1.9d+167)) then
        tmp = x * ((i * (-4.0d0)) + (z * (t * (18.0d0 * y))))
    else if (x <= 4.4d+126) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (27.0d0 * (j * k))
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -1.9e+167) {
		tmp = x * ((i * -4.0) + (z * (t * (18.0 * y))));
	} else if (x <= 4.4e+126) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	} 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):
	tmp = 0
	if x <= -1.9e+167:
		tmp = x * ((i * -4.0) + (z * (t * (18.0 * y))))
	elif x <= 4.4e+126:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k))
	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)
	tmp = 0.0
	if (x <= -1.9e+167)
		tmp = Float64(x * Float64(Float64(i * -4.0) + Float64(z * Float64(t * Float64(18.0 * y)))));
	elseif (x <= 4.4e+126)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - Float64(27.0 * Float64(j * k)));
	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)
	tmp = 0.0;
	if (x <= -1.9e+167)
		tmp = x * ((i * -4.0) + (z * (t * (18.0 * y))));
	elseif (x <= 4.4e+126)
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	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_] := If[LessEqual[x, -1.9e+167], N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(z * N[(t * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e+126], N[(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] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 3 regimes

2. if x < -1.89999999999999997e167

   1. Initial program 64.6%

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

   3. Simplified 71.9%

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

      1. associate-*r* 64.6%

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

      2. distribute-rgt-out-- 64.6%

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

      3. associate-*l* 68.6%

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

      4. *-commutative 68.6%

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

      5. *-commutative 68.6%

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

   6. Applied egg-rr 68.6%

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

   7. Taylor expanded in x around inf 72.6%

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

      1. cancel-sign-sub-inv 72.6%

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

      2. associate-*r* 72.9%

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

      3. metadata-eval 72.9%

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

      4. *-commutative 72.9%

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

   9. Simplified 72.9%

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

   10. Taylor expanded in t around 0 72.6%

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

       1. associate-*r* 72.9%

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

       2. associate-*r* 73.0%

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

       3. *-commutative 73.0%

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

       4. *-commutative 73.0%

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

       5. associate-*r* 72.9%

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

   12. Simplified 72.9%

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

   if -1.89999999999999997e167 < x < 4.39999999999999997e126

   1. Initial program 92.5%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in i around 0 85.0%

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

   if 4.39999999999999997e126 < x

   1. Initial program 62.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in x around inf 80.7%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + z \cdot \left(t \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+126}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+149}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-106}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-126}:\\ \;\;\;\;t_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-27}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (- (* b c) (* 27.0 (* j k))))
        (t_3 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -3.6e+149)
     t_3
     (if (<= t -1.5e+72)
       t_2
       (if (<= t -1.8e-106)
         t_3
         (if (<= t 5.4e-185)
           t_2
           (if (<= t 4.8e-126)
             (+ t_1 (* -4.0 (* x i)))
             (if (<= t 1.15e-27) (+ (* b c) t_1) t_3))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) - (27.0 * (j * k));
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -3.6e+149) {
		tmp = t_3;
	} else if (t <= -1.5e+72) {
		tmp = t_2;
	} else if (t <= -1.8e-106) {
		tmp = t_3;
	} else if (t <= 5.4e-185) {
		tmp = t_2;
	} else if (t <= 4.8e-126) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if (t <= 1.15e-27) {
		tmp = (b * c) + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) - (27.0d0 * (j * k))
    t_3 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-3.6d+149)) then
        tmp = t_3
    else if (t <= (-1.5d+72)) then
        tmp = t_2
    else if (t <= (-1.8d-106)) then
        tmp = t_3
    else if (t <= 5.4d-185) then
        tmp = t_2
    else if (t <= 4.8d-126) then
        tmp = t_1 + ((-4.0d0) * (x * i))
    else if (t <= 1.15d-27) then
        tmp = (b * c) + t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) - (27.0 * (j * k));
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -3.6e+149) {
		tmp = t_3;
	} else if (t <= -1.5e+72) {
		tmp = t_2;
	} else if (t <= -1.8e-106) {
		tmp = t_3;
	} else if (t <= 5.4e-185) {
		tmp = t_2;
	} else if (t <= 4.8e-126) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if (t <= 1.15e-27) {
		tmp = (b * c) + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) - (27.0 * (j * k))
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -3.6e+149:
		tmp = t_3
	elif t <= -1.5e+72:
		tmp = t_2
	elif t <= -1.8e-106:
		tmp = t_3
	elif t <= 5.4e-185:
		tmp = t_2
	elif t <= 4.8e-126:
		tmp = t_1 + (-4.0 * (x * i))
	elif t <= 1.15e-27:
		tmp = (b * c) + t_1
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -3.6e+149)
		tmp = t_3;
	elseif (t <= -1.5e+72)
		tmp = t_2;
	elseif (t <= -1.8e-106)
		tmp = t_3;
	elseif (t <= 5.4e-185)
		tmp = t_2;
	elseif (t <= 4.8e-126)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(x * i)));
	elseif (t <= 1.15e-27)
		tmp = Float64(Float64(b * c) + t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) - (27.0 * (j * k));
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -3.6e+149)
		tmp = t_3;
	elseif (t <= -1.5e+72)
		tmp = t_2;
	elseif (t <= -1.8e-106)
		tmp = t_3;
	elseif (t <= 5.4e-185)
		tmp = t_2;
	elseif (t <= 4.8e-126)
		tmp = t_1 + (-4.0 * (x * i));
	elseif (t <= 1.15e-27)
		tmp = (b * c) + t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+149], t$95$3, If[LessEqual[t, -1.5e+72], t$95$2, If[LessEqual[t, -1.8e-106], t$95$3, If[LessEqual[t, 5.4e-185], t$95$2, If[LessEqual[t, 4.8e-126], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-27], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.59999999999999995e149 or -1.50000000000000001e72 < t < -1.80000000000000006e-106 or 1.15e-27 < t

   1. Initial program 86.7%

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

   3. Simplified 89.1%

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

      1. associate-*r* 89.6%

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

      2. distribute-rgt-out-- 86.7%

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

      3. associate-*l* 81.1%

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

      4. *-commutative 81.1%

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

      5. *-commutative 81.1%

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

   6. Applied egg-rr 81.1%

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

   7. Taylor expanded in t around inf 65.4%

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

   if -3.59999999999999995e149 < t < -1.50000000000000001e72 or -1.80000000000000006e-106 < t < 5.39999999999999976e-185

   1. Initial program 83.4%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in i around 0 78.9%

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

   6. Taylor expanded in b around inf 70.7%

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

   if 5.39999999999999976e-185 < t < 4.80000000000000014e-126

   1. Initial program 66.5%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in i around inf 91.7%

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

   if 4.80000000000000014e-126 < t < 1.15e-27

   1. Initial program 91.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in b around inf 61.6%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+149}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+72}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-185}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-126}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-27}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8.5 \cdot 10^{+19} \lor \neg \left(b \cdot c \leq 5.1 \cdot 10^{+53}\right):\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (or (<= (* b c) -8.5e+19) (not (<= (* b c) 5.1e+53)))
   (- (* b c) (* 27.0 (* j k)))
   (+ (* j (* k -27.0)) (* -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 tmp;
	if (((b * c) <= -8.5e+19) || !((b * c) <= 5.1e+53)) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = (j * (k * -27.0)) + (-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) :: tmp
    if (((b * c) <= (-8.5d+19)) .or. (.not. ((b * c) <= 5.1d+53))) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else
        tmp = (j * (k * (-27.0d0))) + ((-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 tmp;
	if (((b * c) <= -8.5e+19) || !((b * c) <= 5.1e+53)) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = (j * (k * -27.0)) + (-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):
	tmp = 0
	if ((b * c) <= -8.5e+19) or not ((b * c) <= 5.1e+53):
		tmp = (b * c) - (27.0 * (j * k))
	else:
		tmp = (j * (k * -27.0)) + (-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)
	tmp = 0.0
	if ((Float64(b * c) <= -8.5e+19) || !(Float64(b * c) <= 5.1e+53))
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + 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)
	tmp = 0.0;
	if (((b * c) <= -8.5e+19) || ~(((b * c) <= 5.1e+53)))
		tmp = (b * c) - (27.0 * (j * k));
	else
		tmp = (j * (k * -27.0)) + (-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_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -8.5e+19], N[Not[LessEqual[N[(b * c), $MachinePrecision], 5.1e+53]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -8.5e19 or 5.0999999999999998e53 < (*.f64 b c)

   1. Initial program 82.7%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in i around 0 82.8%

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

   6. Taylor expanded in b around inf 59.4%

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

   if -8.5e19 < (*.f64 b c) < 5.0999999999999998e53

   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 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 i around inf 53.5%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8.5 \cdot 10^{+19} \lor \neg \left(b \cdot c \leq 5.1 \cdot 10^{+53}\right):\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + z \cdot \left(t \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+67}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (<= x -4.6e+52)
   (* x (+ (* i -4.0) (* z (* t (* 18.0 y)))))
   (if (<= x 4e+67)
     (- (+ (* b c) (* -4.0 (* t a))) (* 27.0 (* j k)))
     (* 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 tmp;
	if (x <= -4.6e+52) {
		tmp = x * ((i * -4.0) + (z * (t * (18.0 * y))));
	} else if (x <= 4e+67) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-4.6d+52)) then
        tmp = x * ((i * (-4.0d0)) + (z * (t * (18.0d0 * y))))
    else if (x <= 4d+67) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (27.0d0 * (j * k))
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -4.6e+52) {
		tmp = x * ((i * -4.0) + (z * (t * (18.0 * y))));
	} else if (x <= 4e+67) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} 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):
	tmp = 0
	if x <= -4.6e+52:
		tmp = x * ((i * -4.0) + (z * (t * (18.0 * y))))
	elif x <= 4e+67:
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k))
	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)
	tmp = 0.0
	if (x <= -4.6e+52)
		tmp = Float64(x * Float64(Float64(i * -4.0) + Float64(z * Float64(t * Float64(18.0 * y)))));
	elseif (x <= 4e+67)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(27.0 * Float64(j * k)));
	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)
	tmp = 0.0;
	if (x <= -4.6e+52)
		tmp = x * ((i * -4.0) + (z * (t * (18.0 * y))));
	elseif (x <= 4e+67)
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	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_] := If[LessEqual[x, -4.6e+52], N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(z * N[(t * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e+67], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 3 regimes

2. if x < -4.6e52

   1. Initial program 75.3%

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

   3. Simplified 79.0%

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

      1. associate-*r* 75.2%

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

      2. distribute-rgt-out-- 75.2%

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

      3. associate-*l* 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. *-commutative 77.3%

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

      5. *-commutative 77.3%

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

   6. Applied egg-rr 77.3%

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

   7. Taylor expanded in x around inf 67.4%

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

      1. cancel-sign-sub-inv 67.4%

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

      2. associate-*r* 65.8%

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

      3. metadata-eval 65.8%

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

      4. *-commutative 65.8%

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

   9. Simplified 65.8%

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

   10. Taylor expanded in t around 0 67.4%

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

       1. associate-*r* 65.8%

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

       2. associate-*r* 65.7%

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

       3. *-commutative 65.7%

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

       4. *-commutative 65.7%

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

       5. associate-*r* 65.7%

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

   12. Simplified 65.7%

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

   if -4.6e52 < x < 3.99999999999999993e67

   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 94.3%

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

   5. Taylor expanded in x around 0 79.9%

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

   if 3.99999999999999993e67 < x

   1. Initial program 68.1%

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

   3. Simplified 73.7%

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

   5. Taylor expanded in x around inf 76.1%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + z \cdot \left(t \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+67}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 45.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ t_2 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;i \leq -6.6 \cdot 10^{+187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -6.4 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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) (* j (* k -27.0)))) (t_2 (* x (* i -4.0))))
   (if (<= i -6.6e+187)
     t_2
     (if (<= i -8.5e+113)
       t_1
       (if (<= i -6.4e+64) (* t (* a -4.0)) (if (<= i 4.1e+173) 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) + (j * (k * -27.0));
	double t_2 = x * (i * -4.0);
	double tmp;
	if (i <= -6.6e+187) {
		tmp = t_2;
	} else if (i <= -8.5e+113) {
		tmp = t_1;
	} else if (i <= -6.4e+64) {
		tmp = t * (a * -4.0);
	} else if (i <= 4.1e+173) {
		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) + (j * (k * (-27.0d0)))
    t_2 = x * (i * (-4.0d0))
    if (i <= (-6.6d+187)) then
        tmp = t_2
    else if (i <= (-8.5d+113)) then
        tmp = t_1
    else if (i <= (-6.4d+64)) then
        tmp = t * (a * (-4.0d0))
    else if (i <= 4.1d+173) 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) + (j * (k * -27.0));
	double t_2 = x * (i * -4.0);
	double tmp;
	if (i <= -6.6e+187) {
		tmp = t_2;
	} else if (i <= -8.5e+113) {
		tmp = t_1;
	} else if (i <= -6.4e+64) {
		tmp = t * (a * -4.0);
	} else if (i <= 4.1e+173) {
		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) + (j * (k * -27.0))
	t_2 = x * (i * -4.0)
	tmp = 0
	if i <= -6.6e+187:
		tmp = t_2
	elif i <= -8.5e+113:
		tmp = t_1
	elif i <= -6.4e+64:
		tmp = t * (a * -4.0)
	elif i <= 4.1e+173:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	t_2 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (i <= -6.6e+187)
		tmp = t_2;
	elseif (i <= -8.5e+113)
		tmp = t_1;
	elseif (i <= -6.4e+64)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (i <= 4.1e+173)
		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) + (j * (k * -27.0));
	t_2 = x * (i * -4.0);
	tmp = 0.0;
	if (i <= -6.6e+187)
		tmp = t_2;
	elseif (i <= -8.5e+113)
		tmp = t_1;
	elseif (i <= -6.4e+64)
		tmp = t * (a * -4.0);
	elseif (i <= 4.1e+173)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6.6e+187], t$95$2, If[LessEqual[i, -8.5e+113], t$95$1, If[LessEqual[i, -6.4e+64], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.1e+173], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -6.6000000000000003e187 or 4.09999999999999976e173 < i

   1. Initial program 80.3%

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

   3. Simplified 83.9%

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

      1. associate-*r* 80.4%

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

      2. distribute-rgt-out-- 80.4%

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

      3. associate-*l* 76.9%

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

      4. *-commutative 76.9%

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

      5. *-commutative 76.9%

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

   6. Applied egg-rr 76.9%

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

   7. Taylor expanded in i around inf 53.9%

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

      1. *-commutative 53.9%

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

      2. *-commutative 53.9%

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

      3. associate-*l* 53.9%

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

   9. Simplified 53.9%

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

   if -6.6000000000000003e187 < i < -8.5000000000000001e113 or -6.40000000000000037e64 < i < 4.09999999999999976e173

   1. Initial program 86.0%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in b around inf 53.4%

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

   if -8.5000000000000001e113 < i < -6.40000000000000037e64

   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 92.2%

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

      1. associate-*r* 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* 92.1%

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

      4. *-commutative 92.1%

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

      5. *-commutative 92.1%

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

   6. Applied egg-rr 92.1%

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

   7. Taylor expanded in a around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. *-commutative 50.1%

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

      3. associate-*r* 50.1%

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

   9. Simplified 50.1%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.6 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq -6.4 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{+173}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 45.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_2 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;i \leq -9 \cdot 10^{+185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -5 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;i \leq 1.06 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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) (* 27.0 (* j k)))) (t_2 (* x (* i -4.0))))
   (if (<= i -9e+185)
     t_2
     (if (<= i -1.6e+113)
       t_1
       (if (<= i -5e+64) (* t (* a -4.0)) (if (<= i 1.06e+173) 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) - (27.0 * (j * k));
	double t_2 = x * (i * -4.0);
	double tmp;
	if (i <= -9e+185) {
		tmp = t_2;
	} else if (i <= -1.6e+113) {
		tmp = t_1;
	} else if (i <= -5e+64) {
		tmp = t * (a * -4.0);
	} else if (i <= 1.06e+173) {
		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) - (27.0d0 * (j * k))
    t_2 = x * (i * (-4.0d0))
    if (i <= (-9d+185)) then
        tmp = t_2
    else if (i <= (-1.6d+113)) then
        tmp = t_1
    else if (i <= (-5d+64)) then
        tmp = t * (a * (-4.0d0))
    else if (i <= 1.06d+173) 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) - (27.0 * (j * k));
	double t_2 = x * (i * -4.0);
	double tmp;
	if (i <= -9e+185) {
		tmp = t_2;
	} else if (i <= -1.6e+113) {
		tmp = t_1;
	} else if (i <= -5e+64) {
		tmp = t * (a * -4.0);
	} else if (i <= 1.06e+173) {
		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) - (27.0 * (j * k))
	t_2 = x * (i * -4.0)
	tmp = 0
	if i <= -9e+185:
		tmp = t_2
	elif i <= -1.6e+113:
		tmp = t_1
	elif i <= -5e+64:
		tmp = t * (a * -4.0)
	elif i <= 1.06e+173:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (i <= -9e+185)
		tmp = t_2;
	elseif (i <= -1.6e+113)
		tmp = t_1;
	elseif (i <= -5e+64)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (i <= 1.06e+173)
		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) - (27.0 * (j * k));
	t_2 = x * (i * -4.0);
	tmp = 0.0;
	if (i <= -9e+185)
		tmp = t_2;
	elseif (i <= -1.6e+113)
		tmp = t_1;
	elseif (i <= -5e+64)
		tmp = t * (a * -4.0);
	elseif (i <= 1.06e+173)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9e+185], t$95$2, If[LessEqual[i, -1.6e+113], t$95$1, If[LessEqual[i, -5e+64], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.06e+173], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -9.0000000000000004e185 or 1.06e173 < i

   1. Initial program 80.3%

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

   3. Simplified 83.9%

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

      1. associate-*r* 80.4%

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

      2. distribute-rgt-out-- 80.4%

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

      3. associate-*l* 76.9%

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

      4. *-commutative 76.9%

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

      5. *-commutative 76.9%

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

   6. Applied egg-rr 76.9%

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

   7. Taylor expanded in i around inf 53.9%

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

      1. *-commutative 53.9%

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

      2. *-commutative 53.9%

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

      3. associate-*l* 53.9%

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

   9. Simplified 53.9%

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

   if -9.0000000000000004e185 < i < -1.5999999999999999e113 or -5e64 < i < 1.06e173

   1. Initial program 86.0%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in i around 0 83.6%

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

   6. Taylor expanded in b around inf 53.5%

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

   if -1.5999999999999999e113 < i < -5e64

   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 92.2%

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

      1. associate-*r* 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* 92.1%

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

      4. *-commutative 92.1%

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

      5. *-commutative 92.1%

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

   6. Applied egg-rr 92.1%

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

   7. Taylor expanded in a around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. *-commutative 50.1%

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

      3. associate-*r* 50.1%

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

   9. Simplified 50.1%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{+113}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;i \leq -5 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;i \leq 1.06 \cdot 10^{+173}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+93}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-13}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-294}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= b -7.5e+93)
     (* b c)
     (if (<= b -7.2e+23)
       t_1
       (if (<= b -3.7e-13)
         (* b c)
         (if (<= b 2.3e-294)
           (* (* j k) -27.0)
           (if (<= b 1.65e-123) t_1 (* b c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (b <= -7.5e+93) {
		tmp = b * c;
	} else if (b <= -7.2e+23) {
		tmp = t_1;
	} else if (b <= -3.7e-13) {
		tmp = b * c;
	} else if (b <= 2.3e-294) {
		tmp = (j * k) * -27.0;
	} else if (b <= 1.65e-123) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (b <= (-7.5d+93)) then
        tmp = b * c
    else if (b <= (-7.2d+23)) then
        tmp = t_1
    else if (b <= (-3.7d-13)) then
        tmp = b * c
    else if (b <= 2.3d-294) then
        tmp = (j * k) * (-27.0d0)
    else if (b <= 1.65d-123) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (b <= -7.5e+93) {
		tmp = b * c;
	} else if (b <= -7.2e+23) {
		tmp = t_1;
	} else if (b <= -3.7e-13) {
		tmp = b * c;
	} else if (b <= 2.3e-294) {
		tmp = (j * k) * -27.0;
	} else if (b <= 1.65e-123) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if b <= -7.5e+93:
		tmp = b * c
	elif b <= -7.2e+23:
		tmp = t_1
	elif b <= -3.7e-13:
		tmp = b * c
	elif b <= 2.3e-294:
		tmp = (j * k) * -27.0
	elif b <= 1.65e-123:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (b <= -7.5e+93)
		tmp = Float64(b * c);
	elseif (b <= -7.2e+23)
		tmp = t_1;
	elseif (b <= -3.7e-13)
		tmp = Float64(b * c);
	elseif (b <= 2.3e-294)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (b <= 1.65e-123)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (b <= -7.5e+93)
		tmp = b * c;
	elseif (b <= -7.2e+23)
		tmp = t_1;
	elseif (b <= -3.7e-13)
		tmp = b * c;
	elseif (b <= 2.3e-294)
		tmp = (j * k) * -27.0;
	elseif (b <= 1.65e-123)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.5e+93], N[(b * c), $MachinePrecision], If[LessEqual[b, -7.2e+23], t$95$1, If[LessEqual[b, -3.7e-13], N[(b * c), $MachinePrecision], If[LessEqual[b, 2.3e-294], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[b, 1.65e-123], t$95$1, N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.5000000000000002e93 or -7.1999999999999997e23 < b < -3.69999999999999989e-13 or 1.6500000000000001e-123 < b

   1. Initial program 82.6%

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

   3. Simplified 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. Step-by-step derivation

      1. associate-*r* 83.3%

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

      2. distribute-rgt-out-- 82.6%

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

      3. associate-*l* 81.3%

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

      4. *-commutative 81.3%

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

      5. *-commutative 81.3%

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

   6. Applied egg-rr 81.3%

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

   7. Taylor expanded in b around inf 40.4%

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

   if -7.5000000000000002e93 < b < -7.1999999999999997e23 or 2.30000000000000016e-294 < b < 1.6500000000000001e-123

   1. Initial program 93.1%

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

   3. Simplified 88.9%

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

      1. associate-*r* 93.1%

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

      2. distribute-rgt-out-- 93.1%

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

      3. associate-*l* 88.5%

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

      4. *-commutative 88.5%

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

      5. *-commutative 88.5%

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

   6. Applied egg-rr 88.5%

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

   7. Taylor expanded in a around inf 36.9%

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

      1. *-commutative 36.9%

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

      2. *-commutative 36.9%

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

      3. associate-*r* 36.9%

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

   9. Simplified 36.9%

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

   if -3.69999999999999989e-13 < b < 2.30000000000000016e-294

   1. Initial program 85.1%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in j around inf 35.2%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+93}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-13}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-294}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 32.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+95}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-13}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-298}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= b -1.6e+95)
   (* b c)
   (if (<= b -4.2e+23)
     (* t (* a -4.0))
     (if (<= b -3.8e-13)
       (* b c)
       (if (<= b -8e-298)
         (* (* j k) -27.0)
         (if (<= b 9e+39) (* x (* i -4.0)) (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (b <= -1.6e+95) {
		tmp = b * c;
	} else if (b <= -4.2e+23) {
		tmp = t * (a * -4.0);
	} else if (b <= -3.8e-13) {
		tmp = b * c;
	} else if (b <= -8e-298) {
		tmp = (j * k) * -27.0;
	} else if (b <= 9e+39) {
		tmp = x * (i * -4.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (b <= (-1.6d+95)) then
        tmp = b * c
    else if (b <= (-4.2d+23)) then
        tmp = t * (a * (-4.0d0))
    else if (b <= (-3.8d-13)) then
        tmp = b * c
    else if (b <= (-8d-298)) then
        tmp = (j * k) * (-27.0d0)
    else if (b <= 9d+39) then
        tmp = x * (i * (-4.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (b <= -1.6e+95) {
		tmp = b * c;
	} else if (b <= -4.2e+23) {
		tmp = t * (a * -4.0);
	} else if (b <= -3.8e-13) {
		tmp = b * c;
	} else if (b <= -8e-298) {
		tmp = (j * k) * -27.0;
	} else if (b <= 9e+39) {
		tmp = x * (i * -4.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if b <= -1.6e+95:
		tmp = b * c
	elif b <= -4.2e+23:
		tmp = t * (a * -4.0)
	elif b <= -3.8e-13:
		tmp = b * c
	elif b <= -8e-298:
		tmp = (j * k) * -27.0
	elif b <= 9e+39:
		tmp = x * (i * -4.0)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (b <= -1.6e+95)
		tmp = Float64(b * c);
	elseif (b <= -4.2e+23)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (b <= -3.8e-13)
		tmp = Float64(b * c);
	elseif (b <= -8e-298)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (b <= 9e+39)
		tmp = Float64(x * Float64(i * -4.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (b <= -1.6e+95)
		tmp = b * c;
	elseif (b <= -4.2e+23)
		tmp = t * (a * -4.0);
	elseif (b <= -3.8e-13)
		tmp = b * c;
	elseif (b <= -8e-298)
		tmp = (j * k) * -27.0;
	elseif (b <= 9e+39)
		tmp = x * (i * -4.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[b, -1.6e+95], N[(b * c), $MachinePrecision], If[LessEqual[b, -4.2e+23], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.8e-13], N[(b * c), $MachinePrecision], If[LessEqual[b, -8e-298], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[b, 9e+39], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.6e95 or -4.2000000000000003e23 < b < -3.8e-13 or 8.99999999999999991e39 < b

   1. Initial program 81.3%

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

   3. Simplified 83.2%

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

      1. associate-*r* 82.2%

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

      2. distribute-rgt-out-- 81.3%

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

      3. associate-*l* 80.4%

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

      4. *-commutative 80.4%

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

      5. *-commutative 80.4%

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

   6. Applied egg-rr 80.4%

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

   7. Taylor expanded in b around inf 47.6%

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

   if -1.6e95 < b < -4.2000000000000003e23

   1. Initial program 93.3%

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

   3. Simplified 93.2%

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

      1. associate-*r* 93.2%

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

      2. distribute-rgt-out-- 93.2%

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

      3. associate-*l* 93.1%

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

      4. *-commutative 93.1%

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

      5. *-commutative 93.1%

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

   6. Applied egg-rr 93.1%

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

   7. Taylor expanded in a around inf 31.8%

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

      1. *-commutative 31.8%

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

      2. *-commutative 31.8%

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

      3. associate-*r* 31.8%

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

   9. Simplified 31.8%

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

   if -3.8e-13 < b < -7.9999999999999993e-298

   1. Initial program 84.2%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in j around inf 36.7%

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

   if -7.9999999999999993e-298 < b < 8.99999999999999991e39

   1. Initial program 89.8%

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

   3. Simplified 89.0%

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

      1. associate-*r* 89.8%

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

      2. distribute-rgt-out-- 89.8%

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

      3. associate-*l* 84.7%

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

      4. *-commutative 84.7%

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

      5. *-commutative 84.7%

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

   6. Applied egg-rr 84.7%

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

   7. Taylor expanded in i around inf 25.5%

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

      1. *-commutative 25.5%

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

      2. *-commutative 25.5%

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

      3. associate-*l* 25.5%

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

   9. Simplified 25.5%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+95}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-13}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-298}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 32.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{-15} \lor \neg \left(b \leq 8.5 \cdot 10^{+39}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= b -2.7e-15) (not (<= b 8.5e+39))) (* b c) (* (* j k) -27.0)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b <= -2.7e-15) || !(b <= 8.5e+39)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-2.7d-15)) .or. (.not. (b <= 8.5d+39))) then
        tmp = b * c
    else
        tmp = (j * k) * (-27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -2.7e-15) || !(b <= 8.5e+39)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b <= -2.7e-15) or not (b <= 8.5e+39):
		tmp = b * c
	else:
		tmp = (j * k) * -27.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((b <= -2.7e-15) || !(b <= 8.5e+39))
		tmp = Float64(b * c);
	else
		tmp = Float64(Float64(j * k) * -27.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b <= -2.7e-15) || ~((b <= 8.5e+39)))
		tmp = b * c;
	else
		tmp = (j * k) * -27.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[b, -2.7e-15], N[Not[LessEqual[b, 8.5e+39]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.70000000000000009e-15 or 8.49999999999999971e39 < b

   1. Initial program 82.9%

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

   3. Simplified 84.5%

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

      1. associate-*r* 83.7%

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

      2. distribute-rgt-out-- 82.9%

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

      3. associate-*l* 82.1%

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

      4. *-commutative 82.1%

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

      5. *-commutative 82.1%

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

   6. Applied egg-rr 82.1%

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

   7. Taylor expanded in b around inf 44.2%

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

   if -2.70000000000000009e-15 < b < 8.49999999999999971e39

   1. Initial program 87.1%

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

   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 j around inf 28.4%

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

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{-15} \lor \neg \left(b \leq 8.5 \cdot 10^{+39}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 23.4% 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 85.1%

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

3. Simplified 87.1%

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

   1. associate-*r* 86.6%

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

   2. distribute-rgt-out-- 85.1%

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

   3. associate-*l* 83.2%

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

   4. *-commutative 83.2%

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

   5. *-commutative 83.2%

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

6. Applied egg-rr 83.2%

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

7. Taylor expanded in b around inf 25.7%

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

8. Final simplification 25.7%

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

Developer target: 88.8% accurate, 0.9× 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 2024010 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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