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

Percentage Accurate: 84.7% → 92.3%

Time: 22.6s

Alternatives: 22

Speedup: 0.7×

• 51.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.7% 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: 92.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - t\_1\\ t_3 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+296}:\\ \;\;\;\;\left(\left(b \cdot c + t\_3\right) - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2
         (-
          (-
           (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
           (* (* x 4.0) i))
          t_1))
        (t_3 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<= t_2 -5e+296)
     (- (- (+ (* b c) t_3) (* 4.0 (* t a))) t_1)
     (if (<= t_2 INFINITY) t_2 t_3))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1;
	double t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (t_2 <= -5e+296) {
		tmp = (((b * c) + t_3) - (4.0 * (t * a))) - t_1;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1;
	double t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (t_2 <= -5e+296) {
		tmp = (((b * c) + t_3) - (4.0 * (t * a))) - t_1;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1
	t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if t_2 <= -5e+296:
		tmp = (((b * c) + t_3) - (4.0 * (t * a))) - t_1
	elif t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - t_1)
	t_3 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (t_2 <= -5e+296)
		tmp = Float64(Float64(Float64(Float64(b * c) + t_3) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1;
	t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (t_2 <= -5e+296)
		tmp = (((b * c) + t_3) - (4.0 * (t * a))) - t_1;
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+296], N[(N[(N[(N[(b * c), $MachinePrecision] + t$95$3), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$2, t$95$3]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < -5.0000000000000001e296

   1. Initial program 92.6%

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

   3. Taylor expanded in x around 0 100.0%

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

   if -5.0000000000000001e296 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 97.0%

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

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

   1. Initial program 0.0%

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

   3. Simplified 13.8%

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

   5. Taylor expanded in x around inf 58.9%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+296}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+263}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(-27 \cdot \frac{j \cdot k}{i} + x \cdot -4\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 (- INFINITY))
     (* k (* j -27.0))
     (if (<= t_1 2e+263)
       (-
        (-
         (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
         (* 4.0 (* t a)))
        t_1)
       (* i (+ (* -27.0 (/ (* j k) i)) (* x -4.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = k * (j * -27.0);
	} else if (t_1 <= 2e+263) {
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = i * ((-27.0 * ((j * k) / i)) + (x * -4.0));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = k * (j * -27.0);
	} else if (t_1 <= 2e+263) {
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = i * ((-27.0 * ((j * k) / i)) + (x * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -math.inf:
		tmp = k * (j * -27.0)
	elif t_1 <= 2e+263:
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - t_1
	else:
		tmp = i * ((-27.0 * ((j * k) / i)) + (x * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(k * Float64(j * -27.0));
	elseif (t_1 <= 2e+263)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))) - Float64(4.0 * Float64(t * a))) - t_1);
	else
		tmp = Float64(i * Float64(Float64(-27.0 * Float64(Float64(j * k) / i)) + Float64(x * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = k * (j * -27.0);
	elseif (t_1 <= 2e+263)
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - t_1;
	else
		tmp = i * ((-27.0 * ((j * k) / i)) + (x * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+263], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(i * N[(N[(-27.0 * N[(N[(j * k), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision] + N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -inf.0

   1. Initial program 63.6%

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

   3. Simplified 63.6%

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

   5. Taylor expanded in j around inf 90.9%

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

      1. associate-*r* 90.9%

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

      2. *-commutative 90.9%

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

      3. metadata-eval 90.9%

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

      4. distribute-rgt-neg-in 90.9%

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

      5. *-commutative 90.9%

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

      6. distribute-rgt-neg-in 90.9%

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

      7. metadata-eval 90.9%

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

      8. *-commutative 90.9%

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

   7. Simplified 90.9%

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

   if -inf.0 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.00000000000000003e263

   1. Initial program 87.7%

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

   3. Taylor expanded in x around 0 91.2%

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

   if 2.00000000000000003e263 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 66.6%

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

   3. Simplified 61.9%

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

   5. Taylor expanded in i around inf 76.1%

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

      1. metadata-eval 76.1%

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

      2. distribute-lft-neg-in 76.1%

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

      3. *-commutative 76.1%

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

      4. associate-*r* 76.1%

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

      5. distribute-rgt-neg-in 76.1%

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

      6. distribute-rgt-neg-in 76.1%

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

      7. metadata-eval 76.1%

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

      8. *-commutative 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in i around inf 85.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -\infty:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+263}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(-27 \cdot \frac{j \cdot k}{i} + x \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+216}:\\ \;\;\;\;k \cdot \left(\frac{b \cdot c}{k} - \left(j \cdot 27 + 4 \cdot \frac{t \cdot a + x \cdot i}{k}\right)\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+263}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(-27 \cdot \frac{j \cdot k}{i} + x \cdot -4\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+216)
     (* k (- (/ (* b c) k) (+ (* j 27.0) (* 4.0 (/ (+ (* t a) (* x i)) k)))))
     (if (<= t_1 2e+263)
       (-
        (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
        (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
       (* i (+ (* -27.0 (/ (* j k) i)) (* x -4.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+216) {
		tmp = k * (((b * c) / k) - ((j * 27.0) + (4.0 * (((t * a) + (x * i)) / k))));
	} else if (t_1 <= 2e+263) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = i * ((-27.0 * ((j * k) / i)) + (x * -4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-2d+216)) then
        tmp = k * (((b * c) / k) - ((j * 27.0d0) + (4.0d0 * (((t * a) + (x * i)) / k))))
    else if (t_1 <= 2d+263) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = i * (((-27.0d0) * ((j * k) / i)) + (x * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+216) {
		tmp = k * (((b * c) / k) - ((j * 27.0) + (4.0 * (((t * a) + (x * i)) / k))));
	} else if (t_1 <= 2e+263) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = i * ((-27.0 * ((j * k) / i)) + (x * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+216:
		tmp = k * (((b * c) / k) - ((j * 27.0) + (4.0 * (((t * a) + (x * i)) / k))))
	elif t_1 <= 2e+263:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = i * ((-27.0 * ((j * k) / i)) + (x * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+216)
		tmp = Float64(k * Float64(Float64(Float64(b * c) / k) - Float64(Float64(j * 27.0) + Float64(4.0 * Float64(Float64(Float64(t * a) + Float64(x * i)) / k)))));
	elseif (t_1 <= 2e+263)
		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(i * Float64(Float64(-27.0 * Float64(Float64(j * k) / i)) + Float64(x * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+216)
		tmp = k * (((b * c) / k) - ((j * 27.0) + (4.0 * (((t * a) + (x * i)) / k))));
	elseif (t_1 <= 2e+263)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = i * ((-27.0 * ((j * k) / i)) + (x * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+216], N[(k * N[(N[(N[(b * c), $MachinePrecision] / k), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] + N[(4.0 * N[(N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision] / k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+263], 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[(i * N[(N[(-27.0 * N[(N[(j * k), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision] + N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e216

   1. Initial program 66.6%

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

   3. Taylor expanded in y around 0 76.1%

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

      1. distribute-lft-out 76.1%

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

      2. *-commutative 76.1%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in k around inf 80.9%

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

   if -2e216 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.00000000000000003e263

   1. Initial program 88.5%

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

   3. Simplified 90.3%

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

   if 2.00000000000000003e263 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 66.6%

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

   3. Simplified 61.9%

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

   5. Taylor expanded in i around inf 76.1%

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

      1. metadata-eval 76.1%

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

      2. distribute-lft-neg-in 76.1%

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

      3. *-commutative 76.1%

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

      4. associate-*r* 76.1%

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

      5. distribute-rgt-neg-in 76.1%

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

      6. distribute-rgt-neg-in 76.1%

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

      7. metadata-eval 76.1%

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

      8. *-commutative 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in i around inf 85.6%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+216}:\\ \;\;\;\;k \cdot \left(\frac{b \cdot c}{k} - \left(j \cdot 27 + 4 \cdot \frac{t \cdot a + x \cdot i}{k}\right)\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+263}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(-27 \cdot \frac{j \cdot k}{i} + x \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 36.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.4 \cdot 10^{+278}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.8 \cdot 10^{-23}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -3.8 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.16 \cdot 10^{+67}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 5.7 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -2.4e+278)
   (* b c)
   (if (<= (* b c) -1.8e-23)
     (* 18.0 (* t (* x (* y z))))
     (if (<= (* b c) -3.8e-305)
       (* x (* i -4.0))
       (if (<= (* b c) 1.16e+67)
         (* k (* j -27.0))
         (if (<= (* b c) 5.7e+147) (* x (* z (* y (* 18.0 t)))) (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2.4e+278) {
		tmp = b * c;
	} else if ((b * c) <= -1.8e-23) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= -3.8e-305) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 1.16e+67) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 5.7e+147) {
		tmp = x * (z * (y * (18.0 * t)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-2.4d+278)) then
        tmp = b * c
    else if ((b * c) <= (-1.8d-23)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if ((b * c) <= (-3.8d-305)) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= 1.16d+67) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 5.7d+147) then
        tmp = x * (z * (y * (18.0d0 * t)))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2.4e+278) {
		tmp = b * c;
	} else if ((b * c) <= -1.8e-23) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= -3.8e-305) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 1.16e+67) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 5.7e+147) {
		tmp = x * (z * (y * (18.0 * t)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -2.4e+278:
		tmp = b * c
	elif (b * c) <= -1.8e-23:
		tmp = 18.0 * (t * (x * (y * z)))
	elif (b * c) <= -3.8e-305:
		tmp = x * (i * -4.0)
	elif (b * c) <= 1.16e+67:
		tmp = k * (j * -27.0)
	elif (b * c) <= 5.7e+147:
		tmp = x * (z * (y * (18.0 * t)))
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -2.4e+278)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.8e-23)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (Float64(b * c) <= -3.8e-305)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= 1.16e+67)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 5.7e+147)
		tmp = Float64(x * Float64(z * Float64(y * Float64(18.0 * t))));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -2.4e+278)
		tmp = b * c;
	elseif ((b * c) <= -1.8e-23)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif ((b * c) <= -3.8e-305)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= 1.16e+67)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 5.7e+147)
		tmp = x * (z * (y * (18.0 * t)));
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -2.4e+278], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.8e-23], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.8e-305], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.16e+67], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5.7e+147], N[(x * N[(z * N[(y * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -2.39999999999999985e278 or 5.69999999999999991e147 < (*.f64 b c)

   1. Initial program 78.6%

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

   3. Taylor expanded in x around 0 83.3%

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

   4. Taylor expanded in b around inf 72.5%

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

   if -2.39999999999999985e278 < (*.f64 b c) < -1.7999999999999999e-23

   1. Initial program 90.3%

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

      1. pow1 90.3%

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

      2. associate-*l* 84.6%

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

      3. *-commutative 84.6%

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

   4. Applied egg-rr 84.6%

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

      1. unpow1 84.6%

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

      2. associate-*r* 84.6%

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

      3. *-commutative 84.6%

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

      4. *-commutative 84.6%

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

      5. *-commutative 84.6%

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

   6. Simplified 84.6%

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

      1. associate-+l- 84.6%

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

      2. associate-*l* 84.6%

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

      3. *-commutative 84.6%

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

   8. Applied egg-rr 84.6%

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

   9. Taylor expanded in y around inf 38.2%

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

       1. *-commutative 38.2%

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

   11. Simplified 38.2%

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

   if -1.7999999999999999e-23 < (*.f64 b c) < -3.8e-305

   1. Initial program 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in x around inf 62.7%

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

   6. Taylor expanded in t around 0 45.1%

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

      1. *-commutative 45.1%

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

   8. Simplified 45.1%

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

   if -3.8e-305 < (*.f64 b c) < 1.15999999999999994e67

   1. Initial program 85.0%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in j around inf 33.8%

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

      1. associate-*r* 33.8%

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

      2. *-commutative 33.8%

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

      3. metadata-eval 33.8%

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

      4. distribute-rgt-neg-in 33.8%

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

      5. *-commutative 33.8%

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

      6. distribute-rgt-neg-in 33.8%

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

      7. metadata-eval 33.8%

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

      8. *-commutative 33.8%

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

   7. Simplified 33.8%

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

   if 1.15999999999999994e67 < (*.f64 b c) < 5.69999999999999991e147

   1. Initial program 83.9%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in x around inf 67.3%

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

   6. Taylor expanded in t around inf 67.3%

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

      1. pow1 67.3%

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

      2. associate-*r* 67.3%

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

   8. Applied egg-rr 67.3%

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

      1. unpow1 67.3%

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

      2. associate-*r* 67.3%

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

   10. Simplified 67.3%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.4 \cdot 10^{+278}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.8 \cdot 10^{-23}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -3.8 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.16 \cdot 10^{+67}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 5.7 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 36.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.3 \cdot 10^{+280}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.9 \cdot 10^{-18}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -1.5 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.85 \cdot 10^{+68}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.4 \cdot 10^{+143}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -3.3e+280)
   (* b c)
   (if (<= (* b c) -2.9e-18)
     (* 18.0 (* t (* x (* y z))))
     (if (<= (* b c) -1.5e-306)
       (* x (* i -4.0))
       (if (<= (* b c) 1.85e+68)
         (* k (* j -27.0))
         (if (<= (* b c) 1.4e+143) (* x (* z (* y (* 18.0 t)))) (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -3.3e+280) {
		tmp = b * c;
	} else if ((b * c) <= -2.9e-18) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= -1.5e-306) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 1.85e+68) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 1.4e+143) {
		tmp = x * (z * (y * (18.0 * t)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-3.3d+280)) then
        tmp = b * c
    else if ((b * c) <= (-2.9d-18)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if ((b * c) <= (-1.5d-306)) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= 1.85d+68) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 1.4d+143) then
        tmp = x * (z * (y * (18.0d0 * t)))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -3.3e+280) {
		tmp = b * c;
	} else if ((b * c) <= -2.9e-18) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= -1.5e-306) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 1.85e+68) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 1.4e+143) {
		tmp = x * (z * (y * (18.0 * t)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -3.3e+280:
		tmp = b * c
	elif (b * c) <= -2.9e-18:
		tmp = 18.0 * (t * (x * (y * z)))
	elif (b * c) <= -1.5e-306:
		tmp = x * (i * -4.0)
	elif (b * c) <= 1.85e+68:
		tmp = k * (j * -27.0)
	elif (b * c) <= 1.4e+143:
		tmp = x * (z * (y * (18.0 * t)))
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -3.3e+280)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.9e-18)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (Float64(b * c) <= -1.5e-306)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= 1.85e+68)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 1.4e+143)
		tmp = Float64(x * Float64(z * Float64(y * Float64(18.0 * t))));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -3.3e+280)
		tmp = b * c;
	elseif ((b * c) <= -2.9e-18)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif ((b * c) <= -1.5e-306)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= 1.85e+68)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 1.4e+143)
		tmp = x * (z * (y * (18.0 * t)));
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -3.3e+280], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.9e-18], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.5e-306], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.85e+68], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.4e+143], N[(x * N[(z * N[(y * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -3.30000000000000003e280 or 1.39999999999999999e143 < (*.f64 b c)

   1. Initial program 78.6%

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

   3. Taylor expanded in x around 0 83.3%

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

   4. Taylor expanded in b around inf 72.5%

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

   if -3.30000000000000003e280 < (*.f64 b c) < -2.9e-18

   1. Initial program 90.3%

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

   3. Taylor expanded in x around 0 85.1%

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

   4. Taylor expanded in y around inf 38.2%

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

   if -2.9e-18 < (*.f64 b c) < -1.50000000000000012e-306

   1. Initial program 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in x around inf 62.7%

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

   6. Taylor expanded in t around 0 45.1%

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

      1. *-commutative 45.1%

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

   8. Simplified 45.1%

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

   if -1.50000000000000012e-306 < (*.f64 b c) < 1.84999999999999999e68

   1. Initial program 85.0%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in j around inf 33.8%

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

      1. associate-*r* 33.8%

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

      2. *-commutative 33.8%

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

      3. metadata-eval 33.8%

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

      4. distribute-rgt-neg-in 33.8%

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

      5. *-commutative 33.8%

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

      6. distribute-rgt-neg-in 33.8%

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

      7. metadata-eval 33.8%

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

      8. *-commutative 33.8%

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

   7. Simplified 33.8%

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

   if 1.84999999999999999e68 < (*.f64 b c) < 1.39999999999999999e143

   1. Initial program 83.9%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in x around inf 67.3%

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

   6. Taylor expanded in t around inf 67.3%

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

      1. pow1 67.3%

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

      2. associate-*r* 67.3%

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

   8. Applied egg-rr 67.3%

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

      1. unpow1 67.3%

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

      2. associate-*r* 67.3%

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

   10. Simplified 67.3%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.3 \cdot 10^{+280}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.9 \cdot 10^{-18}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -1.5 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.85 \cdot 10^{+68}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.4 \cdot 10^{+143}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.4 \cdot 10^{+278}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.4 \cdot 10^{-19}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -4.3 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 8.8 \cdot 10^{+67}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 3.65 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -2.4e+278)
   (* b c)
   (if (<= (* b c) -3.4e-19)
     (* 18.0 (* t (* x (* y z))))
     (if (<= (* b c) -4.3e-305)
       (* x (* i -4.0))
       (if (<= (* b c) 8.8e+67)
         (* k (* j -27.0))
         (if (<= (* b c) 3.65e+144) (* x (* 18.0 (* t (* y z)))) (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2.4e+278) {
		tmp = b * c;
	} else if ((b * c) <= -3.4e-19) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= -4.3e-305) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 8.8e+67) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 3.65e+144) {
		tmp = x * (18.0 * (t * (y * z)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-2.4d+278)) then
        tmp = b * c
    else if ((b * c) <= (-3.4d-19)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if ((b * c) <= (-4.3d-305)) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= 8.8d+67) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 3.65d+144) then
        tmp = x * (18.0d0 * (t * (y * z)))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2.4e+278) {
		tmp = b * c;
	} else if ((b * c) <= -3.4e-19) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= -4.3e-305) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 8.8e+67) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 3.65e+144) {
		tmp = x * (18.0 * (t * (y * z)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -2.4e+278:
		tmp = b * c
	elif (b * c) <= -3.4e-19:
		tmp = 18.0 * (t * (x * (y * z)))
	elif (b * c) <= -4.3e-305:
		tmp = x * (i * -4.0)
	elif (b * c) <= 8.8e+67:
		tmp = k * (j * -27.0)
	elif (b * c) <= 3.65e+144:
		tmp = x * (18.0 * (t * (y * z)))
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -2.4e+278)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.4e-19)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (Float64(b * c) <= -4.3e-305)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= 8.8e+67)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 3.65e+144)
		tmp = Float64(x * Float64(18.0 * Float64(t * Float64(y * z))));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -2.4e+278)
		tmp = b * c;
	elseif ((b * c) <= -3.4e-19)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif ((b * c) <= -4.3e-305)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= 8.8e+67)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 3.65e+144)
		tmp = x * (18.0 * (t * (y * z)));
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -2.4e+278], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.4e-19], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -4.3e-305], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 8.8e+67], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.65e+144], N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -2.39999999999999985e278 or 3.6499999999999997e144 < (*.f64 b c)

   1. Initial program 78.6%

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

   3. Taylor expanded in x around 0 83.3%

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

   4. Taylor expanded in b around inf 72.5%

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

   if -2.39999999999999985e278 < (*.f64 b c) < -3.4000000000000002e-19

   1. Initial program 90.3%

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

   3. Taylor expanded in x around 0 85.1%

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

   4. Taylor expanded in y around inf 38.2%

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

   if -3.4000000000000002e-19 < (*.f64 b c) < -4.3000000000000002e-305

   1. Initial program 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in x around inf 62.7%

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

   6. Taylor expanded in t around 0 45.1%

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

      1. *-commutative 45.1%

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

   8. Simplified 45.1%

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

   if -4.3000000000000002e-305 < (*.f64 b c) < 8.8e67

   1. Initial program 85.0%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in j around inf 33.8%

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

      1. associate-*r* 33.8%

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

      2. *-commutative 33.8%

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

      3. metadata-eval 33.8%

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

      4. distribute-rgt-neg-in 33.8%

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

      5. *-commutative 33.8%

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

      6. distribute-rgt-neg-in 33.8%

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

      7. metadata-eval 33.8%

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

      8. *-commutative 33.8%

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

   7. Simplified 33.8%

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

   if 8.8e67 < (*.f64 b c) < 3.6499999999999997e144

   1. Initial program 83.9%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in x around inf 67.3%

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

   6. Taylor expanded in t around inf 67.3%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.4 \cdot 10^{+278}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.4 \cdot 10^{-19}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -4.3 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 8.8 \cdot 10^{+67}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 3.65 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-202}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-77}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-53} \lor \neg \left(t \leq 1.2 \cdot 10^{+63}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + i \cdot \left(x \cdot -4\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (* t (- (* 18.0 (* z (* x y))) (* a 4.0)))))
   (if (<= t -3.4e-38)
     t_2
     (if (<= t 6.2e-202)
       (- (* b c) (* x (* 4.0 i)))
       (if (<= t 1.6e-77)
         (+ (* b c) t_1)
         (if (or (<= t 2.9e-53) (not (<= t 1.2e+63)))
           t_2
           (+ t_1 (* i (* x -4.0)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	double tmp;
	if (t <= -3.4e-38) {
		tmp = t_2;
	} else if (t <= 6.2e-202) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 1.6e-77) {
		tmp = (b * c) + t_1;
	} else if ((t <= 2.9e-53) || !(t <= 1.2e+63)) {
		tmp = t_2;
	} else {
		tmp = t_1 + (i * (x * -4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t * ((18.0d0 * (z * (x * y))) - (a * 4.0d0))
    if (t <= (-3.4d-38)) then
        tmp = t_2
    else if (t <= 6.2d-202) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if (t <= 1.6d-77) then
        tmp = (b * c) + t_1
    else if ((t <= 2.9d-53) .or. (.not. (t <= 1.2d+63))) then
        tmp = t_2
    else
        tmp = t_1 + (i * (x * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	double tmp;
	if (t <= -3.4e-38) {
		tmp = t_2;
	} else if (t <= 6.2e-202) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 1.6e-77) {
		tmp = (b * c) + t_1;
	} else if ((t <= 2.9e-53) || !(t <= 1.2e+63)) {
		tmp = t_2;
	} else {
		tmp = t_1 + (i * (x * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t * ((18.0 * (z * (x * y))) - (a * 4.0))
	tmp = 0
	if t <= -3.4e-38:
		tmp = t_2
	elif t <= 6.2e-202:
		tmp = (b * c) - (x * (4.0 * i))
	elif t <= 1.6e-77:
		tmp = (b * c) + t_1
	elif (t <= 2.9e-53) or not (t <= 1.2e+63):
		tmp = t_2
	else:
		tmp = t_1 + (i * (x * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -3.4e-38)
		tmp = t_2;
	elseif (t <= 6.2e-202)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (t <= 1.6e-77)
		tmp = Float64(Float64(b * c) + t_1);
	elseif ((t <= 2.9e-53) || !(t <= 1.2e+63))
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(i * Float64(x * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -3.4e-38)
		tmp = t_2;
	elseif (t <= 6.2e-202)
		tmp = (b * c) - (x * (4.0 * i));
	elseif (t <= 1.6e-77)
		tmp = (b * c) + t_1;
	elseif ((t <= 2.9e-53) || ~((t <= 1.2e+63)))
		tmp = t_2;
	else
		tmp = t_1 + (i * (x * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e-38], t$95$2, If[LessEqual[t, 6.2e-202], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e-77], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[Or[LessEqual[t, 2.9e-53], N[Not[LessEqual[t, 1.2e+63]], $MachinePrecision]], t$95$2, N[(t$95$1 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.4000000000000002e-38 or 1.6e-77 < t < 2.8999999999999998e-53 or 1.2e63 < t

   1. Initial program 84.9%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in t around inf 70.9%

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

      1. pow1 70.9%

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

   7. Applied egg-rr 70.9%

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

      1. unpow1 70.9%

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

      2. associate-*r* 71.1%

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

   9. Simplified 71.1%

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

   if -3.4000000000000002e-38 < t < 6.2e-202

   1. Initial program 81.3%

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

   3. Taylor expanded in y around 0 89.5%

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

      1. distribute-lft-out 89.5%

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

      2. *-commutative 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in x around inf 86.7%

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

   7. Taylor expanded in j around 0 70.7%

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

   8. Taylor expanded in x around inf 69.2%

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

      1. associate-*r* 69.2%

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

      2. *-commutative 69.2%

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

   10. Simplified 69.2%

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

   if 6.2e-202 < t < 1.6e-77

   1. Initial program 88.3%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in b around inf 73.0%

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

   if 2.8999999999999998e-53 < t < 1.2e63

   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 87.6%

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

   5. Taylor expanded in i around inf 59.8%

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

      1. metadata-eval 59.8%

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

      2. distribute-lft-neg-in 59.8%

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

      3. *-commutative 59.8%

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

      4. associate-*r* 59.8%

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

      5. distribute-rgt-neg-in 59.8%

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

      6. distribute-rgt-neg-in 59.8%

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

      7. metadata-eval 59.8%

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

      8. *-commutative 59.8%

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

   7. Simplified 59.8%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-202}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-77}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-53} \lor \neg \left(t \leq 1.2 \cdot 10^{+63}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-206}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-77}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-53} \lor \neg \left(t \leq 1.8 \cdot 10^{+65}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 + i \cdot \left(x \cdot -4\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -1e-38)
     t_2
     (if (<= t 7e-206)
       (- (* b c) (* x (* 4.0 i)))
       (if (<= t 1.65e-77)
         (+ (* b c) t_1)
         (if (or (<= t 2.6e-53) (not (<= t 1.8e+65)))
           t_2
           (+ t_1 (* i (* x -4.0)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1e-38) {
		tmp = t_2;
	} else if (t <= 7e-206) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 1.65e-77) {
		tmp = (b * c) + t_1;
	} else if ((t <= 2.6e-53) || !(t <= 1.8e+65)) {
		tmp = t_2;
	} else {
		tmp = t_1 + (i * (x * -4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-1d-38)) then
        tmp = t_2
    else if (t <= 7d-206) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if (t <= 1.65d-77) then
        tmp = (b * c) + t_1
    else if ((t <= 2.6d-53) .or. (.not. (t <= 1.8d+65))) then
        tmp = t_2
    else
        tmp = t_1 + (i * (x * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1e-38) {
		tmp = t_2;
	} else if (t <= 7e-206) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 1.65e-77) {
		tmp = (b * c) + t_1;
	} else if ((t <= 2.6e-53) || !(t <= 1.8e+65)) {
		tmp = t_2;
	} else {
		tmp = t_1 + (i * (x * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -1e-38:
		tmp = t_2
	elif t <= 7e-206:
		tmp = (b * c) - (x * (4.0 * i))
	elif t <= 1.65e-77:
		tmp = (b * c) + t_1
	elif (t <= 2.6e-53) or not (t <= 1.8e+65):
		tmp = t_2
	else:
		tmp = t_1 + (i * (x * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -1e-38)
		tmp = t_2;
	elseif (t <= 7e-206)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (t <= 1.65e-77)
		tmp = Float64(Float64(b * c) + t_1);
	elseif ((t <= 2.6e-53) || !(t <= 1.8e+65))
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(i * Float64(x * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -1e-38)
		tmp = t_2;
	elseif (t <= 7e-206)
		tmp = (b * c) - (x * (4.0 * i));
	elseif (t <= 1.65e-77)
		tmp = (b * c) + t_1;
	elseif ((t <= 2.6e-53) || ~((t <= 1.8e+65)))
		tmp = t_2;
	else
		tmp = t_1 + (i * (x * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e-38], t$95$2, If[LessEqual[t, 7e-206], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e-77], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[Or[LessEqual[t, 2.6e-53], N[Not[LessEqual[t, 1.8e+65]], $MachinePrecision]], t$95$2, N[(t$95$1 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.9999999999999996e-39 or 1.64999999999999996e-77 < t < 2.59999999999999996e-53 or 1.79999999999999989e65 < t

   1. Initial program 84.9%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in t around inf 70.9%

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

   if -9.9999999999999996e-39 < t < 6.99999999999999979e-206

   1. Initial program 81.3%

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

   3. Taylor expanded in y around 0 89.5%

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

      1. distribute-lft-out 89.5%

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

      2. *-commutative 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in x around inf 86.7%

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

   7. Taylor expanded in j around 0 70.7%

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

   8. Taylor expanded in x around inf 69.2%

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

      1. associate-*r* 69.2%

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

      2. *-commutative 69.2%

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

   10. Simplified 69.2%

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

   if 6.99999999999999979e-206 < t < 1.64999999999999996e-77

   1. Initial program 88.3%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in b around inf 73.0%

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

   if 2.59999999999999996e-53 < t < 1.79999999999999989e65

   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 87.6%

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

   5. Taylor expanded in i around inf 59.8%

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

      1. metadata-eval 59.8%

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

      2. distribute-lft-neg-in 59.8%

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

      3. *-commutative 59.8%

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

      4. associate-*r* 59.8%

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

      5. distribute-rgt-neg-in 59.8%

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

      6. distribute-rgt-neg-in 59.8%

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

      7. metadata-eval 59.8%

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

      8. *-commutative 59.8%

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

   7. Simplified 59.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-206}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-77}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-53} \lor \neg \left(t \leq 1.8 \cdot 10^{+65}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+39}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-38} \lor \neg \left(t \leq 3.4 \cdot 10^{+64}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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 (<= t -6.4e+80)
   (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
   (if (<= t -3e+39)
     (+ (* 18.0 (* (* y z) (* x t))) (* j (* k -27.0)))
     (if (or (<= t -3.2e-38) (not (<= t 3.4e+64)))
       (* t (- (* 18.0 (* z (* x y))) (* a 4.0)))
       (- (- (* b c) (* 4.0 (* x i))) (* (* j 27.0) k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -6.4e+80) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -3e+39) {
		tmp = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0));
	} else if ((t <= -3.2e-38) || !(t <= 3.4e+64)) {
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-6.4d+80)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= (-3d+39)) then
        tmp = (18.0d0 * ((y * z) * (x * t))) + (j * (k * (-27.0d0)))
    else if ((t <= (-3.2d-38)) .or. (.not. (t <= 3.4d+64))) then
        tmp = t * ((18.0d0 * (z * (x * y))) - (a * 4.0d0))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -6.4e+80) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -3e+39) {
		tmp = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0));
	} else if ((t <= -3.2e-38) || !(t <= 3.4e+64)) {
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -6.4e+80:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= -3e+39:
		tmp = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0))
	elif (t <= -3.2e-38) or not (t <= 3.4e+64):
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -6.4e+80)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= -3e+39)
		tmp = Float64(Float64(18.0 * Float64(Float64(y * z) * Float64(x * t))) + Float64(j * Float64(k * -27.0)));
	elseif ((t <= -3.2e-38) || !(t <= 3.4e+64))
		tmp = Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) - Float64(a * 4.0)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -6.4e+80)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= -3e+39)
		tmp = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0));
	elseif ((t <= -3.2e-38) || ~((t <= 3.4e+64)))
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -6.4e+80], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3e+39], N[(N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -3.2e-38], N[Not[LessEqual[t, 3.4e+64]], $MachinePrecision]], N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.39999999999999979e80

   1. Initial program 86.8%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in t around inf 83.4%

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

   if -6.39999999999999979e80 < t < -3e39

   1. Initial program 90.6%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in y around inf 72.4%

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

      1. associate-*r* 81.2%

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

   7. Simplified 81.2%

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

   if -3e39 < t < -3.19999999999999977e-38 or 3.4000000000000002e64 < t

   1. Initial program 83.0%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in t around inf 67.9%

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

      1. pow1 67.9%

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

   7. Applied egg-rr 67.9%

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

      1. unpow1 67.9%

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

      2. associate-*r* 68.2%

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

   9. Simplified 68.2%

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

   if -3.19999999999999977e-38 < t < 3.4000000000000002e64

   1. Initial program 84.7%

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

   3. Taylor expanded in t around 0 82.0%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+39}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-38} \lor \neg \left(t \leq 3.4 \cdot 10^{+64}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;z \leq 3.3 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+80}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;z \leq 2.02 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) (* (* j 27.0) k))))
   (if (<= z 3.3e+48)
     t_1
     (if (<= z 3.1e+80)
       (+ (* 18.0 (* (* y z) (* x t))) (* j (* k -27.0)))
       (if (<= z 2.02e+164) t_1 (* t (- (* 18.0 (* z (* x y))) (* a 4.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	double tmp;
	if (z <= 3.3e+48) {
		tmp = t_1;
	} else if (z <= 3.1e+80) {
		tmp = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0));
	} else if (z <= 2.02e+164) {
		tmp = t_1;
	} else {
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - ((j * 27.0d0) * k)
    if (z <= 3.3d+48) then
        tmp = t_1
    else if (z <= 3.1d+80) then
        tmp = (18.0d0 * ((y * z) * (x * t))) + (j * (k * (-27.0d0)))
    else if (z <= 2.02d+164) then
        tmp = t_1
    else
        tmp = t * ((18.0d0 * (z * (x * y))) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	double tmp;
	if (z <= 3.3e+48) {
		tmp = t_1;
	} else if (z <= 3.1e+80) {
		tmp = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0));
	} else if (z <= 2.02e+164) {
		tmp = t_1;
	} else {
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k)
	tmp = 0
	if z <= 3.3e+48:
		tmp = t_1
	elif z <= 3.1e+80:
		tmp = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0))
	elif z <= 2.02e+164:
		tmp = t_1
	else:
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (z <= 3.3e+48)
		tmp = t_1;
	elseif (z <= 3.1e+80)
		tmp = Float64(Float64(18.0 * Float64(Float64(y * z) * Float64(x * t))) + Float64(j * Float64(k * -27.0)));
	elseif (z <= 2.02e+164)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	tmp = 0.0;
	if (z <= 3.3e+48)
		tmp = t_1;
	elseif (z <= 3.1e+80)
		tmp = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0));
	elseif (z <= 2.02e+164)
		tmp = t_1;
	else
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 3.3e+48], t$95$1, If[LessEqual[z, 3.1e+80], N[(N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.02e+164], t$95$1, N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < 3.30000000000000023e48 or 3.09999999999999988e80 < z < 2.02e164

   1. Initial program 85.9%

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

   3. Taylor expanded in y around 0 79.1%

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

      1. distribute-lft-out 79.1%

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

      2. *-commutative 79.1%

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

   5. Simplified 79.1%

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

   if 3.30000000000000023e48 < z < 3.09999999999999988e80

   1. Initial program 83.3%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 99.7%

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

      1. associate-*r* 99.7%

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

   7. Simplified 99.7%

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

   if 2.02e164 < z

   1. Initial program 76.9%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in t around inf 77.3%

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

      1. pow1 77.3%

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

   7. Applied egg-rr 77.3%

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

      1. unpow1 77.3%

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

      2. associate-*r* 77.2%

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

   9. Simplified 77.2%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.3 \cdot 10^{+48}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+80}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;z \leq 2.02 \cdot 10^{+164}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) + j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+164}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* 18.0 (* (* y z) (* x t))) (* j (* k -27.0))))
        (t_2 (- (* b c) (* 4.0 (+ (* t a) (* x i))))))
   (if (<= z -1.3e-85)
     t_1
     (if (<= z 2.35e+48)
       t_2
       (if (<= z 6e+86)
         t_1
         (if (<= z 4.3e+164)
           t_2
           (* t (- (* 18.0 (* z (* x y))) (* a 4.0)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0));
	double t_2 = (b * c) - (4.0 * ((t * a) + (x * i)));
	double tmp;
	if (z <= -1.3e-85) {
		tmp = t_1;
	} else if (z <= 2.35e+48) {
		tmp = t_2;
	} else if (z <= 6e+86) {
		tmp = t_1;
	} else if (z <= 4.3e+164) {
		tmp = t_2;
	} else {
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (18.0d0 * ((y * z) * (x * t))) + (j * (k * (-27.0d0)))
    t_2 = (b * c) - (4.0d0 * ((t * a) + (x * i)))
    if (z <= (-1.3d-85)) then
        tmp = t_1
    else if (z <= 2.35d+48) then
        tmp = t_2
    else if (z <= 6d+86) then
        tmp = t_1
    else if (z <= 4.3d+164) then
        tmp = t_2
    else
        tmp = t * ((18.0d0 * (z * (x * y))) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0));
	double t_2 = (b * c) - (4.0 * ((t * a) + (x * i)));
	double tmp;
	if (z <= -1.3e-85) {
		tmp = t_1;
	} else if (z <= 2.35e+48) {
		tmp = t_2;
	} else if (z <= 6e+86) {
		tmp = t_1;
	} else if (z <= 4.3e+164) {
		tmp = t_2;
	} else {
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0))
	t_2 = (b * c) - (4.0 * ((t * a) + (x * i)))
	tmp = 0
	if z <= -1.3e-85:
		tmp = t_1
	elif z <= 2.35e+48:
		tmp = t_2
	elif z <= 6e+86:
		tmp = t_1
	elif z <= 4.3e+164:
		tmp = t_2
	else:
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(18.0 * Float64(Float64(y * z) * Float64(x * t))) + Float64(j * Float64(k * -27.0)))
	t_2 = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i))))
	tmp = 0.0
	if (z <= -1.3e-85)
		tmp = t_1;
	elseif (z <= 2.35e+48)
		tmp = t_2;
	elseif (z <= 6e+86)
		tmp = t_1;
	elseif (z <= 4.3e+164)
		tmp = t_2;
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (18.0 * ((y * z) * (x * t))) + (j * (k * -27.0));
	t_2 = (b * c) - (4.0 * ((t * a) + (x * i)));
	tmp = 0.0;
	if (z <= -1.3e-85)
		tmp = t_1;
	elseif (z <= 2.35e+48)
		tmp = t_2;
	elseif (z <= 6e+86)
		tmp = t_1;
	elseif (z <= 4.3e+164)
		tmp = t_2;
	else
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e-85], t$95$1, If[LessEqual[z, 2.35e+48], t$95$2, If[LessEqual[z, 6e+86], t$95$1, If[LessEqual[z, 4.3e+164], t$95$2, N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.30000000000000006e-85 or 2.35000000000000006e48 < z < 5.99999999999999954e86

   1. Initial program 83.3%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in y around inf 50.9%

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

      1. associate-*r* 54.2%

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

   7. Simplified 54.2%

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

   if -1.30000000000000006e-85 < z < 2.35000000000000006e48 or 5.99999999999999954e86 < z < 4.3e164

   1. Initial program 87.4%

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

   3. Taylor expanded in y around 0 84.3%

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

      1. distribute-lft-out 84.3%

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

      2. *-commutative 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in j around 0 69.1%

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

   if 4.3e164 < z

   1. Initial program 76.9%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in t around inf 77.3%

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

      1. pow1 77.3%

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

   7. Applied egg-rr 77.3%

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

      1. unpow1 77.3%

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

      2. associate-*r* 77.2%

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

   9. Simplified 77.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-85}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+48}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+86}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+164}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.4 \cdot 10^{+278}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.3 \cdot 10^{-17}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -5.4 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 4.4 \cdot 10^{+74}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -2.4e+278)
   (* b c)
   (if (<= (* b c) -2.3e-17)
     (* 18.0 (* t (* x (* y z))))
     (if (<= (* b c) -5.4e-305)
       (* x (* i -4.0))
       (if (<= (* b c) 4.4e+74) (* -27.0 (* j k)) (* b c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2.4e+278) {
		tmp = b * c;
	} else if ((b * c) <= -2.3e-17) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= -5.4e-305) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 4.4e+74) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-2.4d+278)) then
        tmp = b * c
    else if ((b * c) <= (-2.3d-17)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if ((b * c) <= (-5.4d-305)) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= 4.4d+74) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2.4e+278) {
		tmp = b * c;
	} else if ((b * c) <= -2.3e-17) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= -5.4e-305) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 4.4e+74) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -2.4e+278:
		tmp = b * c
	elif (b * c) <= -2.3e-17:
		tmp = 18.0 * (t * (x * (y * z)))
	elif (b * c) <= -5.4e-305:
		tmp = x * (i * -4.0)
	elif (b * c) <= 4.4e+74:
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -2.4e+278)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.3e-17)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (Float64(b * c) <= -5.4e-305)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= 4.4e+74)
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -2.4e+278)
		tmp = b * c;
	elseif ((b * c) <= -2.3e-17)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif ((b * c) <= -5.4e-305)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= 4.4e+74)
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -2.4e+278], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.3e-17], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5.4e-305], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.4e+74], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.39999999999999985e278 or 4.4000000000000002e74 < (*.f64 b c)

   1. Initial program 78.7%

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

   3. Taylor expanded in x around 0 84.1%

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

   4. Taylor expanded in b around inf 66.2%

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

   if -2.39999999999999985e278 < (*.f64 b c) < -2.30000000000000009e-17

   1. Initial program 90.3%

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

   3. Taylor expanded in x around 0 85.1%

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

   4. Taylor expanded in y around inf 38.2%

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

   if -2.30000000000000009e-17 < (*.f64 b c) < -5.3999999999999998e-305

   1. Initial program 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in x around inf 62.7%

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

   6. Taylor expanded in t around 0 45.1%

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

      1. *-commutative 45.1%

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

   8. Simplified 45.1%

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

   if -5.3999999999999998e-305 < (*.f64 b c) < 4.4000000000000002e74

   1. Initial program 85.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in j around inf 33.8%

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

Alternative 13: 83.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{-92} \lor \neg \left(x \leq 1.42 \cdot 10^{+21}\right):\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= x -2.2e-92) (not (<= x 1.42e+21)))
     (- (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))) t_1)
     (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((x <= -2.2e-92) || !(x <= 1.42e+21)) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((x <= (-2.2d-92)) .or. (.not. (x <= 1.42d+21))) then
        tmp = ((b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))) - t_1
    else
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((x <= -2.2e-92) || !(x <= 1.42e+21)) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (x <= -2.2e-92) or not (x <= 1.42e+21):
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1
	else:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((x <= -2.2e-92) || !(x <= 1.42e+21))
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((x <= -2.2e-92) || ~((x <= 1.42e+21)))
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1;
	else
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[x, -2.2e-92], N[Not[LessEqual[x, 1.42e+21]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.19999999999999987e-92 or 1.42e21 < x

   1. Initial program 78.4%

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

   3. Taylor expanded in x around 0 88.4%

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

   4. Taylor expanded in a around 0 83.1%

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

   if -2.19999999999999987e-92 < x < 1.42e21

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0 92.1%

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

      1. distribute-lft-out 92.1%

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

      2. *-commutative 92.1%

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

   5. Simplified 92.1%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-92} \lor \neg \left(x \leq 1.42 \cdot 10^{+21}\right):\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-282}:\\ \;\;\;\;-4 \cdot \left(x \cdot \left(i + \frac{t \cdot a}{x}\right)\right)\\ \mathbf{elif}\;y \leq 0.095:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* k -27.0)))))
   (if (<= y -2.7e+170)
     (* x (* 18.0 (* t (* y z))))
     (if (<= y -4.6e-28)
       t_1
       (if (<= y 1.6e-282)
         (* -4.0 (* x (+ i (/ (* t a) x))))
         (if (<= y 0.095) t_1 (* x (* z (* y (* 18.0 t))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (y <= -2.7e+170) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if (y <= -4.6e-28) {
		tmp = t_1;
	} else if (y <= 1.6e-282) {
		tmp = -4.0 * (x * (i + ((t * a) / x)));
	} else if (y <= 0.095) {
		tmp = t_1;
	} else {
		tmp = x * (z * (y * (18.0 * t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    if (y <= (-2.7d+170)) then
        tmp = x * (18.0d0 * (t * (y * z)))
    else if (y <= (-4.6d-28)) then
        tmp = t_1
    else if (y <= 1.6d-282) then
        tmp = (-4.0d0) * (x * (i + ((t * a) / x)))
    else if (y <= 0.095d0) then
        tmp = t_1
    else
        tmp = x * (z * (y * (18.0d0 * t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (y <= -2.7e+170) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if (y <= -4.6e-28) {
		tmp = t_1;
	} else if (y <= 1.6e-282) {
		tmp = -4.0 * (x * (i + ((t * a) / x)));
	} else if (y <= 0.095) {
		tmp = t_1;
	} else {
		tmp = x * (z * (y * (18.0 * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if y <= -2.7e+170:
		tmp = x * (18.0 * (t * (y * z)))
	elif y <= -4.6e-28:
		tmp = t_1
	elif y <= 1.6e-282:
		tmp = -4.0 * (x * (i + ((t * a) / x)))
	elif y <= 0.095:
		tmp = t_1
	else:
		tmp = x * (z * (y * (18.0 * t)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (y <= -2.7e+170)
		tmp = Float64(x * Float64(18.0 * Float64(t * Float64(y * z))));
	elseif (y <= -4.6e-28)
		tmp = t_1;
	elseif (y <= 1.6e-282)
		tmp = Float64(-4.0 * Float64(x * Float64(i + Float64(Float64(t * a) / x))));
	elseif (y <= 0.095)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(z * Float64(y * Float64(18.0 * t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (y <= -2.7e+170)
		tmp = x * (18.0 * (t * (y * z)));
	elseif (y <= -4.6e-28)
		tmp = t_1;
	elseif (y <= 1.6e-282)
		tmp = -4.0 * (x * (i + ((t * a) / x)));
	elseif (y <= 0.095)
		tmp = t_1;
	else
		tmp = x * (z * (y * (18.0 * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+170], N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.6e-28], t$95$1, If[LessEqual[y, 1.6e-282], N[(-4.0 * N[(x * N[(i + N[(N[(t * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.095], t$95$1, N[(x * N[(z * N[(y * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7000000000000002e170

   1. Initial program 83.9%

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

   3. Simplified 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. Taylor expanded in x around inf 65.9%

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

   6. Taylor expanded in t around inf 60.4%

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

   if -2.7000000000000002e170 < y < -4.59999999999999971e-28 or 1.59999999999999991e-282 < y < 0.095000000000000001

   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%

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

   5. Taylor expanded in b around inf 59.3%

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

   if -4.59999999999999971e-28 < y < 1.59999999999999991e-282

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0 92.2%

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

      1. distribute-lft-out 92.2%

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

      2. *-commutative 92.2%

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

   5. Simplified 92.2%

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

   6. Taylor expanded in x around inf 84.9%

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

   7. Taylor expanded in j around 0 73.5%

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

   8. Taylor expanded in b around 0 64.1%

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

   if 0.095000000000000001 < y

   1. Initial program 80.2%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in x around inf 54.1%

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

   6. Taylor expanded in t around inf 37.3%

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

      1. pow1 37.3%

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

      2. associate-*r* 37.3%

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

   8. Applied egg-rr 37.3%

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

      1. unpow1 37.3%

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

      2. associate-*r* 40.0%

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

   10. Simplified 40.0%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-28}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-282}:\\ \;\;\;\;-4 \cdot \left(x \cdot \left(i + \frac{t \cdot a}{x}\right)\right)\\ \mathbf{elif}\;y \leq 0.095:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 47.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-277}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;y \leq 2200:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* k -27.0)))))
   (if (<= y -2.15e+170)
     (* x (* 18.0 (* t (* y z))))
     (if (<= y -2e+22)
       t_1
       (if (<= y -3.2e-277)
         (- (* b c) (* x (* 4.0 i)))
         (if (<= y 2200.0) t_1 (* x (* z (* y (* 18.0 t))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (y <= -2.15e+170) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if (y <= -2e+22) {
		tmp = t_1;
	} else if (y <= -3.2e-277) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (y <= 2200.0) {
		tmp = t_1;
	} else {
		tmp = x * (z * (y * (18.0 * t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    if (y <= (-2.15d+170)) then
        tmp = x * (18.0d0 * (t * (y * z)))
    else if (y <= (-2d+22)) then
        tmp = t_1
    else if (y <= (-3.2d-277)) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if (y <= 2200.0d0) then
        tmp = t_1
    else
        tmp = x * (z * (y * (18.0d0 * t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (y <= -2.15e+170) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if (y <= -2e+22) {
		tmp = t_1;
	} else if (y <= -3.2e-277) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (y <= 2200.0) {
		tmp = t_1;
	} else {
		tmp = x * (z * (y * (18.0 * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if y <= -2.15e+170:
		tmp = x * (18.0 * (t * (y * z)))
	elif y <= -2e+22:
		tmp = t_1
	elif y <= -3.2e-277:
		tmp = (b * c) - (x * (4.0 * i))
	elif y <= 2200.0:
		tmp = t_1
	else:
		tmp = x * (z * (y * (18.0 * t)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (y <= -2.15e+170)
		tmp = Float64(x * Float64(18.0 * Float64(t * Float64(y * z))));
	elseif (y <= -2e+22)
		tmp = t_1;
	elseif (y <= -3.2e-277)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (y <= 2200.0)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(z * Float64(y * Float64(18.0 * t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (y <= -2.15e+170)
		tmp = x * (18.0 * (t * (y * z)));
	elseif (y <= -2e+22)
		tmp = t_1;
	elseif (y <= -3.2e-277)
		tmp = (b * c) - (x * (4.0 * i));
	elseif (y <= 2200.0)
		tmp = t_1;
	else
		tmp = x * (z * (y * (18.0 * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.15e+170], N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e+22], t$95$1, If[LessEqual[y, -3.2e-277], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2200.0], t$95$1, N[(x * N[(z * N[(y * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.1499999999999999e170

   1. Initial program 83.9%

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

   3. Simplified 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. Taylor expanded in x around inf 65.9%

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

   6. Taylor expanded in t around inf 60.4%

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

   if -2.1499999999999999e170 < y < -2e22 or -3.1999999999999998e-277 < y < 2200

   1. Initial program 85.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in b around inf 54.2%

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

   if -2e22 < y < -3.1999999999999998e-277

   1. Initial program 91.8%

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

   3. Taylor expanded in y around 0 91.7%

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

      1. distribute-lft-out 91.7%

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

      2. *-commutative 91.7%

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

   5. Simplified 91.7%

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

   6. Taylor expanded in x around inf 89.8%

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

   7. Taylor expanded in j around 0 75.7%

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

   8. Taylor expanded in x around inf 57.9%

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

      1. associate-*r* 57.9%

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

      2. *-commutative 57.9%

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

   10. Simplified 57.9%

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

   if 2200 < y

   1. Initial program 79.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in x around inf 55.0%

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

   6. Taylor expanded in t around inf 37.4%

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

      1. pow1 37.4%

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

      2. associate-*r* 37.4%

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

   8. Applied egg-rr 37.4%

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

      1. unpow1 37.4%

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

      2. associate-*r* 40.1%

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

   10. Simplified 40.1%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+22}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-277}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;y \leq 2200:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.95 \cdot 10^{+76}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.35 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+73}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1.95e+76)
   (* b c)
   (if (<= (* b c) -1.35e-306)
     (* x (* i -4.0))
     (if (<= (* b c) 5e+73) (* -27.0 (* j k)) (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.95e+76) {
		tmp = b * c;
	} else if ((b * c) <= -1.35e-306) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 5e+73) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-1.95d+76)) then
        tmp = b * c
    else if ((b * c) <= (-1.35d-306)) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= 5d+73) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.95e+76) {
		tmp = b * c;
	} else if ((b * c) <= -1.35e-306) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 5e+73) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.95e+76:
		tmp = b * c
	elif (b * c) <= -1.35e-306:
		tmp = x * (i * -4.0)
	elif (b * c) <= 5e+73:
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1.95e+76)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.35e-306)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= 5e+73)
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1.95e+76)
		tmp = b * c;
	elseif ((b * c) <= -1.35e-306)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= 5e+73)
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1.95e+76], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.35e-306], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+73], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.94999999999999995e76 or 4.99999999999999976e73 < (*.f64 b c)

   1. Initial program 81.4%

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

   3. Taylor expanded in x around 0 84.2%

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

   4. Taylor expanded in b around inf 52.2%

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

   if -1.94999999999999995e76 < (*.f64 b c) < -1.35000000000000005e-306

   1. Initial program 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in x around inf 56.8%

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

   6. Taylor expanded in t around 0 36.3%

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

      1. *-commutative 36.3%

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

   8. Simplified 36.3%

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

   if -1.35000000000000005e-306 < (*.f64 b c) < 4.99999999999999976e73

   1. Initial program 85.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in j around inf 33.8%

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

Alternative 17: 47.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -9.6e+203)
   (* x (* 18.0 (* t (* y z))))
   (if (<= x -1.9e+144)
     (* x (* i -4.0))
     (if (<= x 8.2e+26)
       (+ (* b c) (* j (* k -27.0)))
       (* 18.0 (* t (* x (* y z))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -9.6e+203) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if (x <= -1.9e+144) {
		tmp = x * (i * -4.0);
	} else if (x <= 8.2e+26) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = 18.0 * (t * (x * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-9.6d+203)) then
        tmp = x * (18.0d0 * (t * (y * z)))
    else if (x <= (-1.9d+144)) then
        tmp = x * (i * (-4.0d0))
    else if (x <= 8.2d+26) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = 18.0d0 * (t * (x * (y * z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -9.6e+203) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if (x <= -1.9e+144) {
		tmp = x * (i * -4.0);
	} else if (x <= 8.2e+26) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = 18.0 * (t * (x * (y * z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -9.6e+203:
		tmp = x * (18.0 * (t * (y * z)))
	elif x <= -1.9e+144:
		tmp = x * (i * -4.0)
	elif x <= 8.2e+26:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = 18.0 * (t * (x * (y * z)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -9.6e+203)
		tmp = Float64(x * Float64(18.0 * Float64(t * Float64(y * z))));
	elseif (x <= -1.9e+144)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (x <= 8.2e+26)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -9.6e+203)
		tmp = x * (18.0 * (t * (y * z)));
	elseif (x <= -1.9e+144)
		tmp = x * (i * -4.0);
	elseif (x <= 8.2e+26)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = 18.0 * (t * (x * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -9.6e+203], N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.9e+144], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e+26], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.6000000000000004e203

   1. Initial program 74.1%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in x around inf 70.5%

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

   6. Taylor expanded in t around inf 49.3%

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

   if -9.6000000000000004e203 < x < -1.90000000000000013e144

   1. Initial program 55.2%

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

   3. Simplified 55.2%

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

   5. Taylor expanded in x around inf 90.9%

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

   6. Taylor expanded in t around 0 81.8%

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

      1. *-commutative 81.8%

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

   8. Simplified 81.8%

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

   if -1.90000000000000013e144 < x < 8.19999999999999967e26

   1. Initial program 92.8%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in b around inf 51.2%

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

   if 8.19999999999999967e26 < x

   1. Initial program 75.8%

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

      1. pow1 75.8%

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

      2. associate-*l* 72.6%

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

      3. *-commutative 72.6%

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

   4. Applied egg-rr 72.6%

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

      1. unpow1 72.6%

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

      2. associate-*r* 72.6%

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

      3. *-commutative 72.6%

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

      4. *-commutative 72.6%

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

      5. *-commutative 72.6%

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

   6. Simplified 72.6%

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

      1. associate-+l- 72.6%

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

      2. associate-*l* 72.6%

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

      3. *-commutative 72.6%

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

   8. Applied egg-rr 72.6%

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

   9. Taylor expanded in y around inf 48.1%

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

       1. *-commutative 48.1%

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

   11. Simplified 48.1%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 62.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.029 \lor \neg \left(z \leq 1.8 \cdot 10^{+164}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= z -0.029) (not (<= z 1.8e+164)))
   (* t (- (* 18.0 (* z (* x y))) (* a 4.0)))
   (- (* b c) (* 4.0 (+ (* t a) (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 ((z <= -0.029) || !(z <= 1.8e+164)) {
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	} else {
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 ((z <= (-0.029d0)) .or. (.not. (z <= 1.8d+164))) then
        tmp = t * ((18.0d0 * (z * (x * y))) - (a * 4.0d0))
    else
        tmp = (b * c) - (4.0d0 * ((t * a) + (x * i)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 ((z <= -0.029) || !(z <= 1.8e+164)) {
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	} else {
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (z <= -0.029) or not (z <= 1.8e+164):
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0))
	else:
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((z <= -0.029) || !(z <= 1.8e+164))
		tmp = Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) - Float64(a * 4.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((z <= -0.029) || ~((z <= 1.8e+164)))
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	else
		tmp = (b * c) - (4.0 * ((t * a) + (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[z, -0.029], N[Not[LessEqual[z, 1.8e+164]], $MachinePrecision]], N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0290000000000000015 or 1.79999999999999995e164 < z

   1. Initial program 80.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in t around inf 54.2%

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

      1. pow1 54.2%

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

   7. Applied egg-rr 54.2%

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

      1. unpow1 54.2%

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

      2. associate-*r* 54.4%

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

   9. Simplified 54.4%

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

   if -0.0290000000000000015 < z < 1.79999999999999995e164

   1. Initial program 87.7%

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

   3. Taylor expanded in y around 0 82.5%

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

      1. distribute-lft-out 82.5%

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

      2. *-commutative 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in j around 0 66.9%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.029 \lor \neg \left(z \leq 1.8 \cdot 10^{+164}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 31.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+116}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-253}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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 -2.2e+116)
   (* b c)
   (if (<= b -9.8e-253)
     (* k (* j -27.0))
     (if (<= b 3.4e-60) (* t (* a -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 <= -2.2e+116) {
		tmp = b * c;
	} else if (b <= -9.8e-253) {
		tmp = k * (j * -27.0);
	} else if (b <= 3.4e-60) {
		tmp = t * (a * -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 <= (-2.2d+116)) then
        tmp = b * c
    else if (b <= (-9.8d-253)) then
        tmp = k * (j * (-27.0d0))
    else if (b <= 3.4d-60) then
        tmp = t * (a * (-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 <= -2.2e+116) {
		tmp = b * c;
	} else if (b <= -9.8e-253) {
		tmp = k * (j * -27.0);
	} else if (b <= 3.4e-60) {
		tmp = t * (a * -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 <= -2.2e+116:
		tmp = b * c
	elif b <= -9.8e-253:
		tmp = k * (j * -27.0)
	elif b <= 3.4e-60:
		tmp = t * (a * -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 <= -2.2e+116)
		tmp = Float64(b * c);
	elseif (b <= -9.8e-253)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (b <= 3.4e-60)
		tmp = Float64(t * Float64(a * -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 <= -2.2e+116)
		tmp = b * c;
	elseif (b <= -9.8e-253)
		tmp = k * (j * -27.0);
	elseif (b <= 3.4e-60)
		tmp = t * (a * -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, -2.2e+116], N[(b * c), $MachinePrecision], If[LessEqual[b, -9.8e-253], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e-60], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.2e116 or 3.40000000000000007e-60 < b

   1. Initial program 82.0%

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

   3. Taylor expanded in x around 0 82.9%

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

   4. Taylor expanded in b around inf 40.8%

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

   if -2.2e116 < b < -9.7999999999999999e-253

   1. Initial program 88.9%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in j around inf 31.2%

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

      1. associate-*r* 31.2%

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

      2. *-commutative 31.2%

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

      3. metadata-eval 31.2%

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

      4. distribute-rgt-neg-in 31.2%

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

      5. *-commutative 31.2%

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

      6. distribute-rgt-neg-in 31.2%

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

      7. metadata-eval 31.2%

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

      8. *-commutative 31.2%

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

   7. Simplified 31.2%

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

   if -9.7999999999999999e-253 < b < 3.40000000000000007e-60

   1. Initial program 84.7%

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

   3. Taylor expanded in x around 0 89.0%

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

   4. Taylor expanded in a around inf 31.4%

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

      1. associate-*r* 31.4%

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

      2. metadata-eval 31.4%

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

      3. distribute-lft-neg-in 31.4%

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

      4. distribute-lft-neg-in 31.4%

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

      5. *-commutative 31.4%

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

      6. distribute-rgt-neg-in 31.4%

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

      7. distribute-lft-neg-in 31.4%

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

      8. metadata-eval 31.4%

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

      9. *-commutative 31.4%

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

   6. Simplified 31.4%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+116}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-253}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+73} \lor \neg \left(b \cdot c \leq 4.6 \cdot 10^{+75}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -1e+73) (not (<= (* b c) 4.6e+75)))
   (* 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 * c) <= -1e+73) || !((b * c) <= 4.6e+75)) {
		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 * c) <= (-1d+73)) .or. (.not. ((b * c) <= 4.6d+75))) 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 * c) <= -1e+73) || !((b * c) <= 4.6e+75)) {
		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 * c) <= -1e+73) or not ((b * c) <= 4.6e+75):
		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 ((Float64(b * c) <= -1e+73) || !(Float64(b * c) <= 4.6e+75))
		tmp = Float64(b * c);
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -1e+73) || ~(((b * c) <= 4.6e+75)))
		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[N[(b * c), $MachinePrecision], -1e+73], N[Not[LessEqual[N[(b * c), $MachinePrecision], 4.6e+75]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -9.99999999999999983e72 or 4.5999999999999997e75 < (*.f64 b c)

   1. Initial program 81.6%

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

   3. Taylor expanded in x around 0 84.4%

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

   4. Taylor expanded in b around inf 51.8%

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

   if -9.99999999999999983e72 < (*.f64 b c) < 4.5999999999999997e75

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0 89.8%

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

   4. Taylor expanded in j around inf 27.7%

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

      1. metadata-eval 27.7%

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

      2. distribute-lft-neg-in 27.7%

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

      3. *-commutative 27.7%

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

      4. associate-*l* 27.7%

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

      5. *-commutative 27.7%

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

      6. distribute-rgt-neg-in 27.7%

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

      7. distribute-lft-neg-in 27.7%

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

      8. metadata-eval 27.7%

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

      9. *-commutative 27.7%

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

   6. Simplified 27.7%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+73} \lor \neg \left(b \cdot c \leq 4.6 \cdot 10^{+75}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 37.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+73} \lor \neg \left(b \cdot c \leq 8.2 \cdot 10^{+75}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -1e+73) (not (<= (* b c) 8.2e+75)))
   (* b c)
   (* -27.0 (* j k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -1e+73) || !((b * c) <= 8.2e+75)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-1d+73)) .or. (.not. ((b * c) <= 8.2d+75))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -1e+73) || !((b * c) <= 8.2e+75)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -1e+73) or not ((b * c) <= 8.2e+75):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -1e+73) || !(Float64(b * c) <= 8.2e+75))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -1e+73) || ~(((b * c) <= 8.2e+75)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -1e+73], N[Not[LessEqual[N[(b * c), $MachinePrecision], 8.2e+75]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -9.99999999999999983e72 or 8.1999999999999997e75 < (*.f64 b c)

   1. Initial program 81.6%

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

   3. Taylor expanded in x around 0 84.4%

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

   4. Taylor expanded in b around inf 51.8%

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

   if -9.99999999999999983e72 < (*.f64 b c) < 8.1999999999999997e75

   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 90.2%

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

   5. Taylor expanded in j around inf 27.7%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+73} \lor \neg \left(b \cdot c \leq 8.2 \cdot 10^{+75}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 23.5% 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 84.9%

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

3. Taylor expanded in x around 0 87.6%

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

4. Taylor expanded in b around inf 23.5%

   \[\leadsto \color{blue}{b \cdot c} \]
5. Add Preprocessing

Developer target: 88.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024103 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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