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

Percentage Accurate: 84.0% → 89.1%

Time: 41.3s

Alternatives: 25

Speedup: 0.8×

• 51.6% 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: 84.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.1%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0 26.9%

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

   4. Taylor expanded in j around 0 65.4%

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

4. Final simplification 92.1%

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

Alternative 2: 61.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\\ t_3 := x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -48000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-51}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-220}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-299}:\\ \;\;\;\;t\_1 + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-131}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;t\_1 + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+122}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 (* k -27.0)))
        (t_2 (- (* b c) (+ (* 4.0 (* t a)) (* 4.0 (* x i)))))
        (t_3 (* x (- (* 18.0 (* z (* y t))) (* 4.0 i)))))
   (if (<= x -48000000000.0)
     t_3
     (if (<= x -4.2e-51)
       (+ (* b c) t_1)
       (if (<= x -1.55e-220)
         t_2
         (if (<= x 3e-299)
           (+ t_1 (* (* t a) -4.0))
           (if (<= x 2.9e-131)
             t_2
             (if (<= x 3.8e-77)
               (+ t_1 (* 18.0 (* t (* x (* y z)))))
               (if (<= x 1.7e+122) 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 * (k * -27.0);
	double t_2 = (b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)));
	double t_3 = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	double tmp;
	if (x <= -48000000000.0) {
		tmp = t_3;
	} else if (x <= -4.2e-51) {
		tmp = (b * c) + t_1;
	} else if (x <= -1.55e-220) {
		tmp = t_2;
	} else if (x <= 3e-299) {
		tmp = t_1 + ((t * a) * -4.0);
	} else if (x <= 2.9e-131) {
		tmp = t_2;
	} else if (x <= 3.8e-77) {
		tmp = t_1 + (18.0 * (t * (x * (y * z))));
	} else if (x <= 1.7e+122) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) - ((4.0d0 * (t * a)) + (4.0d0 * (x * i)))
    t_3 = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    if (x <= (-48000000000.0d0)) then
        tmp = t_3
    else if (x <= (-4.2d-51)) then
        tmp = (b * c) + t_1
    else if (x <= (-1.55d-220)) then
        tmp = t_2
    else if (x <= 3d-299) then
        tmp = t_1 + ((t * a) * (-4.0d0))
    else if (x <= 2.9d-131) then
        tmp = t_2
    else if (x <= 3.8d-77) then
        tmp = t_1 + (18.0d0 * (t * (x * (y * z))))
    else if (x <= 1.7d+122) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)));
	double t_3 = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	double tmp;
	if (x <= -48000000000.0) {
		tmp = t_3;
	} else if (x <= -4.2e-51) {
		tmp = (b * c) + t_1;
	} else if (x <= -1.55e-220) {
		tmp = t_2;
	} else if (x <= 3e-299) {
		tmp = t_1 + ((t * a) * -4.0);
	} else if (x <= 2.9e-131) {
		tmp = t_2;
	} else if (x <= 3.8e-77) {
		tmp = t_1 + (18.0 * (t * (x * (y * z))));
	} else if (x <= 1.7e+122) {
		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 * (k * -27.0)
	t_2 = (b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))
	t_3 = x * ((18.0 * (z * (y * t))) - (4.0 * i))
	tmp = 0
	if x <= -48000000000.0:
		tmp = t_3
	elif x <= -4.2e-51:
		tmp = (b * c) + t_1
	elif x <= -1.55e-220:
		tmp = t_2
	elif x <= 3e-299:
		tmp = t_1 + ((t * a) * -4.0)
	elif x <= 2.9e-131:
		tmp = t_2
	elif x <= 3.8e-77:
		tmp = t_1 + (18.0 * (t * (x * (y * z))))
	elif x <= 1.7e+122:
		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(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + Float64(4.0 * Float64(x * i))))
	t_3 = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -48000000000.0)
		tmp = t_3;
	elseif (x <= -4.2e-51)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= -1.55e-220)
		tmp = t_2;
	elseif (x <= 3e-299)
		tmp = Float64(t_1 + Float64(Float64(t * a) * -4.0));
	elseif (x <= 2.9e-131)
		tmp = t_2;
	elseif (x <= 3.8e-77)
		tmp = Float64(t_1 + Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))));
	elseif (x <= 1.7e+122)
		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 * (k * -27.0);
	t_2 = (b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)));
	t_3 = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	tmp = 0.0;
	if (x <= -48000000000.0)
		tmp = t_3;
	elseif (x <= -4.2e-51)
		tmp = (b * c) + t_1;
	elseif (x <= -1.55e-220)
		tmp = t_2;
	elseif (x <= 3e-299)
		tmp = t_1 + ((t * a) * -4.0);
	elseif (x <= 2.9e-131)
		tmp = t_2;
	elseif (x <= 3.8e-77)
		tmp = t_1 + (18.0 * (t * (x * (y * z))));
	elseif (x <= 1.7e+122)
		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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -48000000000.0], t$95$3, If[LessEqual[x, -4.2e-51], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, -1.55e-220], t$95$2, If[LessEqual[x, 3e-299], N[(t$95$1 + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e-131], t$95$2, If[LessEqual[x, 3.8e-77], N[(t$95$1 + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+122], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.8e10 or 1.7e122 < x

   1. Initial program 73.4%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in x around inf 74.9%

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

      1. pow1 74.9%

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

   7. Applied egg-rr 74.9%

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

      1. unpow1 74.9%

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

      2. associate-*r* 76.9%

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

   9. Simplified 76.9%

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

   if -4.8e10 < x < -4.20000000000000003e-51

   1. Initial program 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in b around inf 80.5%

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

   if -4.20000000000000003e-51 < x < -1.55000000000000006e-220 or 2.99999999999999984e-299 < x < 2.9000000000000002e-131 or 3.7999999999999999e-77 < x < 1.7e122

   1. Initial program 92.0%

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

   3. Taylor expanded in y around 0 78.0%

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

   4. Taylor expanded in j around 0 66.9%

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

   if -1.55000000000000006e-220 < x < 2.99999999999999984e-299

   1. Initial program 99.8%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in a around inf 83.4%

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

      1. *-commutative 83.4%

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

   7. Simplified 83.4%

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

   if 2.9000000000000002e-131 < x < 3.7999999999999999e-77

   1. Initial program 94.6%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 69.8%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -48000000000:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-51}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-220}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-299}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-131}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+122}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-205}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-307}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \left(t \cdot \left(y \cdot \left(18 \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+67}:\\ \;\;\;\;t\_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ (* b c) t_1)))
   (if (<= t -5.2e+68)
     (* t (+ (* 18.0 (* y (* x z))) (* a -4.0)))
     (if (<= t -9.8e-58)
       (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
       (if (<= t -5e-205)
         t_2
         (if (<= t -2.5e-261)
           (* x (- (* 18.0 (* z (* y t))) (* 4.0 i)))
           (if (<= t 2.3e-307)
             t_2
             (if (<= t 7e-302)
               (* x (- (* t (* y (* 18.0 z))) (* 4.0 i)))
               (if (<= t 7.8e+67)
                 (+ t_1 (* x (* i -4.0)))
                 (* t (- (* a (- 4.0)) (* (* z (* x y)) -18.0))))))))))))

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 = (b * c) + t_1;
	double tmp;
	if (t <= -5.2e+68) {
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	} else if (t <= -9.8e-58) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= -5e-205) {
		tmp = t_2;
	} else if (t <= -2.5e-261) {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	} else if (t <= 2.3e-307) {
		tmp = t_2;
	} else if (t <= 7e-302) {
		tmp = x * ((t * (y * (18.0 * z))) - (4.0 * i));
	} else if (t <= 7.8e+67) {
		tmp = t_1 + (x * (i * -4.0));
	} else {
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	}
	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 = (b * c) + t_1
    if (t <= (-5.2d+68)) then
        tmp = t * ((18.0d0 * (y * (x * z))) + (a * (-4.0d0)))
    else if (t <= (-9.8d-58)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (t <= (-5d-205)) then
        tmp = t_2
    else if (t <= (-2.5d-261)) then
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    else if (t <= 2.3d-307) then
        tmp = t_2
    else if (t <= 7d-302) then
        tmp = x * ((t * (y * (18.0d0 * z))) - (4.0d0 * i))
    else if (t <= 7.8d+67) then
        tmp = t_1 + (x * (i * (-4.0d0)))
    else
        tmp = t * ((a * -4.0d0) - ((z * (x * y)) * (-18.0d0)))
    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 = (b * c) + t_1;
	double tmp;
	if (t <= -5.2e+68) {
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	} else if (t <= -9.8e-58) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= -5e-205) {
		tmp = t_2;
	} else if (t <= -2.5e-261) {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	} else if (t <= 2.3e-307) {
		tmp = t_2;
	} else if (t <= 7e-302) {
		tmp = x * ((t * (y * (18.0 * z))) - (4.0 * i));
	} else if (t <= 7.8e+67) {
		tmp = t_1 + (x * (i * -4.0));
	} else {
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	}
	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 = (b * c) + t_1
	tmp = 0
	if t <= -5.2e+68:
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0))
	elif t <= -9.8e-58:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif t <= -5e-205:
		tmp = t_2
	elif t <= -2.5e-261:
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i))
	elif t <= 2.3e-307:
		tmp = t_2
	elif t <= 7e-302:
		tmp = x * ((t * (y * (18.0 * z))) - (4.0 * i))
	elif t <= 7.8e+67:
		tmp = t_1 + (x * (i * -4.0))
	else:
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0))
	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(Float64(b * c) + t_1)
	tmp = 0.0
	if (t <= -5.2e+68)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(a * -4.0)));
	elseif (t <= -9.8e-58)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (t <= -5e-205)
		tmp = t_2;
	elseif (t <= -2.5e-261)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i)));
	elseif (t <= 2.3e-307)
		tmp = t_2;
	elseif (t <= 7e-302)
		tmp = Float64(x * Float64(Float64(t * Float64(y * Float64(18.0 * z))) - Float64(4.0 * i)));
	elseif (t <= 7.8e+67)
		tmp = Float64(t_1 + Float64(x * Float64(i * -4.0)));
	else
		tmp = Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(Float64(z * Float64(x * y)) * -18.0)));
	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 = (b * c) + t_1;
	tmp = 0.0;
	if (t <= -5.2e+68)
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	elseif (t <= -9.8e-58)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (t <= -5e-205)
		tmp = t_2;
	elseif (t <= -2.5e-261)
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	elseif (t <= 2.3e-307)
		tmp = t_2;
	elseif (t <= 7e-302)
		tmp = x * ((t * (y * (18.0 * z))) - (4.0 * i));
	elseif (t <= 7.8e+67)
		tmp = t_1 + (x * (i * -4.0));
	else
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	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[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t, -5.2e+68], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.8e-58], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e-205], t$95$2, If[LessEqual[t, -2.5e-261], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e-307], t$95$2, If[LessEqual[t, 7e-302], N[(x * N[(N[(t * N[(y * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+67], N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -5.1999999999999996e68

   1. Initial program 83.7%

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

   3. Taylor expanded in x around 0 77.7%

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

   4. Taylor expanded in t around inf 65.0%

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

      1. cancel-sign-sub-inv 65.0%

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

      2. *-commutative 65.0%

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

      3. associate-*l* 68.6%

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

      4. metadata-eval 68.6%

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

   6. Simplified 68.6%

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

   if -5.1999999999999996e68 < t < -9.80000000000000061e-58

   1. Initial program 96.2%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around inf 68.8%

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

   if -9.80000000000000061e-58 < t < -5.00000000000000001e-205 or -2.4999999999999999e-261 < t < 2.2999999999999999e-307

   1. Initial program 84.5%

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

   3. Simplified 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 81.2%

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

   if -5.00000000000000001e-205 < t < -2.4999999999999999e-261

   1. Initial program 65.3%

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

   3. Simplified 65.3%

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

   5. Taylor expanded in x around inf 58.2%

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

      1. pow1 58.2%

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

   7. Applied egg-rr 58.2%

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

      1. unpow1 58.2%

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

      2. associate-*r* 70.6%

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

   9. Simplified 70.6%

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

   if 2.2999999999999999e-307 < t < 7.0000000000000003e-302

   1. Initial program 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in x around inf 99.5%

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

      1. pow1 99.5%

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

      2. associate-*r* 99.5%

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

      3. *-commutative 99.5%

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

      4. associate-*r* 99.5%

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

   7. Applied egg-rr 99.5%

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

      1. unpow1 99.5%

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

      2. associate-*l* 100.0%

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

      3. associate-*l* 100.0%

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

   9. Simplified 100.0%

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

   if 7.0000000000000003e-302 < t < 7.80000000000000013e67

   1. Initial program 91.0%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in i around inf 67.2%

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

      1. associate-*r* 67.2%

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

      2. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   if 7.80000000000000013e67 < t

   1. Initial program 81.7%

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

   3. Taylor expanded in t around -inf 78.7%

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

      1. associate-*r* 78.7%

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

      2. neg-mul-1 78.7%

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

      3. cancel-sign-sub-inv 78.7%

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

      4. *-commutative 78.7%

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

      5. associate-*r* 78.7%

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

      6. metadata-eval 78.7%

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

      7. *-commutative 78.7%

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

   5. Simplified 78.7%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(\left(\left(x \cdot y\right) \cdot z\right) \cdot -18 + a \cdot 4\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-205}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-307}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \left(t \cdot \left(y \cdot \left(18 \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+67}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ t_3 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-57}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-205}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-302}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+68}:\\ \;\;\;\;t\_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

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 (* j (* k -27.0)))
        (t_2 (+ (* b c) t_1))
        (t_3 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<= t -1.1e+62)
     (* t (+ (* 18.0 (* y (* x z))) (* a -4.0)))
     (if (<= t -3.9e-57)
       t_3
       (if (<= t -1.7e-205)
         t_2
         (if (<= t -1.62e-261)
           (* x (- (* 18.0 (* z (* y t))) (* 4.0 i)))
           (if (<= t 3.6e-308)
             t_2
             (if (<= t 7e-302)
               t_3
               (if (<= t 1.1e+68)
                 (+ t_1 (* x (* i -4.0)))
                 (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (t <= -1.1e+62) {
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	} else if (t <= -3.9e-57) {
		tmp = t_3;
	} else if (t <= -1.7e-205) {
		tmp = t_2;
	} else if (t <= -1.62e-261) {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	} else if (t <= 3.6e-308) {
		tmp = t_2;
	} else if (t <= 7e-302) {
		tmp = t_3;
	} else if (t <= 1.1e+68) {
		tmp = t_1 + (x * (i * -4.0));
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (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) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    t_3 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (t <= (-1.1d+62)) then
        tmp = t * ((18.0d0 * (y * (x * z))) + (a * (-4.0d0)))
    else if (t <= (-3.9d-57)) then
        tmp = t_3
    else if (t <= (-1.7d-205)) then
        tmp = t_2
    else if (t <= (-1.62d-261)) then
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    else if (t <= 3.6d-308) then
        tmp = t_2
    else if (t <= 7d-302) then
        tmp = t_3
    else if (t <= 1.1d+68) then
        tmp = t_1 + (x * (i * (-4.0d0)))
    else
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (t <= -1.1e+62) {
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	} else if (t <= -3.9e-57) {
		tmp = t_3;
	} else if (t <= -1.7e-205) {
		tmp = t_2;
	} else if (t <= -1.62e-261) {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	} else if (t <= 3.6e-308) {
		tmp = t_2;
	} else if (t <= 7e-302) {
		tmp = t_3;
	} else if (t <= 1.1e+68) {
		tmp = t_1 + (x * (i * -4.0));
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if t <= -1.1e+62:
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0))
	elif t <= -3.9e-57:
		tmp = t_3
	elif t <= -1.7e-205:
		tmp = t_2
	elif t <= -1.62e-261:
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i))
	elif t <= 3.6e-308:
		tmp = t_2
	elif t <= 7e-302:
		tmp = t_3
	elif t <= 1.1e+68:
		tmp = t_1 + (x * (i * -4.0))
	else:
		tmp = t * ((18.0 * (x * (y * z))) - (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(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (t <= -1.1e+62)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(a * -4.0)));
	elseif (t <= -3.9e-57)
		tmp = t_3;
	elseif (t <= -1.7e-205)
		tmp = t_2;
	elseif (t <= -1.62e-261)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i)));
	elseif (t <= 3.6e-308)
		tmp = t_2;
	elseif (t <= 7e-302)
		tmp = t_3;
	elseif (t <= 1.1e+68)
		tmp = Float64(t_1 + Float64(x * Float64(i * -4.0)));
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - 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 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	t_3 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (t <= -1.1e+62)
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	elseif (t <= -3.9e-57)
		tmp = t_3;
	elseif (t <= -1.7e-205)
		tmp = t_2;
	elseif (t <= -1.62e-261)
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	elseif (t <= 3.6e-308)
		tmp = t_2;
	elseif (t <= 7e-302)
		tmp = t_3;
	elseif (t <= 1.1e+68)
		tmp = t_1 + (x * (i * -4.0));
	else
		tmp = t * ((18.0 * (x * (y * z))) - (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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+62], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.9e-57], t$95$3, If[LessEqual[t, -1.7e-205], t$95$2, If[LessEqual[t, -1.62e-261], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-308], t$95$2, If[LessEqual[t, 7e-302], t$95$3, If[LessEqual[t, 1.1e+68], N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.10000000000000007e62

   1. Initial program 83.7%

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

   3. Taylor expanded in x around 0 77.7%

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

   4. Taylor expanded in t around inf 65.0%

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

      1. cancel-sign-sub-inv 65.0%

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

      2. *-commutative 65.0%

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

      3. associate-*l* 68.6%

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

      4. metadata-eval 68.6%

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

   6. Simplified 68.6%

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

   if -1.10000000000000007e62 < t < -3.90000000000000006e-57 or 3.5999999999999999e-308 < t < 7.0000000000000003e-302

   1. Initial program 93.4%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in x around inf 71.9%

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

   if -3.90000000000000006e-57 < t < -1.7000000000000001e-205 or -1.62000000000000006e-261 < t < 3.5999999999999999e-308

   1. Initial program 84.5%

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

   3. Simplified 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 81.2%

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

   if -1.7000000000000001e-205 < t < -1.62000000000000006e-261

   1. Initial program 65.3%

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

   3. Simplified 65.3%

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

   5. Taylor expanded in x around inf 58.2%

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

      1. pow1 58.2%

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

   7. Applied egg-rr 58.2%

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

      1. unpow1 58.2%

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

      2. associate-*r* 70.6%

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

   9. Simplified 70.6%

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

   if 7.0000000000000003e-302 < t < 1.09999999999999994e68

   1. Initial program 91.0%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in i around inf 67.2%

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

      1. associate-*r* 67.2%

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

      2. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   if 1.09999999999999994e68 < t

   1. Initial program 81.7%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in t around inf 78.7%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-205}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-308}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+68}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t\_1\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-205}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.92 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-307}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \left(t \cdot \left(y \cdot \left(18 \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+62}:\\ \;\;\;\;t\_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

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 (* j (* k -27.0))) (t_2 (+ (* b c) t_1)))
   (if (<= t -6.2e+72)
     (* t (+ (* 18.0 (* y (* x z))) (* a -4.0)))
     (if (<= t -3.7e-56)
       (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
       (if (<= t -4.6e-205)
         t_2
         (if (<= t -1.92e-261)
           (* x (- (* 18.0 (* z (* y t))) (* 4.0 i)))
           (if (<= t 2.5e-307)
             t_2
             (if (<= t 7e-302)
               (* x (- (* t (* y (* 18.0 z))) (* 4.0 i)))
               (if (<= t 3.3e+62)
                 (+ t_1 (* x (* i -4.0)))
                 (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if (t <= -6.2e+72) {
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	} else if (t <= -3.7e-56) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= -4.6e-205) {
		tmp = t_2;
	} else if (t <= -1.92e-261) {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	} else if (t <= 2.5e-307) {
		tmp = t_2;
	} else if (t <= 7e-302) {
		tmp = x * ((t * (y * (18.0 * z))) - (4.0 * i));
	} else if (t <= 3.3e+62) {
		tmp = t_1 + (x * (i * -4.0));
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (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 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    if (t <= (-6.2d+72)) then
        tmp = t * ((18.0d0 * (y * (x * z))) + (a * (-4.0d0)))
    else if (t <= (-3.7d-56)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (t <= (-4.6d-205)) then
        tmp = t_2
    else if (t <= (-1.92d-261)) then
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    else if (t <= 2.5d-307) then
        tmp = t_2
    else if (t <= 7d-302) then
        tmp = x * ((t * (y * (18.0d0 * z))) - (4.0d0 * i))
    else if (t <= 3.3d+62) then
        tmp = t_1 + (x * (i * (-4.0d0)))
    else
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if (t <= -6.2e+72) {
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	} else if (t <= -3.7e-56) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= -4.6e-205) {
		tmp = t_2;
	} else if (t <= -1.92e-261) {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	} else if (t <= 2.5e-307) {
		tmp = t_2;
	} else if (t <= 7e-302) {
		tmp = x * ((t * (y * (18.0 * z))) - (4.0 * i));
	} else if (t <= 3.3e+62) {
		tmp = t_1 + (x * (i * -4.0));
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	tmp = 0
	if t <= -6.2e+72:
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0))
	elif t <= -3.7e-56:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif t <= -4.6e-205:
		tmp = t_2
	elif t <= -1.92e-261:
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i))
	elif t <= 2.5e-307:
		tmp = t_2
	elif t <= 7e-302:
		tmp = x * ((t * (y * (18.0 * z))) - (4.0 * i))
	elif t <= 3.3e+62:
		tmp = t_1 + (x * (i * -4.0))
	else:
		tmp = t * ((18.0 * (x * (y * z))) - (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(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (t <= -6.2e+72)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(a * -4.0)));
	elseif (t <= -3.7e-56)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (t <= -4.6e-205)
		tmp = t_2;
	elseif (t <= -1.92e-261)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i)));
	elseif (t <= 2.5e-307)
		tmp = t_2;
	elseif (t <= 7e-302)
		tmp = Float64(x * Float64(Float64(t * Float64(y * Float64(18.0 * z))) - Float64(4.0 * i)));
	elseif (t <= 3.3e+62)
		tmp = Float64(t_1 + Float64(x * Float64(i * -4.0)));
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - 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 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	tmp = 0.0;
	if (t <= -6.2e+72)
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	elseif (t <= -3.7e-56)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (t <= -4.6e-205)
		tmp = t_2;
	elseif (t <= -1.92e-261)
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	elseif (t <= 2.5e-307)
		tmp = t_2;
	elseif (t <= 7e-302)
		tmp = x * ((t * (y * (18.0 * z))) - (4.0 * i));
	elseif (t <= 3.3e+62)
		tmp = t_1 + (x * (i * -4.0));
	else
		tmp = t * ((18.0 * (x * (y * z))) - (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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t, -6.2e+72], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.7e-56], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.6e-205], t$95$2, If[LessEqual[t, -1.92e-261], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-307], t$95$2, If[LessEqual[t, 7e-302], N[(x * N[(N[(t * N[(y * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+62], N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -6.19999999999999977e72

   1. Initial program 83.7%

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

   3. Taylor expanded in x around 0 77.7%

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

   4. Taylor expanded in t around inf 65.0%

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

      1. cancel-sign-sub-inv 65.0%

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

      2. *-commutative 65.0%

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

      3. associate-*l* 68.6%

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

      4. metadata-eval 68.6%

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

   6. Simplified 68.6%

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

   if -6.19999999999999977e72 < t < -3.7000000000000002e-56

   1. Initial program 96.2%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around inf 68.8%

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

   if -3.7000000000000002e-56 < t < -4.5999999999999998e-205 or -1.92e-261 < t < 2.50000000000000007e-307

   1. Initial program 84.5%

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

   3. Simplified 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 81.2%

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

   if -4.5999999999999998e-205 < t < -1.92e-261

   1. Initial program 65.3%

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

   3. Simplified 65.3%

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

   5. Taylor expanded in x around inf 58.2%

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

      1. pow1 58.2%

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

   7. Applied egg-rr 58.2%

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

      1. unpow1 58.2%

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

      2. associate-*r* 70.6%

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

   9. Simplified 70.6%

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

   if 2.50000000000000007e-307 < t < 7.0000000000000003e-302

   1. Initial program 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in x around inf 99.5%

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

      1. pow1 99.5%

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

      2. associate-*r* 99.5%

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

      3. *-commutative 99.5%

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

      4. associate-*r* 99.5%

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

   7. Applied egg-rr 99.5%

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

      1. unpow1 99.5%

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

      2. associate-*l* 100.0%

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

      3. associate-*l* 100.0%

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

   9. Simplified 100.0%

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

   if 7.0000000000000003e-302 < t < 3.3e62

   1. Initial program 91.0%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in i around inf 67.2%

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

      1. associate-*r* 67.2%

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

      2. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   if 3.3e62 < t

   1. Initial program 81.7%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in t around inf 78.7%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-205}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -1.92 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-307}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \left(t \cdot \left(y \cdot \left(18 \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 31.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(t \cdot a\right) \cdot -4\\ t_2 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -48000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-167}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-280}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+195}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* t a) -4.0)) (t_2 (* 18.0 (* t (* x (* y z))))))
   (if (<= x -48000000000.0)
     t_2
     (if (<= x -4.8e-167)
       (* b c)
       (if (<= x 1.9e-280)
         (* j (* k -27.0))
         (if (<= x 7.5e-118)
           t_1
           (if (<= x 3.8e+57)
             t_2
             (if (<= x 7.8e+127)
               t_1
               (if (<= x 2.3e+195) t_2 (* (* x i) -4.0))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double t_2 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (x <= -48000000000.0) {
		tmp = t_2;
	} else if (x <= -4.8e-167) {
		tmp = b * c;
	} else if (x <= 1.9e-280) {
		tmp = j * (k * -27.0);
	} else if (x <= 7.5e-118) {
		tmp = t_1;
	} else if (x <= 3.8e+57) {
		tmp = t_2;
	} else if (x <= 7.8e+127) {
		tmp = t_1;
	} else if (x <= 2.3e+195) {
		tmp = t_2;
	} else {
		tmp = (x * i) * -4.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t * a) * (-4.0d0)
    t_2 = 18.0d0 * (t * (x * (y * z)))
    if (x <= (-48000000000.0d0)) then
        tmp = t_2
    else if (x <= (-4.8d-167)) then
        tmp = b * c
    else if (x <= 1.9d-280) then
        tmp = j * (k * (-27.0d0))
    else if (x <= 7.5d-118) then
        tmp = t_1
    else if (x <= 3.8d+57) then
        tmp = t_2
    else if (x <= 7.8d+127) then
        tmp = t_1
    else if (x <= 2.3d+195) then
        tmp = t_2
    else
        tmp = (x * i) * (-4.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double t_2 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (x <= -48000000000.0) {
		tmp = t_2;
	} else if (x <= -4.8e-167) {
		tmp = b * c;
	} else if (x <= 1.9e-280) {
		tmp = j * (k * -27.0);
	} else if (x <= 7.5e-118) {
		tmp = t_1;
	} else if (x <= 3.8e+57) {
		tmp = t_2;
	} else if (x <= 7.8e+127) {
		tmp = t_1;
	} else if (x <= 2.3e+195) {
		tmp = t_2;
	} else {
		tmp = (x * i) * -4.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (t * a) * -4.0
	t_2 = 18.0 * (t * (x * (y * z)))
	tmp = 0
	if x <= -48000000000.0:
		tmp = t_2
	elif x <= -4.8e-167:
		tmp = b * c
	elif x <= 1.9e-280:
		tmp = j * (k * -27.0)
	elif x <= 7.5e-118:
		tmp = t_1
	elif x <= 3.8e+57:
		tmp = t_2
	elif x <= 7.8e+127:
		tmp = t_1
	elif x <= 2.3e+195:
		tmp = t_2
	else:
		tmp = (x * i) * -4.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(t * a) * -4.0)
	t_2 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (x <= -48000000000.0)
		tmp = t_2;
	elseif (x <= -4.8e-167)
		tmp = Float64(b * c);
	elseif (x <= 1.9e-280)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (x <= 7.5e-118)
		tmp = t_1;
	elseif (x <= 3.8e+57)
		tmp = t_2;
	elseif (x <= 7.8e+127)
		tmp = t_1;
	elseif (x <= 2.3e+195)
		tmp = t_2;
	else
		tmp = Float64(Float64(x * i) * -4.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (t * a) * -4.0;
	t_2 = 18.0 * (t * (x * (y * z)));
	tmp = 0.0;
	if (x <= -48000000000.0)
		tmp = t_2;
	elseif (x <= -4.8e-167)
		tmp = b * c;
	elseif (x <= 1.9e-280)
		tmp = j * (k * -27.0);
	elseif (x <= 7.5e-118)
		tmp = t_1;
	elseif (x <= 3.8e+57)
		tmp = t_2;
	elseif (x <= 7.8e+127)
		tmp = t_1;
	elseif (x <= 2.3e+195)
		tmp = t_2;
	else
		tmp = (x * i) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -48000000000.0], t$95$2, If[LessEqual[x, -4.8e-167], N[(b * c), $MachinePrecision], If[LessEqual[x, 1.9e-280], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-118], t$95$1, If[LessEqual[x, 3.8e+57], t$95$2, If[LessEqual[x, 7.8e+127], t$95$1, If[LessEqual[x, 2.3e+195], t$95$2, N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.8e10 or 7.49999999999999978e-118 < x < 3.7999999999999999e57 or 7.79999999999999962e127 < x < 2.3000000000000001e195

   1. Initial program 79.0%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in x around inf 61.7%

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

   6. Taylor expanded in t around inf 47.6%

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

   if -4.8e10 < x < -4.79999999999999986e-167

   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 90.4%

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

   4. Taylor expanded in b around inf 43.1%

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

   if -4.79999999999999986e-167 < x < 1.9000000000000001e-280

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 71.9%

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

   4. Taylor expanded in j around inf 50.5%

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

      1. *-commutative 50.5%

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

      2. associate-*r* 50.5%

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

   6. Simplified 50.5%

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

   if 1.9000000000000001e-280 < x < 7.49999999999999978e-118 or 3.7999999999999999e57 < x < 7.79999999999999962e127

   1. Initial program 95.6%

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

   3. Taylor expanded in x around 0 89.4%

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

   4. Taylor expanded in a around inf 42.8%

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

      1. *-commutative 42.8%

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

   6. Simplified 42.8%

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

   if 2.3000000000000001e195 < x

   1. Initial program 74.4%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in x around inf 85.7%

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

   6. Taylor expanded in t around 0 56.7%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -48000000000:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-167}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-280}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-118}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+57}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+195}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 31.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(t \cdot a\right) \cdot -4\\ t_2 := 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -80000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-164}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-279}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+52}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+195}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* t a) -4.0)) (t_2 (* 18.0 (* t (* y (* x z))))))
   (if (<= x -80000000000.0)
     t_2
     (if (<= x -3.2e-164)
       (* b c)
       (if (<= x 1.45e-279)
         (* j (* k -27.0))
         (if (<= x 7.4e-118)
           t_1
           (if (<= x 1.8e+52)
             (* 18.0 (* t (* x (* y z))))
             (if (<= x 7.8e+127)
               t_1
               (if (<= x 2.2e+195) t_2 (* (* x i) -4.0))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double t_2 = 18.0 * (t * (y * (x * z)));
	double tmp;
	if (x <= -80000000000.0) {
		tmp = t_2;
	} else if (x <= -3.2e-164) {
		tmp = b * c;
	} else if (x <= 1.45e-279) {
		tmp = j * (k * -27.0);
	} else if (x <= 7.4e-118) {
		tmp = t_1;
	} else if (x <= 1.8e+52) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= 7.8e+127) {
		tmp = t_1;
	} else if (x <= 2.2e+195) {
		tmp = t_2;
	} else {
		tmp = (x * i) * -4.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t * a) * (-4.0d0)
    t_2 = 18.0d0 * (t * (y * (x * z)))
    if (x <= (-80000000000.0d0)) then
        tmp = t_2
    else if (x <= (-3.2d-164)) then
        tmp = b * c
    else if (x <= 1.45d-279) then
        tmp = j * (k * (-27.0d0))
    else if (x <= 7.4d-118) then
        tmp = t_1
    else if (x <= 1.8d+52) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (x <= 7.8d+127) then
        tmp = t_1
    else if (x <= 2.2d+195) then
        tmp = t_2
    else
        tmp = (x * i) * (-4.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double t_2 = 18.0 * (t * (y * (x * z)));
	double tmp;
	if (x <= -80000000000.0) {
		tmp = t_2;
	} else if (x <= -3.2e-164) {
		tmp = b * c;
	} else if (x <= 1.45e-279) {
		tmp = j * (k * -27.0);
	} else if (x <= 7.4e-118) {
		tmp = t_1;
	} else if (x <= 1.8e+52) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (x <= 7.8e+127) {
		tmp = t_1;
	} else if (x <= 2.2e+195) {
		tmp = t_2;
	} else {
		tmp = (x * i) * -4.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (t * a) * -4.0
	t_2 = 18.0 * (t * (y * (x * z)))
	tmp = 0
	if x <= -80000000000.0:
		tmp = t_2
	elif x <= -3.2e-164:
		tmp = b * c
	elif x <= 1.45e-279:
		tmp = j * (k * -27.0)
	elif x <= 7.4e-118:
		tmp = t_1
	elif x <= 1.8e+52:
		tmp = 18.0 * (t * (x * (y * z)))
	elif x <= 7.8e+127:
		tmp = t_1
	elif x <= 2.2e+195:
		tmp = t_2
	else:
		tmp = (x * i) * -4.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(t * a) * -4.0)
	t_2 = Float64(18.0 * Float64(t * Float64(y * Float64(x * z))))
	tmp = 0.0
	if (x <= -80000000000.0)
		tmp = t_2;
	elseif (x <= -3.2e-164)
		tmp = Float64(b * c);
	elseif (x <= 1.45e-279)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (x <= 7.4e-118)
		tmp = t_1;
	elseif (x <= 1.8e+52)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (x <= 7.8e+127)
		tmp = t_1;
	elseif (x <= 2.2e+195)
		tmp = t_2;
	else
		tmp = Float64(Float64(x * i) * -4.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (t * a) * -4.0;
	t_2 = 18.0 * (t * (y * (x * z)));
	tmp = 0.0;
	if (x <= -80000000000.0)
		tmp = t_2;
	elseif (x <= -3.2e-164)
		tmp = b * c;
	elseif (x <= 1.45e-279)
		tmp = j * (k * -27.0);
	elseif (x <= 7.4e-118)
		tmp = t_1;
	elseif (x <= 1.8e+52)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (x <= 7.8e+127)
		tmp = t_1;
	elseif (x <= 2.2e+195)
		tmp = t_2;
	else
		tmp = (x * i) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -80000000000.0], t$95$2, If[LessEqual[x, -3.2e-164], N[(b * c), $MachinePrecision], If[LessEqual[x, 1.45e-279], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e-118], t$95$1, If[LessEqual[x, 1.8e+52], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e+127], t$95$1, If[LessEqual[x, 2.2e+195], t$95$2, N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -8e10 or 7.79999999999999962e127 < x < 2.2e195

   1. Initial program 72.3%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in x around inf 70.0%

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

   6. Taylor expanded in t around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. associate-*l* 55.0%

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

   8. Simplified 55.0%

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

   if -8e10 < x < -3.2e-164

   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 90.4%

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

   4. Taylor expanded in b around inf 43.1%

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

   if -3.2e-164 < x < 1.45e-279

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 71.9%

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

   4. Taylor expanded in j around inf 50.5%

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

      1. *-commutative 50.5%

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

      2. associate-*r* 50.5%

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

   6. Simplified 50.5%

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

   if 1.45e-279 < x < 7.40000000000000029e-118 or 1.8e52 < x < 7.79999999999999962e127

   1. Initial program 95.6%

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

   3. Taylor expanded in x around 0 89.4%

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

   4. Taylor expanded in a around inf 42.8%

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

      1. *-commutative 42.8%

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

   6. Simplified 42.8%

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

   if 7.40000000000000029e-118 < x < 1.8e52

   1. Initial program 91.9%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in x around inf 45.7%

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

   6. Taylor expanded in t around inf 36.1%

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

   if 2.2e195 < x

   1. Initial program 74.4%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in x around inf 85.7%

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

   6. Taylor expanded in t around 0 56.7%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -80000000000:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-164}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-279}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-118}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+52}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+195}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 31.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(t \cdot a\right) \cdot -4\\ t_2 := 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -54000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-165}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-280}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(18 \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+193}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* t a) -4.0)) (t_2 (* 18.0 (* t (* y (* x z))))))
   (if (<= x -54000000000.0)
     t_2
     (if (<= x -1.55e-165)
       (* b c)
       (if (<= x 8e-280)
         (* j (* k -27.0))
         (if (<= x 3.7e-118)
           t_1
           (if (<= x 4.2e+69)
             (* (* y z) (* 18.0 (* x t)))
             (if (<= x 7.8e+127)
               t_1
               (if (<= x 6.6e+193) t_2 (* (* x i) -4.0))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double t_2 = 18.0 * (t * (y * (x * z)));
	double tmp;
	if (x <= -54000000000.0) {
		tmp = t_2;
	} else if (x <= -1.55e-165) {
		tmp = b * c;
	} else if (x <= 8e-280) {
		tmp = j * (k * -27.0);
	} else if (x <= 3.7e-118) {
		tmp = t_1;
	} else if (x <= 4.2e+69) {
		tmp = (y * z) * (18.0 * (x * t));
	} else if (x <= 7.8e+127) {
		tmp = t_1;
	} else if (x <= 6.6e+193) {
		tmp = t_2;
	} else {
		tmp = (x * i) * -4.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t * a) * (-4.0d0)
    t_2 = 18.0d0 * (t * (y * (x * z)))
    if (x <= (-54000000000.0d0)) then
        tmp = t_2
    else if (x <= (-1.55d-165)) then
        tmp = b * c
    else if (x <= 8d-280) then
        tmp = j * (k * (-27.0d0))
    else if (x <= 3.7d-118) then
        tmp = t_1
    else if (x <= 4.2d+69) then
        tmp = (y * z) * (18.0d0 * (x * t))
    else if (x <= 7.8d+127) then
        tmp = t_1
    else if (x <= 6.6d+193) then
        tmp = t_2
    else
        tmp = (x * i) * (-4.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (t * a) * -4.0;
	double t_2 = 18.0 * (t * (y * (x * z)));
	double tmp;
	if (x <= -54000000000.0) {
		tmp = t_2;
	} else if (x <= -1.55e-165) {
		tmp = b * c;
	} else if (x <= 8e-280) {
		tmp = j * (k * -27.0);
	} else if (x <= 3.7e-118) {
		tmp = t_1;
	} else if (x <= 4.2e+69) {
		tmp = (y * z) * (18.0 * (x * t));
	} else if (x <= 7.8e+127) {
		tmp = t_1;
	} else if (x <= 6.6e+193) {
		tmp = t_2;
	} else {
		tmp = (x * i) * -4.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (t * a) * -4.0
	t_2 = 18.0 * (t * (y * (x * z)))
	tmp = 0
	if x <= -54000000000.0:
		tmp = t_2
	elif x <= -1.55e-165:
		tmp = b * c
	elif x <= 8e-280:
		tmp = j * (k * -27.0)
	elif x <= 3.7e-118:
		tmp = t_1
	elif x <= 4.2e+69:
		tmp = (y * z) * (18.0 * (x * t))
	elif x <= 7.8e+127:
		tmp = t_1
	elif x <= 6.6e+193:
		tmp = t_2
	else:
		tmp = (x * i) * -4.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(t * a) * -4.0)
	t_2 = Float64(18.0 * Float64(t * Float64(y * Float64(x * z))))
	tmp = 0.0
	if (x <= -54000000000.0)
		tmp = t_2;
	elseif (x <= -1.55e-165)
		tmp = Float64(b * c);
	elseif (x <= 8e-280)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (x <= 3.7e-118)
		tmp = t_1;
	elseif (x <= 4.2e+69)
		tmp = Float64(Float64(y * z) * Float64(18.0 * Float64(x * t)));
	elseif (x <= 7.8e+127)
		tmp = t_1;
	elseif (x <= 6.6e+193)
		tmp = t_2;
	else
		tmp = Float64(Float64(x * i) * -4.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (t * a) * -4.0;
	t_2 = 18.0 * (t * (y * (x * z)));
	tmp = 0.0;
	if (x <= -54000000000.0)
		tmp = t_2;
	elseif (x <= -1.55e-165)
		tmp = b * c;
	elseif (x <= 8e-280)
		tmp = j * (k * -27.0);
	elseif (x <= 3.7e-118)
		tmp = t_1;
	elseif (x <= 4.2e+69)
		tmp = (y * z) * (18.0 * (x * t));
	elseif (x <= 7.8e+127)
		tmp = t_1;
	elseif (x <= 6.6e+193)
		tmp = t_2;
	else
		tmp = (x * i) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -54000000000.0], t$95$2, If[LessEqual[x, -1.55e-165], N[(b * c), $MachinePrecision], If[LessEqual[x, 8e-280], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e-118], t$95$1, If[LessEqual[x, 4.2e+69], N[(N[(y * z), $MachinePrecision] * N[(18.0 * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e+127], t$95$1, If[LessEqual[x, 6.6e+193], t$95$2, N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -5.4e10 or 7.79999999999999962e127 < x < 6.6e193

   1. Initial program 72.3%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in x around inf 70.0%

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

   6. Taylor expanded in t around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. associate-*l* 55.0%

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

   8. Simplified 55.0%

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

   if -5.4e10 < x < -1.54999999999999998e-165

   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 90.4%

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

   4. Taylor expanded in b around inf 43.1%

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

   if -1.54999999999999998e-165 < x < 7.9999999999999997e-280

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 71.9%

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

   4. Taylor expanded in j around inf 50.5%

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

      1. *-commutative 50.5%

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

      2. associate-*r* 50.5%

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

   6. Simplified 50.5%

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

   if 7.9999999999999997e-280 < x < 3.70000000000000014e-118 or 4.2000000000000003e69 < x < 7.79999999999999962e127

   1. Initial program 97.5%

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

   3. Taylor expanded in x around 0 88.4%

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

   4. Taylor expanded in a around inf 44.4%

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

      1. *-commutative 44.4%

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

   6. Simplified 44.4%

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

   if 3.70000000000000014e-118 < x < 4.2000000000000003e69

   1. Initial program 90.3%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in x around inf 43.8%

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

   6. Taylor expanded in t around inf 32.9%

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

      1. associate-*r* 35.2%

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

      2. associate-*r* 35.2%

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

   8. Simplified 35.2%

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

   if 6.6e193 < x

   1. Initial program 74.4%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in x around inf 85.7%

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

   6. Taylor expanded in t around 0 56.7%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -54000000000:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-165}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-280}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-118}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(18 \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+193}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+61} \lor \neg \left(t \leq 5.2 \cdot 10^{-56}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -5e+61) (not (<= t 5.2e-56)))
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (-
    (- (+ (* b c) (* x (- (* 18.0 (* z (* y t))) (* 4.0 i)))) (* 4.0 (* t a)))
    (* (* 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 <= -5e+61) || !(t <= 5.2e-56)) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (((b * c) + (x * ((18.0 * (z * (y * t))) - (4.0 * i)))) - (4.0 * (t * a))) - ((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 <= (-5d+61)) .or. (.not. (t <= 5.2d-56))) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = (((b * c) + (x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i)))) - (4.0d0 * (t * a))) - ((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 <= -5e+61) || !(t <= 5.2e-56)) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (((b * c) + (x * ((18.0 * (z * (y * t))) - (4.0 * i)))) - (4.0 * (t * a))) - ((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 <= -5e+61) or not (t <= 5.2e-56):
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = (((b * c) + (x * ((18.0 * (z * (y * t))) - (4.0 * i)))) - (4.0 * (t * a))) - ((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 <= -5e+61) || !(t <= 5.2e-56))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i)))) - Float64(4.0 * Float64(t * a))) - 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 <= -5e+61) || ~((t <= 5.2e-56)))
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = (((b * c) + (x * ((18.0 * (z * (y * t))) - (4.0 * i)))) - (4.0 * (t * a))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -5e+61], N[Not[LessEqual[t, 5.2e-56]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.00000000000000018e61 or 5.19999999999999994e-56 < t

   1. Initial program 84.4%

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

   3. Simplified 87.1%

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

   if -5.00000000000000018e61 < t < 5.19999999999999994e-56

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0 92.8%

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

      1. pow1 45.1%

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

   5. Applied egg-rr 92.8%

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

      1. unpow1 45.1%

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

      2. associate-*r* 45.9%

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

   7. Simplified 98.3%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+61} \lor \neg \left(t \leq 5.2 \cdot 10^{-56}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t\_2 + x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-46}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-197}:\\ \;\;\;\;b \cdot c + t\_2\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+64}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (+ (* 18.0 (* y (* x z))) (* a -4.0))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* x (* i -4.0)))))
   (if (<= t -6e-17)
     t_1
     (if (<= t -1e-46)
       t_3
       (if (<= t -3.1e-49)
         t_1
         (if (<= t -1.45e-197)
           (+ (* b c) t_2)
           (if (<= t 4.8e+64) t_3 t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (x * (i * -4.0));
	double tmp;
	if (t <= -6e-17) {
		tmp = t_1;
	} else if (t <= -1e-46) {
		tmp = t_3;
	} else if (t <= -3.1e-49) {
		tmp = t_1;
	} else if (t <= -1.45e-197) {
		tmp = (b * c) + t_2;
	} else if (t <= 4.8e+64) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * ((18.0d0 * (y * (x * z))) + (a * (-4.0d0)))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + (x * (i * (-4.0d0)))
    if (t <= (-6d-17)) then
        tmp = t_1
    else if (t <= (-1d-46)) then
        tmp = t_3
    else if (t <= (-3.1d-49)) then
        tmp = t_1
    else if (t <= (-1.45d-197)) then
        tmp = (b * c) + t_2
    else if (t <= 4.8d+64) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (x * (i * -4.0));
	double tmp;
	if (t <= -6e-17) {
		tmp = t_1;
	} else if (t <= -1e-46) {
		tmp = t_3;
	} else if (t <= -3.1e-49) {
		tmp = t_1;
	} else if (t <= -1.45e-197) {
		tmp = (b * c) + t_2;
	} else if (t <= 4.8e+64) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (y * (x * z))) + (a * -4.0))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (x * (i * -4.0))
	tmp = 0
	if t <= -6e-17:
		tmp = t_1
	elif t <= -1e-46:
		tmp = t_3
	elif t <= -3.1e-49:
		tmp = t_1
	elif t <= -1.45e-197:
		tmp = (b * c) + t_2
	elif t <= 4.8e+64:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(a * -4.0)))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(x * Float64(i * -4.0)))
	tmp = 0.0
	if (t <= -6e-17)
		tmp = t_1;
	elseif (t <= -1e-46)
		tmp = t_3;
	elseif (t <= -3.1e-49)
		tmp = t_1;
	elseif (t <= -1.45e-197)
		tmp = Float64(Float64(b * c) + t_2);
	elseif (t <= 4.8e+64)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (x * (i * -4.0));
	tmp = 0.0;
	if (t <= -6e-17)
		tmp = t_1;
	elseif (t <= -1e-46)
		tmp = t_3;
	elseif (t <= -3.1e-49)
		tmp = t_1;
	elseif (t <= -1.45e-197)
		tmp = (b * c) + t_2;
	elseif (t <= 4.8e+64)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e-17], t$95$1, If[LessEqual[t, -1e-46], t$95$3, If[LessEqual[t, -3.1e-49], t$95$1, If[LessEqual[t, -1.45e-197], N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[t, 4.8e+64], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.00000000000000012e-17 or -1.00000000000000002e-46 < t < -3.1e-49 or 4.79999999999999999e64 < t

   1. Initial program 84.6%

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

   3. Taylor expanded in x around 0 80.9%

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

   4. Taylor expanded in t around inf 71.1%

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

      1. cancel-sign-sub-inv 71.1%

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

      2. *-commutative 71.1%

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

      3. associate-*l* 71.1%

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

      4. metadata-eval 71.1%

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

   6. Simplified 71.1%

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

   if -6.00000000000000012e-17 < t < -1.00000000000000002e-46 or -1.45000000000000011e-197 < t < 4.79999999999999999e64

   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 84.0%

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

   5. Taylor expanded in i around inf 67.0%

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

      1. associate-*r* 67.0%

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

      2. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   if -3.1e-49 < t < -1.45000000000000011e-197

   1. Initial program 91.9%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in b around inf 83.5%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-46}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-197}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+64}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t\_2 + x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-46}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-191}:\\ \;\;\;\;b \cdot c + t\_2\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+65}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

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 (* t (+ (* 18.0 (* y (* x z))) (* a -4.0))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* x (* i -4.0)))))
   (if (<= t -1.05e-17)
     t_1
     (if (<= t -3.5e-46)
       t_3
       (if (<= t -1.8e-50)
         t_1
         (if (<= t -4e-191)
           (+ (* b c) t_2)
           (if (<= t 2.3e+65)
             t_3
             (* t (- (* 18.0 (* x (* y z))) (* 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 = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (x * (i * -4.0));
	double tmp;
	if (t <= -1.05e-17) {
		tmp = t_1;
	} else if (t <= -3.5e-46) {
		tmp = t_3;
	} else if (t <= -1.8e-50) {
		tmp = t_1;
	} else if (t <= -4e-191) {
		tmp = (b * c) + t_2;
	} else if (t <= 2.3e+65) {
		tmp = t_3;
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (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) :: t_3
    real(8) :: tmp
    t_1 = t * ((18.0d0 * (y * (x * z))) + (a * (-4.0d0)))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + (x * (i * (-4.0d0)))
    if (t <= (-1.05d-17)) then
        tmp = t_1
    else if (t <= (-3.5d-46)) then
        tmp = t_3
    else if (t <= (-1.8d-50)) then
        tmp = t_1
    else if (t <= (-4d-191)) then
        tmp = (b * c) + t_2
    else if (t <= 2.3d+65) then
        tmp = t_3
    else
        tmp = t * ((18.0d0 * (x * (y * z))) - (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 = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (x * (i * -4.0));
	double tmp;
	if (t <= -1.05e-17) {
		tmp = t_1;
	} else if (t <= -3.5e-46) {
		tmp = t_3;
	} else if (t <= -1.8e-50) {
		tmp = t_1;
	} else if (t <= -4e-191) {
		tmp = (b * c) + t_2;
	} else if (t <= 2.3e+65) {
		tmp = t_3;
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (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 = t * ((18.0 * (y * (x * z))) + (a * -4.0))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (x * (i * -4.0))
	tmp = 0
	if t <= -1.05e-17:
		tmp = t_1
	elif t <= -3.5e-46:
		tmp = t_3
	elif t <= -1.8e-50:
		tmp = t_1
	elif t <= -4e-191:
		tmp = (b * c) + t_2
	elif t <= 2.3e+65:
		tmp = t_3
	else:
		tmp = t * ((18.0 * (x * (y * z))) - (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(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(a * -4.0)))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(x * Float64(i * -4.0)))
	tmp = 0.0
	if (t <= -1.05e-17)
		tmp = t_1;
	elseif (t <= -3.5e-46)
		tmp = t_3;
	elseif (t <= -1.8e-50)
		tmp = t_1;
	elseif (t <= -4e-191)
		tmp = Float64(Float64(b * c) + t_2);
	elseif (t <= 2.3e+65)
		tmp = t_3;
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - 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 = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (x * (i * -4.0));
	tmp = 0.0;
	if (t <= -1.05e-17)
		tmp = t_1;
	elseif (t <= -3.5e-46)
		tmp = t_3;
	elseif (t <= -1.8e-50)
		tmp = t_1;
	elseif (t <= -4e-191)
		tmp = (b * c) + t_2;
	elseif (t <= 2.3e+65)
		tmp = t_3;
	else
		tmp = t * ((18.0 * (x * (y * z))) - (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[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e-17], t$95$1, If[LessEqual[t, -3.5e-46], t$95$3, If[LessEqual[t, -1.8e-50], t$95$1, If[LessEqual[t, -4e-191], N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[t, 2.3e+65], t$95$3, N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.04999999999999996e-17 or -3.5000000000000002e-46 < t < -1.7999999999999999e-50

   1. Initial program 86.8%

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

   3. Taylor expanded in x around 0 83.8%

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

   4. Taylor expanded in t around inf 65.4%

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

      1. cancel-sign-sub-inv 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-*l* 66.8%

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

      4. metadata-eval 66.8%

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

   6. Simplified 66.8%

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

   if -1.04999999999999996e-17 < t < -3.5000000000000002e-46 or -4.0000000000000001e-191 < t < 2.3e65

   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 84.0%

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

   5. Taylor expanded in i around inf 67.0%

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

      1. associate-*r* 67.0%

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

      2. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   if -1.7999999999999999e-50 < t < -4.0000000000000001e-191

   1. Initial program 91.9%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in b around inf 83.5%

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

   if 2.3e65 < t

   1. Initial program 81.7%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in t around inf 78.7%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-46}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-191}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+65}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+224}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* (* j 27.0) k) -2e+224)
   (+ (* b c) (* j (* k -27.0)))
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((j * 27.0) * k) <= -2e+224) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((j * 27.0d0) * k) <= (-2d+224)) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((j * 27.0) * k) <= -2e+224) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((j * 27.0) * k) <= -2e+224:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(Float64(j * 27.0) * k) <= -2e+224)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((j * 27.0) * k) <= -2e+224)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision], -2e+224], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j 27) k) < -1.99999999999999994e224

   1. Initial program 57.7%

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

   3. Simplified 52.1%

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

   5. Taylor expanded in b around inf 74.2%

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

   if -1.99999999999999994e224 < (*.f64 (*.f64 j 27) k)

   1. Initial program 89.8%

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

   3. Simplified 91.4%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+224}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + \left(t \cdot a\right) \cdot -4\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+144}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(18 \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-20}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-199}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+34}:\\ \;\;\;\;t\_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ t_1 (* (* t a) -4.0))))
   (if (<= t -7.8e+144)
     (* (* y z) (* 18.0 (* x t)))
     (if (<= t -5.6e+51)
       t_2
       (if (<= t -8.4e-20)
         (* 18.0 (* t (* x (* y z))))
         (if (<= t -1.7e-199)
           (+ (* b c) t_1)
           (if (<= t 3.4e+34) (+ t_1 (* x (* i -4.0))) t_2)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + ((t * a) * -4.0);
	double tmp;
	if (t <= -7.8e+144) {
		tmp = (y * z) * (18.0 * (x * t));
	} else if (t <= -5.6e+51) {
		tmp = t_2;
	} else if (t <= -8.4e-20) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t <= -1.7e-199) {
		tmp = (b * c) + t_1;
	} else if (t <= 3.4e+34) {
		tmp = t_1 + (x * (i * -4.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + ((t * a) * (-4.0d0))
    if (t <= (-7.8d+144)) then
        tmp = (y * z) * (18.0d0 * (x * t))
    else if (t <= (-5.6d+51)) then
        tmp = t_2
    else if (t <= (-8.4d-20)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (t <= (-1.7d-199)) then
        tmp = (b * c) + t_1
    else if (t <= 3.4d+34) then
        tmp = t_1 + (x * (i * (-4.0d0)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + ((t * a) * -4.0);
	double tmp;
	if (t <= -7.8e+144) {
		tmp = (y * z) * (18.0 * (x * t));
	} else if (t <= -5.6e+51) {
		tmp = t_2;
	} else if (t <= -8.4e-20) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t <= -1.7e-199) {
		tmp = (b * c) + t_1;
	} else if (t <= 3.4e+34) {
		tmp = t_1 + (x * (i * -4.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + ((t * a) * -4.0)
	tmp = 0
	if t <= -7.8e+144:
		tmp = (y * z) * (18.0 * (x * t))
	elif t <= -5.6e+51:
		tmp = t_2
	elif t <= -8.4e-20:
		tmp = 18.0 * (t * (x * (y * z)))
	elif t <= -1.7e-199:
		tmp = (b * c) + t_1
	elif t <= 3.4e+34:
		tmp = t_1 + (x * (i * -4.0))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(Float64(t * a) * -4.0))
	tmp = 0.0
	if (t <= -7.8e+144)
		tmp = Float64(Float64(y * z) * Float64(18.0 * Float64(x * t)));
	elseif (t <= -5.6e+51)
		tmp = t_2;
	elseif (t <= -8.4e-20)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (t <= -1.7e-199)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (t <= 3.4e+34)
		tmp = Float64(t_1 + Float64(x * Float64(i * -4.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + ((t * a) * -4.0);
	tmp = 0.0;
	if (t <= -7.8e+144)
		tmp = (y * z) * (18.0 * (x * t));
	elseif (t <= -5.6e+51)
		tmp = t_2;
	elseif (t <= -8.4e-20)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (t <= -1.7e-199)
		tmp = (b * c) + t_1;
	elseif (t <= 3.4e+34)
		tmp = t_1 + (x * (i * -4.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+144], N[(N[(y * z), $MachinePrecision] * N[(18.0 * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.6e+51], t$95$2, If[LessEqual[t, -8.4e-20], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-199], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 3.4e+34], N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.80000000000000036e144

   1. Initial program 80.5%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf 60.4%

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

   6. Taylor expanded in t around inf 57.2%

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

      1. associate-*r* 59.9%

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

      2. associate-*r* 59.9%

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

   8. Simplified 59.9%

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

   if -7.80000000000000036e144 < t < -5.60000000000000009e51 or 3.3999999999999999e34 < t

   1. Initial program 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in a around inf 52.7%

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

      1. *-commutative 52.7%

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

   7. Simplified 52.7%

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

   if -5.60000000000000009e51 < t < -8.3999999999999996e-20

   1. Initial program 99.9%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 77.0%

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

   6. Taylor expanded in t around inf 66.1%

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

   if -8.3999999999999996e-20 < t < -1.70000000000000003e-199

   1. Initial program 90.8%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in b around inf 72.5%

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

   if -1.70000000000000003e-199 < t < 3.3999999999999999e34

   1. Initial program 84.3%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in i around inf 67.3%

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

      1. associate-*r* 67.3%

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

      2. *-commutative 67.3%

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

   7. Simplified 67.3%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+144}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(18 \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{+51}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-20}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-199}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(t \cdot a\right) + t\_1\right)\\ \mathbf{elif}\;t \leq -0.00068:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+74}:\\ \;\;\;\;\left(b \cdot c - t\_1\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \end{array} \end{array} \]

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 (* 4.0 (* x i))))
   (if (<= t -7.6e+146)
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
     (if (<= t -4.4e+46)
       (- (* b c) (+ (* 4.0 (* t a)) t_1))
       (if (<= t -0.00068)
         (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
         (if (<= t 6.8e+74)
           (- (- (* b c) t_1) (* (* j 27.0) k))
           (* t (- (* a (- 4.0)) (* (* z (* x y)) -18.0)))))))))

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 = 4.0 * (x * i);
	double tmp;
	if (t <= -7.6e+146) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -4.4e+46) {
		tmp = (b * c) - ((4.0 * (t * a)) + t_1);
	} else if (t <= -0.00068) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= 6.8e+74) {
		tmp = ((b * c) - t_1) - ((j * 27.0) * k);
	} else {
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	}
	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 = 4.0d0 * (x * i)
    if (t <= (-7.6d+146)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= (-4.4d+46)) then
        tmp = (b * c) - ((4.0d0 * (t * a)) + t_1)
    else if (t <= (-0.00068d0)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (t <= 6.8d+74) then
        tmp = ((b * c) - t_1) - ((j * 27.0d0) * k)
    else
        tmp = t * ((a * -4.0d0) - ((z * (x * y)) * (-18.0d0)))
    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 = 4.0 * (x * i);
	double tmp;
	if (t <= -7.6e+146) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -4.4e+46) {
		tmp = (b * c) - ((4.0 * (t * a)) + t_1);
	} else if (t <= -0.00068) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= 6.8e+74) {
		tmp = ((b * c) - t_1) - ((j * 27.0) * k);
	} else {
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	}
	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 = 4.0 * (x * i)
	tmp = 0
	if t <= -7.6e+146:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= -4.4e+46:
		tmp = (b * c) - ((4.0 * (t * a)) + t_1)
	elif t <= -0.00068:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif t <= 6.8e+74:
		tmp = ((b * c) - t_1) - ((j * 27.0) * k)
	else:
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0))
	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(4.0 * Float64(x * i))
	tmp = 0.0
	if (t <= -7.6e+146)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= -4.4e+46)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + t_1));
	elseif (t <= -0.00068)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (t <= 6.8e+74)
		tmp = Float64(Float64(Float64(b * c) - t_1) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(Float64(z * Float64(x * y)) * -18.0)));
	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 = 4.0 * (x * i);
	tmp = 0.0;
	if (t <= -7.6e+146)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= -4.4e+46)
		tmp = (b * c) - ((4.0 * (t * a)) + t_1);
	elseif (t <= -0.00068)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (t <= 6.8e+74)
		tmp = ((b * c) - t_1) - ((j * 27.0) * k);
	else
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	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[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.6e+146], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.4e+46], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -0.00068], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e+74], N[(N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.59999999999999958e146

   1. Initial program 82.4%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in t around inf 78.6%

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

   if -7.59999999999999958e146 < t < -4.4000000000000001e46

   1. Initial program 87.5%

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

   3. Taylor expanded in y around 0 82.0%

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

   4. Taylor expanded in j around 0 71.6%

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

   if -4.4000000000000001e46 < t < -6.8e-4

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 84.7%

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

   if -6.8e-4 < t < 6.7999999999999998e74

   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 t around 0 80.2%

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

   if 6.7999999999999998e74 < t

   1. Initial program 81.7%

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

   3. Taylor expanded in t around -inf 78.7%

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

      1. associate-*r* 78.7%

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

      2. neg-mul-1 78.7%

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

      3. cancel-sign-sub-inv 78.7%

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

      4. *-commutative 78.7%

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

      5. associate-*r* 78.7%

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

      6. metadata-eval 78.7%

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

      7. *-commutative 78.7%

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

   5. Simplified 78.7%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -0.00068:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+74}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+76}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-197}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+62}:\\ \;\;\;\;t\_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

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 (* j (* k -27.0))))
   (if (<= t -2.5e+76)
     (* t (+ (* 18.0 (* y (* x z))) (* a -4.0)))
     (if (<= t -1.05e-55)
       (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
       (if (<= t -9e-197)
         (+ (* b c) t_1)
         (if (<= t 5.5e+62)
           (+ t_1 (* x (* i -4.0)))
           (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (t <= -2.5e+76) {
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	} else if (t <= -1.05e-55) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= -9e-197) {
		tmp = (b * c) + t_1;
	} else if (t <= 5.5e+62) {
		tmp = t_1 + (x * (i * -4.0));
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (t <= (-2.5d+76)) then
        tmp = t * ((18.0d0 * (y * (x * z))) + (a * (-4.0d0)))
    else if (t <= (-1.05d-55)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (t <= (-9d-197)) then
        tmp = (b * c) + t_1
    else if (t <= 5.5d+62) then
        tmp = t_1 + (x * (i * (-4.0d0)))
    else
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (t <= -2.5e+76) {
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	} else if (t <= -1.05e-55) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= -9e-197) {
		tmp = (b * c) + t_1;
	} else if (t <= 5.5e+62) {
		tmp = t_1 + (x * (i * -4.0));
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if t <= -2.5e+76:
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0))
	elif t <= -1.05e-55:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif t <= -9e-197:
		tmp = (b * c) + t_1
	elif t <= 5.5e+62:
		tmp = t_1 + (x * (i * -4.0))
	else:
		tmp = t * ((18.0 * (x * (y * z))) - (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(j * Float64(k * -27.0))
	tmp = 0.0
	if (t <= -2.5e+76)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) + Float64(a * -4.0)));
	elseif (t <= -1.05e-55)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (t <= -9e-197)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (t <= 5.5e+62)
		tmp = Float64(t_1 + Float64(x * Float64(i * -4.0)));
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - 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 = j * (k * -27.0);
	tmp = 0.0;
	if (t <= -2.5e+76)
		tmp = t * ((18.0 * (y * (x * z))) + (a * -4.0));
	elseif (t <= -1.05e-55)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (t <= -9e-197)
		tmp = (b * c) + t_1;
	elseif (t <= 5.5e+62)
		tmp = t_1 + (x * (i * -4.0));
	else
		tmp = t * ((18.0 * (x * (y * z))) - (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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+76], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.05e-55], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e-197], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 5.5e+62], N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.49999999999999996e76

   1. Initial program 83.7%

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

   3. Taylor expanded in x around 0 77.7%

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

   4. Taylor expanded in t around inf 65.0%

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

      1. cancel-sign-sub-inv 65.0%

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

      2. *-commutative 65.0%

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

      3. associate-*l* 68.6%

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

      4. metadata-eval 68.6%

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

   6. Simplified 68.6%

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

   if -2.49999999999999996e76 < t < -1.0500000000000001e-55

   1. Initial program 96.2%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around inf 68.8%

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

   if -1.0500000000000001e-55 < t < -9.0000000000000002e-197

   1. Initial program 91.9%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in b around inf 83.5%

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

   if -9.0000000000000002e-197 < t < 5.4999999999999997e62

   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 82.9%

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

   5. Taylor expanded in i around inf 65.6%

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

      1. associate-*r* 65.6%

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

      2. *-commutative 65.6%

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

   7. Simplified 65.6%

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

   if 5.4999999999999997e62 < t

   1. Initial program 81.7%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in t around inf 78.7%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+76}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-197}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 81.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-18} \lor \neg \left(t \leq 8 \cdot 10^{-37}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + t\_1\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 4.0 (* x i))))
   (if (or (<= t -1.5e-18) (not (<= t 8e-37)))
     (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) t_1)
     (- (- (* b c) (+ (* 4.0 (* t a)) t_1)) (* (* j 27.0) k)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double tmp;
	if ((t <= -1.5e-18) || !(t <= 8e-37)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) - ((4.0 * (t * a)) + t_1)) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    if ((t <= (-1.5d-18)) .or. (.not. (t <= 8d-37))) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - t_1
    else
        tmp = ((b * c) - ((4.0d0 * (t * a)) + t_1)) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double tmp;
	if ((t <= -1.5e-18) || !(t <= 8e-37)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) - ((4.0 * (t * a)) + t_1)) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	tmp = 0
	if (t <= -1.5e-18) or not (t <= 8e-37):
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1
	else:
		tmp = ((b * c) - ((4.0 * (t * a)) + t_1)) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	tmp = 0.0
	if ((t <= -1.5e-18) || !(t <= 8e-37))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + t_1)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	tmp = 0.0;
	if ((t <= -1.5e-18) || ~((t <= 8e-37)))
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	else
		tmp = ((b * c) - ((4.0 * (t * a)) + t_1)) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -1.5e-18], N[Not[LessEqual[t, 8e-37]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.49999999999999991e-18 or 8.00000000000000053e-37 < t

   1. Initial program 85.6%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in j around 0 83.1%

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

   if -1.49999999999999991e-18 < t < 8.00000000000000053e-37

   1. Initial program 85.2%

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

   3. Taylor expanded in y around 0 87.6%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-18} \lor \neg \left(t \leq 8 \cdot 10^{-37}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 77.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+218}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-24}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;y \leq 68000000000000:\\ \;\;\;\;x \cdot \left(t \cdot \left(y \cdot \left(18 \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -1.8e+218)
   (* t (- (* a (- 4.0)) (* (* z (* x y)) -18.0)))
   (if (<= y 1.22e-24)
     (- (- (* b c) (+ (* 4.0 (* t a)) (* 4.0 (* x i)))) (* (* j 27.0) k))
     (if (<= y 68000000000000.0)
       (* x (- (* t (* y (* 18.0 z))) (* 4.0 i)))
       (+ (* j (* k -27.0)) (* 18.0 (* t (* y (* x z)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -1.8e+218) {
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	} else if (y <= 1.22e-24) {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - ((j * 27.0) * k);
	} else if (y <= 68000000000000.0) {
		tmp = x * ((t * (y * (18.0 * z))) - (4.0 * i));
	} else {
		tmp = (j * (k * -27.0)) + (18.0 * (t * (y * (x * z))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (y <= (-1.8d+218)) then
        tmp = t * ((a * -4.0d0) - ((z * (x * y)) * (-18.0d0)))
    else if (y <= 1.22d-24) then
        tmp = ((b * c) - ((4.0d0 * (t * a)) + (4.0d0 * (x * i)))) - ((j * 27.0d0) * k)
    else if (y <= 68000000000000.0d0) then
        tmp = x * ((t * (y * (18.0d0 * z))) - (4.0d0 * i))
    else
        tmp = (j * (k * (-27.0d0))) + (18.0d0 * (t * (y * (x * z))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -1.8e+218) {
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	} else if (y <= 1.22e-24) {
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - ((j * 27.0) * k);
	} else if (y <= 68000000000000.0) {
		tmp = x * ((t * (y * (18.0 * z))) - (4.0 * i));
	} else {
		tmp = (j * (k * -27.0)) + (18.0 * (t * (y * (x * z))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if y <= -1.8e+218:
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0))
	elif y <= 1.22e-24:
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - ((j * 27.0) * k)
	elif y <= 68000000000000.0:
		tmp = x * ((t * (y * (18.0 * z))) - (4.0 * i))
	else:
		tmp = (j * (k * -27.0)) + (18.0 * (t * (y * (x * z))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -1.8e+218)
		tmp = Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(Float64(z * Float64(x * y)) * -18.0)));
	elseif (y <= 1.22e-24)
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + Float64(4.0 * Float64(x * i)))) - Float64(Float64(j * 27.0) * k));
	elseif (y <= 68000000000000.0)
		tmp = Float64(x * Float64(Float64(t * Float64(y * Float64(18.0 * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(18.0 * Float64(t * Float64(y * Float64(x * z)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (y <= -1.8e+218)
		tmp = t * ((a * -4.0) - ((z * (x * y)) * -18.0));
	elseif (y <= 1.22e-24)
		tmp = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - ((j * 27.0) * k);
	elseif (y <= 68000000000000.0)
		tmp = x * ((t * (y * (18.0 * z))) - (4.0 * i));
	else
		tmp = (j * (k * -27.0)) + (18.0 * (t * (y * (x * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -1.8e+218], N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.22e-24], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 68000000000000.0], N[(x * N[(N[(t * N[(y * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.79999999999999995e218

   1. Initial program 76.9%

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

   3. Taylor expanded in t around -inf 82.8%

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

      1. associate-*r* 82.8%

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

      2. neg-mul-1 82.8%

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

      3. cancel-sign-sub-inv 82.8%

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

      4. *-commutative 82.8%

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

      5. associate-*r* 82.9%

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

      6. metadata-eval 82.9%

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

      7. *-commutative 82.9%

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

   5. Simplified 82.9%

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

   if -1.79999999999999995e218 < y < 1.22000000000000004e-24

   1. Initial program 89.0%

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

   3. Taylor expanded in y around 0 81.7%

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

   if 1.22000000000000004e-24 < y < 6.8e13

   1. Initial program 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in x around inf 67.0%

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

      1. pow1 67.0%

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

      2. associate-*r* 67.0%

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

      3. *-commutative 67.0%

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

      4. associate-*r* 67.0%

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

   7. Applied egg-rr 67.0%

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

      1. unpow1 67.0%

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

      2. associate-*l* 67.0%

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

      3. associate-*l* 67.2%

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

   9. Simplified 67.2%

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

   if 6.8e13 < y

   1. Initial program 79.0%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in y around inf 48.7%

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

      1. pow1 48.7%

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

      2. *-commutative 48.7%

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

   7. Applied egg-rr 48.7%

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

      1. unpow1 48.7%

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

      2. associate-*l* 53.3%

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

   9. Simplified 53.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+218}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(z \cdot \left(x \cdot y\right)\right) \cdot -18\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-24}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;y \leq 68000000000000:\\ \;\;\;\;x \cdot \left(t \cdot \left(y \cdot \left(18 \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 45.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+71}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-151}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* k -27.0)))))
   (if (<= x -3.4e+71)
     (* 18.0 (* t (* y (* x z))))
     (if (<= x 3.7e-249)
       t_1
       (if (<= x 7.5e-151)
         (* (* t a) -4.0)
         (if (<= x 1.7e+121) t_1 (* (* x i) -4.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (x <= -3.4e+71) {
		tmp = 18.0 * (t * (y * (x * z)));
	} else if (x <= 3.7e-249) {
		tmp = t_1;
	} else if (x <= 7.5e-151) {
		tmp = (t * a) * -4.0;
	} else if (x <= 1.7e+121) {
		tmp = t_1;
	} else {
		tmp = (x * i) * -4.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    if (x <= (-3.4d+71)) then
        tmp = 18.0d0 * (t * (y * (x * z)))
    else if (x <= 3.7d-249) then
        tmp = t_1
    else if (x <= 7.5d-151) then
        tmp = (t * a) * (-4.0d0)
    else if (x <= 1.7d+121) then
        tmp = t_1
    else
        tmp = (x * i) * (-4.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (x <= -3.4e+71) {
		tmp = 18.0 * (t * (y * (x * z)));
	} else if (x <= 3.7e-249) {
		tmp = t_1;
	} else if (x <= 7.5e-151) {
		tmp = (t * a) * -4.0;
	} else if (x <= 1.7e+121) {
		tmp = t_1;
	} else {
		tmp = (x * i) * -4.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if x <= -3.4e+71:
		tmp = 18.0 * (t * (y * (x * z)))
	elif x <= 3.7e-249:
		tmp = t_1
	elif x <= 7.5e-151:
		tmp = (t * a) * -4.0
	elif x <= 1.7e+121:
		tmp = t_1
	else:
		tmp = (x * i) * -4.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (x <= -3.4e+71)
		tmp = Float64(18.0 * Float64(t * Float64(y * Float64(x * z))));
	elseif (x <= 3.7e-249)
		tmp = t_1;
	elseif (x <= 7.5e-151)
		tmp = Float64(Float64(t * a) * -4.0);
	elseif (x <= 1.7e+121)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * i) * -4.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (x <= -3.4e+71)
		tmp = 18.0 * (t * (y * (x * z)));
	elseif (x <= 3.7e-249)
		tmp = t_1;
	elseif (x <= 7.5e-151)
		tmp = (t * a) * -4.0;
	elseif (x <= 1.7e+121)
		tmp = t_1;
	else
		tmp = (x * i) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e+71], N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e-249], t$95$1, If[LessEqual[x, 7.5e-151], N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[x, 1.7e+121], t$95$1, N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.3999999999999998e71

   1. Initial program 70.1%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in x around inf 71.1%

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

   6. Taylor expanded in t around inf 58.7%

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

      1. *-commutative 58.7%

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

      2. associate-*l* 61.1%

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

   8. Simplified 61.1%

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

   if -3.3999999999999998e71 < x < 3.69999999999999977e-249 or 7.5000000000000004e-151 < x < 1.70000000000000005e121

   1. Initial program 90.0%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in b around inf 54.8%

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

   if 3.69999999999999977e-249 < x < 7.5000000000000004e-151

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.1%

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

   4. Taylor expanded in a around inf 53.6%

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

      1. *-commutative 53.6%

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

   6. Simplified 53.6%

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

   if 1.70000000000000005e121 < x

   1. Initial program 77.7%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in x around inf 85.3%

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

   6. Taylor expanded in t around 0 51.9%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+71}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-249}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-151}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+121}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 47.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+71}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{-99}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+116}:\\ \;\;\;\;t\_1 + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= x -6e+71)
     (* 18.0 (* t (* y (* x z))))
     (if (<= x -5.9e-99)
       (+ (* b c) t_1)
       (if (<= x 8.2e+116) (+ t_1 (* (* t a) -4.0)) (* (* x i) -4.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (x <= -6e+71) {
		tmp = 18.0 * (t * (y * (x * z)));
	} else if (x <= -5.9e-99) {
		tmp = (b * c) + t_1;
	} else if (x <= 8.2e+116) {
		tmp = t_1 + ((t * a) * -4.0);
	} else {
		tmp = (x * i) * -4.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if (x <= (-6d+71)) then
        tmp = 18.0d0 * (t * (y * (x * z)))
    else if (x <= (-5.9d-99)) then
        tmp = (b * c) + t_1
    else if (x <= 8.2d+116) then
        tmp = t_1 + ((t * a) * (-4.0d0))
    else
        tmp = (x * i) * (-4.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if (x <= -6e+71) {
		tmp = 18.0 * (t * (y * (x * z)));
	} else if (x <= -5.9e-99) {
		tmp = (b * c) + t_1;
	} else if (x <= 8.2e+116) {
		tmp = t_1 + ((t * a) * -4.0);
	} else {
		tmp = (x * i) * -4.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if x <= -6e+71:
		tmp = 18.0 * (t * (y * (x * z)))
	elif x <= -5.9e-99:
		tmp = (b * c) + t_1
	elif x <= 8.2e+116:
		tmp = t_1 + ((t * a) * -4.0)
	else:
		tmp = (x * i) * -4.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (x <= -6e+71)
		tmp = Float64(18.0 * Float64(t * Float64(y * Float64(x * z))));
	elseif (x <= -5.9e-99)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= 8.2e+116)
		tmp = Float64(t_1 + Float64(Float64(t * a) * -4.0));
	else
		tmp = Float64(Float64(x * i) * -4.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if (x <= -6e+71)
		tmp = 18.0 * (t * (y * (x * z)));
	elseif (x <= -5.9e-99)
		tmp = (b * c) + t_1;
	elseif (x <= 8.2e+116)
		tmp = t_1 + ((t * a) * -4.0);
	else
		tmp = (x * i) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+71], N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.9e-99], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 8.2e+116], N[(t$95$1 + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.00000000000000025e71

   1. Initial program 70.1%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in x around inf 71.1%

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

   6. Taylor expanded in t around inf 58.7%

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

      1. *-commutative 58.7%

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

      2. associate-*l* 61.1%

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

   8. Simplified 61.1%

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

   if -6.00000000000000025e71 < x < -5.8999999999999999e-99

   1. Initial program 84.6%

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

   3. Simplified 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 60.9%

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

   if -5.8999999999999999e-99 < x < 8.1999999999999996e116

   1. Initial program 93.6%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in a around inf 54.8%

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

      1. *-commutative 54.8%

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

   7. Simplified 54.8%

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

   if 8.1999999999999996e116 < x

   1. Initial program 78.2%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in x around inf 83.4%

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

   6. Taylor expanded in t around 0 50.8%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+71}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{-99}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+116}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(x \cdot i\right) \cdot -4\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -8.5 \cdot 10^{+115}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.12 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{-240}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* x i) -4.0)) (t_2 (* -27.0 (* j k))))
   (if (<= j -8.5e+115)
     t_2
     (if (<= j -1.12e+70)
       t_1
       (if (<= j -9.2e-240) (* b c) (if (<= j 4.5e-109) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * i) * -4.0;
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (j <= -8.5e+115) {
		tmp = t_2;
	} else if (j <= -1.12e+70) {
		tmp = t_1;
	} else if (j <= -9.2e-240) {
		tmp = b * c;
	} else if (j <= 4.5e-109) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * i) * (-4.0d0)
    t_2 = (-27.0d0) * (j * k)
    if (j <= (-8.5d+115)) then
        tmp = t_2
    else if (j <= (-1.12d+70)) then
        tmp = t_1
    else if (j <= (-9.2d-240)) then
        tmp = b * c
    else if (j <= 4.5d-109) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * i) * -4.0;
	double t_2 = -27.0 * (j * k);
	double tmp;
	if (j <= -8.5e+115) {
		tmp = t_2;
	} else if (j <= -1.12e+70) {
		tmp = t_1;
	} else if (j <= -9.2e-240) {
		tmp = b * c;
	} else if (j <= 4.5e-109) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * i) * -4.0
	t_2 = -27.0 * (j * k)
	tmp = 0
	if j <= -8.5e+115:
		tmp = t_2
	elif j <= -1.12e+70:
		tmp = t_1
	elif j <= -9.2e-240:
		tmp = b * c
	elif j <= 4.5e-109:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * i) * -4.0)
	t_2 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (j <= -8.5e+115)
		tmp = t_2;
	elseif (j <= -1.12e+70)
		tmp = t_1;
	elseif (j <= -9.2e-240)
		tmp = Float64(b * c);
	elseif (j <= 4.5e-109)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * i) * -4.0;
	t_2 = -27.0 * (j * k);
	tmp = 0.0;
	if (j <= -8.5e+115)
		tmp = t_2;
	elseif (j <= -1.12e+70)
		tmp = t_1;
	elseif (j <= -9.2e-240)
		tmp = b * c;
	elseif (j <= 4.5e-109)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$2 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.5e+115], t$95$2, If[LessEqual[j, -1.12e+70], t$95$1, If[LessEqual[j, -9.2e-240], N[(b * c), $MachinePrecision], If[LessEqual[j, 4.5e-109], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -8.50000000000000057e115 or 4.5000000000000001e-109 < j

   1. Initial program 82.9%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in j around inf 41.3%

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

   if -8.50000000000000057e115 < j < -1.11999999999999993e70 or -9.19999999999999972e-240 < j < 4.5000000000000001e-109

   1. Initial program 90.9%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in x around inf 52.8%

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

   6. Taylor expanded in t around 0 36.0%

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

   if -1.11999999999999993e70 < j < -9.19999999999999972e-240

   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 90.2%

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

   4. Taylor expanded in b around inf 27.0%

      \[\leadsto \color{blue}{b \cdot c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.5 \cdot 10^{+115}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -1.12 \cdot 10^{+70}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{-240}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-109}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 71.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -540000000000 \lor \neg \left(x \leq 1.6 \cdot 10^{+118}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -540000000000.0) (not (<= x 1.6e+118)))
   (* x (- (* 18.0 (* z (* y t))) (* 4.0 i)))
   (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -540000000000.0) || !(x <= 1.6e+118)) {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-540000000000.0d0)) .or. (.not. (x <= 1.6d+118))) then
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -540000000000.0) || !(x <= 1.6e+118)) {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -540000000000.0) or not (x <= 1.6e+118):
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i))
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -540000000000.0) || !(x <= 1.6e+118))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - 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 ((x <= -540000000000.0) || ~((x <= 1.6e+118)))
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	else
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -540000000000.0], N[Not[LessEqual[x, 1.6e+118]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4e11 or 1.60000000000000008e118 < x

   1. Initial program 73.7%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in x around inf 74.5%

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

      1. pow1 74.5%

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

   7. Applied egg-rr 74.5%

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

      1. unpow1 74.5%

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

      2. associate-*r* 76.5%

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

   9. Simplified 76.5%

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

   if -5.4e11 < x < 1.60000000000000008e118

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 73.0%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -540000000000 \lor \neg \left(x \leq 1.6 \cdot 10^{+118}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 32.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -4.5 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{-132}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))))
   (if (<= k -4.5e-9)
     t_1
     (if (<= k 3.6e-132) (* (* t a) -4.0) (if (<= k 3.6e+47) (* b c) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double tmp;
	if (k <= -4.5e-9) {
		tmp = t_1;
	} else if (k <= 3.6e-132) {
		tmp = (t * a) * -4.0;
	} else if (k <= 3.6e+47) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    if (k <= (-4.5d-9)) then
        tmp = t_1
    else if (k <= 3.6d-132) then
        tmp = (t * a) * (-4.0d0)
    else if (k <= 3.6d+47) then
        tmp = b * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double tmp;
	if (k <= -4.5e-9) {
		tmp = t_1;
	} else if (k <= 3.6e-132) {
		tmp = (t * a) * -4.0;
	} else if (k <= 3.6e+47) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	tmp = 0
	if k <= -4.5e-9:
		tmp = t_1
	elif k <= 3.6e-132:
		tmp = (t * a) * -4.0
	elif k <= 3.6e+47:
		tmp = b * c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (k <= -4.5e-9)
		tmp = t_1;
	elseif (k <= 3.6e-132)
		tmp = Float64(Float64(t * a) * -4.0);
	elseif (k <= 3.6e+47)
		tmp = Float64(b * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	tmp = 0.0;
	if (k <= -4.5e-9)
		tmp = t_1;
	elseif (k <= 3.6e-132)
		tmp = (t * a) * -4.0;
	elseif (k <= 3.6e+47)
		tmp = b * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -4.5e-9], t$95$1, If[LessEqual[k, 3.6e-132], N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[k, 3.6e+47], N[(b * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if k < -4.49999999999999976e-9 or 3.60000000000000008e47 < k

   1. Initial program 80.4%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in j around inf 41.6%

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

   if -4.49999999999999976e-9 < k < 3.60000000000000007e-132

   1. Initial program 91.6%

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

   3. Taylor expanded in x around 0 91.8%

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

   4. Taylor expanded in a around inf 27.4%

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

      1. *-commutative 27.4%

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

   6. Simplified 27.4%

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

   if 3.60000000000000007e-132 < k < 3.60000000000000008e47

   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 x around 0 90.3%

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

   4. Taylor expanded in b around inf 31.5%

      \[\leadsto \color{blue}{b \cdot c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -4.5 \cdot 10^{-9}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{-132}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 31.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -9.2 \cdot 10^{+31}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{-131}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

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 (<= k -9.2e+31)
   (* -27.0 (* j k))
   (if (<= k 2.7e-131)
     (* (* t a) -4.0)
     (if (<= k 2.1e+47) (* 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 (k <= -9.2e+31) {
		tmp = -27.0 * (j * k);
	} else if (k <= 2.7e-131) {
		tmp = (t * a) * -4.0;
	} else if (k <= 2.1e+47) {
		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 (k <= (-9.2d+31)) then
        tmp = (-27.0d0) * (j * k)
    else if (k <= 2.7d-131) then
        tmp = (t * a) * (-4.0d0)
    else if (k <= 2.1d+47) 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 (k <= -9.2e+31) {
		tmp = -27.0 * (j * k);
	} else if (k <= 2.7e-131) {
		tmp = (t * a) * -4.0;
	} else if (k <= 2.1e+47) {
		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 k <= -9.2e+31:
		tmp = -27.0 * (j * k)
	elif k <= 2.7e-131:
		tmp = (t * a) * -4.0
	elif k <= 2.1e+47:
		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 (k <= -9.2e+31)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (k <= 2.7e-131)
		tmp = Float64(Float64(t * a) * -4.0);
	elseif (k <= 2.1e+47)
		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 (k <= -9.2e+31)
		tmp = -27.0 * (j * k);
	elseif (k <= 2.7e-131)
		tmp = (t * a) * -4.0;
	elseif (k <= 2.1e+47)
		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[LessEqual[k, -9.2e+31], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.7e-131], N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[k, 2.1e+47], N[(b * c), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -9.1999999999999998e31

   1. Initial program 78.9%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in j around inf 38.6%

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

   if -9.1999999999999998e31 < k < 2.70000000000000021e-131

   1. Initial program 91.3%

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

   3. Taylor expanded in x around 0 90.5%

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

   4. Taylor expanded in a around inf 28.5%

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

      1. *-commutative 28.5%

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

   6. Simplified 28.5%

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

   if 2.70000000000000021e-131 < k < 2.1e47

   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 x around 0 90.3%

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

   4. Taylor expanded in b around inf 31.5%

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

   if 2.1e47 < k

   1. Initial program 80.8%

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

   3. Taylor expanded in x around 0 82.6%

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

   4. Taylor expanded in j around inf 47.3%

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

      1. *-commutative 47.3%

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

      2. associate-*r* 47.2%

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

   6. Simplified 47.2%

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

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -9.2 \cdot 10^{+31}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{-131}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 36.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.5 \cdot 10^{+213} \lor \neg \left(b \cdot c \leq 7 \cdot 10^{+87}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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) -6.5e+213) (not (<= (* b c) 7e+87)))
   (* 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) <= -6.5e+213) || !((b * c) <= 7e+87)) {
		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) <= (-6.5d+213)) .or. (.not. ((b * c) <= 7d+87))) 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) <= -6.5e+213) || !((b * c) <= 7e+87)) {
		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) <= -6.5e+213) or not ((b * c) <= 7e+87):
		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) <= -6.5e+213) || !(Float64(b * c) <= 7e+87))
		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) <= -6.5e+213) || ~(((b * c) <= 7e+87)))
		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], -6.5e+213], N[Not[LessEqual[N[(b * c), $MachinePrecision], 7e+87]], $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) < -6.49999999999999982e213 or 6.99999999999999972e87 < (*.f64 b c)

   1. Initial program 80.2%

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

   3. Taylor expanded in x around 0 79.1%

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

   4. Taylor expanded in b around inf 57.4%

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

   if -6.49999999999999982e213 < (*.f64 b c) < 6.99999999999999972e87

   1. Initial program 87.2%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in j around inf 30.6%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.5 \cdot 10^{+213} \lor \neg \left(b \cdot c \leq 7 \cdot 10^{+87}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 23.1% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.4%

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

3. Taylor expanded in x around 0 86.1%

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

4. Taylor expanded in b around inf 20.1%

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

5. Final simplification 20.1%

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

Developer target: 88.0% 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 2024050 
(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)))