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

Percentage Accurate: 85.7% → 92.4%

Time: 23.4s

Alternatives: 25

Speedup: 0.8×

• 49.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.9%

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

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

   1. Initial program 0.0%

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

   3. Simplified 16.1%

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

      1. pow1 16.1%

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

      2. associate-*l* 16.1%

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

      3. associate-*r* 16.1%

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

   6. Applied egg-rr 16.1%

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

      1. unpow1 16.1%

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

      2. *-commutative 16.1%

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

   8. Simplified 16.1%

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

   9. Taylor expanded in x around -inf 58.1%

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

       1. associate-*r* 58.1%

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

       2. neg-mul-1 58.1%

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

       3. cancel-sign-sub-inv 58.1%

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

       4. metadata-eval 58.1%

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

       5. associate-*r* 58.1%

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

   11. Simplified 58.1%

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

   12. Taylor expanded in t around 0 58.1%

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

       1. associate-*r* 58.1%

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

       2. *-commutative 58.1%

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

       3. *-commutative 58.1%

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

       4. associate-*l* 58.1%

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

   14. Simplified 58.1%

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

4. Final simplification 92.3%

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

Alternative 2: 35.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -95000000000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.15 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-320}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.3 \cdot 10^{-157}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 5.7 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 9.8 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* i -4.0))))
   (if (<= (* b c) -95000000000.0)
     (* b c)
     (if (<= (* b c) -1.15e-123)
       t_1
       (if (<= (* b c) -5e-320)
         (* -4.0 (* t a))
         (if (<= (* b c) 1.3e-157)
           (* 18.0 (* (* y z) (* x t)))
           (if (<= (* b c) 5.7e-108)
             t_1
             (if (<= (* b c) 9.8e+169)
               (* x (* 18.0 (* z (* y t))))
               (* b c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if ((b * c) <= -95000000000.0) {
		tmp = b * c;
	} else if ((b * c) <= -1.15e-123) {
		tmp = t_1;
	} else if ((b * c) <= -5e-320) {
		tmp = -4.0 * (t * a);
	} else if ((b * c) <= 1.3e-157) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if ((b * c) <= 5.7e-108) {
		tmp = t_1;
	} else if ((b * c) <= 9.8e+169) {
		tmp = x * (18.0 * (z * (y * t)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (i * (-4.0d0))
    if ((b * c) <= (-95000000000.0d0)) then
        tmp = b * c
    else if ((b * c) <= (-1.15d-123)) then
        tmp = t_1
    else if ((b * c) <= (-5d-320)) then
        tmp = (-4.0d0) * (t * a)
    else if ((b * c) <= 1.3d-157) then
        tmp = 18.0d0 * ((y * z) * (x * t))
    else if ((b * c) <= 5.7d-108) then
        tmp = t_1
    else if ((b * c) <= 9.8d+169) then
        tmp = x * (18.0d0 * (z * (y * t)))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if ((b * c) <= -95000000000.0) {
		tmp = b * c;
	} else if ((b * c) <= -1.15e-123) {
		tmp = t_1;
	} else if ((b * c) <= -5e-320) {
		tmp = -4.0 * (t * a);
	} else if ((b * c) <= 1.3e-157) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if ((b * c) <= 5.7e-108) {
		tmp = t_1;
	} else if ((b * c) <= 9.8e+169) {
		tmp = x * (18.0 * (z * (y * t)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (i * -4.0)
	tmp = 0
	if (b * c) <= -95000000000.0:
		tmp = b * c
	elif (b * c) <= -1.15e-123:
		tmp = t_1
	elif (b * c) <= -5e-320:
		tmp = -4.0 * (t * a)
	elif (b * c) <= 1.3e-157:
		tmp = 18.0 * ((y * z) * (x * t))
	elif (b * c) <= 5.7e-108:
		tmp = t_1
	elif (b * c) <= 9.8e+169:
		tmp = x * (18.0 * (z * (y * t)))
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -95000000000.0)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.15e-123)
		tmp = t_1;
	elseif (Float64(b * c) <= -5e-320)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (Float64(b * c) <= 1.3e-157)
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	elseif (Float64(b * c) <= 5.7e-108)
		tmp = t_1;
	elseif (Float64(b * c) <= 9.8e+169)
		tmp = Float64(x * Float64(18.0 * Float64(z * Float64(y * t))));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (i * -4.0);
	tmp = 0.0;
	if ((b * c) <= -95000000000.0)
		tmp = b * c;
	elseif ((b * c) <= -1.15e-123)
		tmp = t_1;
	elseif ((b * c) <= -5e-320)
		tmp = -4.0 * (t * a);
	elseif ((b * c) <= 1.3e-157)
		tmp = 18.0 * ((y * z) * (x * t));
	elseif ((b * c) <= 5.7e-108)
		tmp = t_1;
	elseif ((b * c) <= 9.8e+169)
		tmp = x * (18.0 * (z * (y * t)));
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -95000000000.0], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.15e-123], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -5e-320], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.3e-157], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5.7e-108], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 9.8e+169], N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -9.5e10 or 9.80000000000000053e169 < (*.f64 b c)

   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 80.5%

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

      1. pow1 80.5%

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

      2. associate-*l* 80.5%

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

      3. associate-*r* 80.5%

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

   6. Applied egg-rr 80.5%

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

      1. unpow1 80.5%

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

      2. *-commutative 80.5%

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

   8. Simplified 80.5%

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

   9. Taylor expanded in b around inf 61.5%

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

   if -9.5e10 < (*.f64 b c) < -1.14999999999999993e-123 or 1.29999999999999994e-157 < (*.f64 b c) < 5.7e-108

   1. Initial program 77.2%

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

   3. Simplified 77.5%

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

      1. pow1 77.5%

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

      2. associate-*l* 77.5%

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

      3. associate-*r* 77.5%

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

   6. Applied egg-rr 77.5%

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

      1. unpow1 77.5%

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

      2. *-commutative 77.5%

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

   8. Simplified 77.5%

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

   9. Taylor expanded in i around inf 50.0%

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

       1. metadata-eval 50.0%

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

       2. distribute-lft-neg-in 50.0%

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

       3. associate-*r* 50.0%

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

       4. *-commutative 50.0%

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

       5. distribute-rgt-neg-in 50.0%

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

       6. distribute-lft-neg-in 50.0%

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

       7. metadata-eval 50.0%

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

   11. Simplified 50.0%

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

   if -1.14999999999999993e-123 < (*.f64 b c) < -4.99994e-320

   1. Initial program 92.7%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in j around 0 70.1%

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

   6. Taylor expanded in y around 0 66.5%

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

   7. Taylor expanded in a around inf 40.5%

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

      1. *-commutative 40.5%

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

   9. Simplified 40.5%

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

   if -4.99994e-320 < (*.f64 b c) < 1.29999999999999994e-157

   1. Initial program 89.2%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in x around inf 51.3%

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

   6. Taylor expanded in t around inf 39.2%

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

      1. associate-*r* 38.5%

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

   8. Simplified 38.5%

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

   if 5.7e-108 < (*.f64 b c) < 9.80000000000000053e169

   1. Initial program 91.4%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in x around inf 55.6%

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

   6. Taylor expanded in t around inf 36.3%

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

      1. *-commutative 36.3%

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

      2. associate-*l* 36.2%

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

      3. *-commutative 36.2%

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

   8. Simplified 36.2%

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

   9. Taylor expanded in t around 0 36.3%

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

       1. associate-*r* 36.3%

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

   11. Simplified 36.3%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -95000000000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.15 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-320}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.3 \cdot 10^{-157}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 5.7 \cdot 10^{-108}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 9.8 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 35.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ t_2 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -2600000000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -7.6 \cdot 10^{-124}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-320}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 5.3 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 95:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 4.4 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* (* y z) (* x t)))) (t_2 (* x (* i -4.0))))
   (if (<= (* b c) -2600000000.0)
     (* b c)
     (if (<= (* b c) -7.6e-124)
       t_2
       (if (<= (* b c) -5e-320)
         (* -4.0 (* t a))
         (if (<= (* b c) 5.3e-158)
           t_1
           (if (<= (* b c) 95.0)
             t_2
             (if (<= (* b c) 4.4e+170) t_1 (* b c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * ((y * z) * (x * t));
	double t_2 = x * (i * -4.0);
	double tmp;
	if ((b * c) <= -2600000000.0) {
		tmp = b * c;
	} else if ((b * c) <= -7.6e-124) {
		tmp = t_2;
	} else if ((b * c) <= -5e-320) {
		tmp = -4.0 * (t * a);
	} else if ((b * c) <= 5.3e-158) {
		tmp = t_1;
	} else if ((b * c) <= 95.0) {
		tmp = t_2;
	} else if ((b * c) <= 4.4e+170) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 18.0d0 * ((y * z) * (x * t))
    t_2 = x * (i * (-4.0d0))
    if ((b * c) <= (-2600000000.0d0)) then
        tmp = b * c
    else if ((b * c) <= (-7.6d-124)) then
        tmp = t_2
    else if ((b * c) <= (-5d-320)) then
        tmp = (-4.0d0) * (t * a)
    else if ((b * c) <= 5.3d-158) then
        tmp = t_1
    else if ((b * c) <= 95.0d0) then
        tmp = t_2
    else if ((b * c) <= 4.4d+170) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * ((y * z) * (x * t));
	double t_2 = x * (i * -4.0);
	double tmp;
	if ((b * c) <= -2600000000.0) {
		tmp = b * c;
	} else if ((b * c) <= -7.6e-124) {
		tmp = t_2;
	} else if ((b * c) <= -5e-320) {
		tmp = -4.0 * (t * a);
	} else if ((b * c) <= 5.3e-158) {
		tmp = t_1;
	} else if ((b * c) <= 95.0) {
		tmp = t_2;
	} else if ((b * c) <= 4.4e+170) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * ((y * z) * (x * t))
	t_2 = x * (i * -4.0)
	tmp = 0
	if (b * c) <= -2600000000.0:
		tmp = b * c
	elif (b * c) <= -7.6e-124:
		tmp = t_2
	elif (b * c) <= -5e-320:
		tmp = -4.0 * (t * a)
	elif (b * c) <= 5.3e-158:
		tmp = t_1
	elif (b * c) <= 95.0:
		tmp = t_2
	elif (b * c) <= 4.4e+170:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)))
	t_2 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -2600000000.0)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -7.6e-124)
		tmp = t_2;
	elseif (Float64(b * c) <= -5e-320)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (Float64(b * c) <= 5.3e-158)
		tmp = t_1;
	elseif (Float64(b * c) <= 95.0)
		tmp = t_2;
	elseif (Float64(b * c) <= 4.4e+170)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * ((y * z) * (x * t));
	t_2 = x * (i * -4.0);
	tmp = 0.0;
	if ((b * c) <= -2600000000.0)
		tmp = b * c;
	elseif ((b * c) <= -7.6e-124)
		tmp = t_2;
	elseif ((b * c) <= -5e-320)
		tmp = -4.0 * (t * a);
	elseif ((b * c) <= 5.3e-158)
		tmp = t_1;
	elseif ((b * c) <= 95.0)
		tmp = t_2;
	elseif ((b * c) <= 4.4e+170)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2600000000.0], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -7.6e-124], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -5e-320], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5.3e-158], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 95.0], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 4.4e+170], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.6e9 or 4.39999999999999978e170 < (*.f64 b c)

   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 80.5%

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

      1. pow1 80.5%

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

      2. associate-*l* 80.5%

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

      3. associate-*r* 80.5%

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

   6. Applied egg-rr 80.5%

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

      1. unpow1 80.5%

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

      2. *-commutative 80.5%

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

   8. Simplified 80.5%

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

   9. Taylor expanded in b around inf 61.5%

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

   if -2.6e9 < (*.f64 b c) < -7.60000000000000025e-124 or 5.2999999999999999e-158 < (*.f64 b c) < 95

   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 80.6%

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

      1. pow1 80.6%

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

      2. associate-*l* 80.6%

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

      3. associate-*r* 80.6%

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

   6. Applied egg-rr 80.6%

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

      1. unpow1 80.6%

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

      2. *-commutative 80.6%

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

   8. Simplified 80.6%

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

   9. Taylor expanded in i around inf 42.8%

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

       1. metadata-eval 42.8%

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

       2. distribute-lft-neg-in 42.8%

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

       3. associate-*r* 42.8%

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

       4. *-commutative 42.8%

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

       5. distribute-rgt-neg-in 42.8%

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

       6. distribute-lft-neg-in 42.8%

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

       7. metadata-eval 42.8%

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

   11. Simplified 42.8%

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

   if -7.60000000000000025e-124 < (*.f64 b c) < -4.99994e-320

   1. Initial program 92.7%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in j around 0 70.1%

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

   6. Taylor expanded in y around 0 66.5%

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

   7. Taylor expanded in a around inf 40.5%

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

      1. *-commutative 40.5%

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

   9. Simplified 40.5%

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

   if -4.99994e-320 < (*.f64 b c) < 5.2999999999999999e-158 or 95 < (*.f64 b c) < 4.39999999999999978e170

   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 92.0%

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

   5. Taylor expanded in x around inf 53.5%

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

   6. Taylor expanded in t around inf 38.9%

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

      1. associate-*r* 38.4%

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

   8. Simplified 38.4%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2600000000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -7.6 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-320}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 5.3 \cdot 10^{-158}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 95:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 4.4 \cdot 10^{+170}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ t_3 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+220}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-259}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-261}:\\ \;\;\;\;b \cdot c + t\_3\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-125}:\\ \;\;\;\;t\_3 + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 5000000:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* x i))))
        (t_2 (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))
        (t_3 (* j (* k -27.0))))
   (if (<= t -6e+220)
     t_2
     (if (<= t -2.2e+96)
       t_1
       (if (<= t -1.32e-33)
         t_2
         (if (<= t -6.5e-259)
           t_1
           (if (<= t 4.2e-261)
             (+ (* b c) t_3)
             (if (<= t 6.8e-125)
               (+ t_3 (* i (* x -4.0)))
               (if (<= t 5000000.0) (+ (* b c) (* -4.0 (* t a))) t_2)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double t_3 = j * (k * -27.0);
	double tmp;
	if (t <= -6e+220) {
		tmp = t_2;
	} else if (t <= -2.2e+96) {
		tmp = t_1;
	} else if (t <= -1.32e-33) {
		tmp = t_2;
	} else if (t <= -6.5e-259) {
		tmp = t_1;
	} else if (t <= 4.2e-261) {
		tmp = (b * c) + t_3;
	} else if (t <= 6.8e-125) {
		tmp = t_3 + (i * (x * -4.0));
	} else if (t <= 5000000.0) {
		tmp = (b * c) + (-4.0 * (t * a));
	} 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.
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 = (b * c) - (4.0d0 * (x * i))
    t_2 = t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))
    t_3 = j * (k * (-27.0d0))
    if (t <= (-6d+220)) then
        tmp = t_2
    else if (t <= (-2.2d+96)) then
        tmp = t_1
    else if (t <= (-1.32d-33)) then
        tmp = t_2
    else if (t <= (-6.5d-259)) then
        tmp = t_1
    else if (t <= 4.2d-261) then
        tmp = (b * c) + t_3
    else if (t <= 6.8d-125) then
        tmp = t_3 + (i * (x * (-4.0d0)))
    else if (t <= 5000000.0d0) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double t_3 = j * (k * -27.0);
	double tmp;
	if (t <= -6e+220) {
		tmp = t_2;
	} else if (t <= -2.2e+96) {
		tmp = t_1;
	} else if (t <= -1.32e-33) {
		tmp = t_2;
	} else if (t <= -6.5e-259) {
		tmp = t_1;
	} else if (t <= 4.2e-261) {
		tmp = (b * c) + t_3;
	} else if (t <= 6.8e-125) {
		tmp = t_3 + (i * (x * -4.0));
	} else if (t <= 5000000.0) {
		tmp = (b * c) + (-4.0 * (t * a));
	} 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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (x * i))
	t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0))
	t_3 = j * (k * -27.0)
	tmp = 0
	if t <= -6e+220:
		tmp = t_2
	elif t <= -2.2e+96:
		tmp = t_1
	elif t <= -1.32e-33:
		tmp = t_2
	elif t <= -6.5e-259:
		tmp = t_1
	elif t <= 4.2e-261:
		tmp = (b * c) + t_3
	elif t <= 6.8e-125:
		tmp = t_3 + (i * (x * -4.0))
	elif t <= 5000000.0:
		tmp = (b * c) + (-4.0 * (t * a))
	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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0)))
	t_3 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (t <= -6e+220)
		tmp = t_2;
	elseif (t <= -2.2e+96)
		tmp = t_1;
	elseif (t <= -1.32e-33)
		tmp = t_2;
	elseif (t <= -6.5e-259)
		tmp = t_1;
	elseif (t <= 4.2e-261)
		tmp = Float64(Float64(b * c) + t_3);
	elseif (t <= 6.8e-125)
		tmp = Float64(t_3 + Float64(i * Float64(x * -4.0)));
	elseif (t <= 5000000.0)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (x * i));
	t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	t_3 = j * (k * -27.0);
	tmp = 0.0;
	if (t <= -6e+220)
		tmp = t_2;
	elseif (t <= -2.2e+96)
		tmp = t_1;
	elseif (t <= -1.32e-33)
		tmp = t_2;
	elseif (t <= -6.5e-259)
		tmp = t_1;
	elseif (t <= 4.2e-261)
		tmp = (b * c) + t_3;
	elseif (t <= 6.8e-125)
		tmp = t_3 + (i * (x * -4.0));
	elseif (t <= 5000000.0)
		tmp = (b * c) + (-4.0 * (t * a));
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+220], t$95$2, If[LessEqual[t, -2.2e+96], t$95$1, If[LessEqual[t, -1.32e-33], t$95$2, If[LessEqual[t, -6.5e-259], t$95$1, If[LessEqual[t, 4.2e-261], N[(N[(b * c), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[t, 6.8e-125], N[(t$95$3 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5000000.0], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.00000000000000048e220 or -2.1999999999999999e96 < t < -1.31999999999999993e-33 or 5e6 < t

   1. Initial program 88.6%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in j around 0 86.8%

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

   6. Taylor expanded in y around 0 84.9%

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

   7. Taylor expanded in t around inf 73.4%

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

   if -6.00000000000000048e220 < t < -2.1999999999999999e96 or -1.31999999999999993e-33 < t < -6.50000000000000045e-259

   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 t around 0 73.8%

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

   4. Taylor expanded in j around 0 66.4%

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

   if -6.50000000000000045e-259 < t < 4.19999999999999991e-261

   1. Initial program 87.1%

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

   3. Simplified 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 b around inf 75.6%

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

   if 4.19999999999999991e-261 < t < 6.7999999999999995e-125

   1. Initial program 74.2%

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

   3. Simplified 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 i around inf 69.8%

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

      1. associate-*r* 69.8%

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

      2. *-commutative 69.8%

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

      3. associate-*r* 69.8%

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

      4. *-commutative 69.8%

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

      5. *-commutative 69.8%

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

   7. Simplified 69.8%

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

   if 6.7999999999999995e-125 < t < 5e6

   1. Initial program 83.0%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in j around 0 69.9%

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

   6. Taylor expanded in y around 0 69.9%

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

   7. Taylor expanded in x around 0 58.3%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+220}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+96}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-259}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-261}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-125}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 5000000:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 35.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -35000000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -8.5 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -4.9 \cdot 10^{-281}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{-197}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.4 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* i -4.0))))
   (if (<= (* b c) -35000000.0)
     (* b c)
     (if (<= (* b c) -8.5e-124)
       t_1
       (if (<= (* b c) -4.9e-281)
         (* -4.0 (* t a))
         (if (<= (* b c) 1.05e-197)
           (* j (* k -27.0))
           (if (<= (* b c) 2.4e+125) t_1 (* b c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if ((b * c) <= -35000000.0) {
		tmp = b * c;
	} else if ((b * c) <= -8.5e-124) {
		tmp = t_1;
	} else if ((b * c) <= -4.9e-281) {
		tmp = -4.0 * (t * a);
	} else if ((b * c) <= 1.05e-197) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 2.4e+125) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (i * (-4.0d0))
    if ((b * c) <= (-35000000.0d0)) then
        tmp = b * c
    else if ((b * c) <= (-8.5d-124)) then
        tmp = t_1
    else if ((b * c) <= (-4.9d-281)) then
        tmp = (-4.0d0) * (t * a)
    else if ((b * c) <= 1.05d-197) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 2.4d+125) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if ((b * c) <= -35000000.0) {
		tmp = b * c;
	} else if ((b * c) <= -8.5e-124) {
		tmp = t_1;
	} else if ((b * c) <= -4.9e-281) {
		tmp = -4.0 * (t * a);
	} else if ((b * c) <= 1.05e-197) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 2.4e+125) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (i * -4.0)
	tmp = 0
	if (b * c) <= -35000000.0:
		tmp = b * c
	elif (b * c) <= -8.5e-124:
		tmp = t_1
	elif (b * c) <= -4.9e-281:
		tmp = -4.0 * (t * a)
	elif (b * c) <= 1.05e-197:
		tmp = j * (k * -27.0)
	elif (b * c) <= 2.4e+125:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -35000000.0)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -8.5e-124)
		tmp = t_1;
	elseif (Float64(b * c) <= -4.9e-281)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (Float64(b * c) <= 1.05e-197)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 2.4e+125)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (i * -4.0);
	tmp = 0.0;
	if ((b * c) <= -35000000.0)
		tmp = b * c;
	elseif ((b * c) <= -8.5e-124)
		tmp = t_1;
	elseif ((b * c) <= -4.9e-281)
		tmp = -4.0 * (t * a);
	elseif ((b * c) <= 1.05e-197)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 2.4e+125)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -35000000.0], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -8.5e-124], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -4.9e-281], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.05e-197], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.4e+125], t$95$1, N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -3.5e7 or 2.4e125 < (*.f64 b c)

   1. Initial program 81.1%

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

   3. Simplified 81.1%

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

      1. pow1 81.1%

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

      2. associate-*l* 81.1%

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

      3. associate-*r* 81.1%

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

   6. Applied egg-rr 81.1%

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

      1. unpow1 81.1%

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

      2. *-commutative 81.1%

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

   8. Simplified 81.1%

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

   9. Taylor expanded in b around inf 58.2%

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

   if -3.5e7 < (*.f64 b c) < -8.5000000000000002e-124 or 1.05e-197 < (*.f64 b c) < 2.4e125

   1. Initial program 85.2%

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

   3. Simplified 87.8%

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

      1. pow1 87.8%

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

      2. associate-*l* 87.8%

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

      3. associate-*r* 87.8%

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

   6. Applied egg-rr 87.8%

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

      1. unpow1 87.8%

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

      2. *-commutative 87.8%

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

   8. Simplified 87.8%

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

   9. Taylor expanded in i around inf 36.4%

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

       1. metadata-eval 36.4%

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

       2. distribute-lft-neg-in 36.4%

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

       3. associate-*r* 36.4%

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

       4. *-commutative 36.4%

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

       5. distribute-rgt-neg-in 36.4%

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

       6. distribute-lft-neg-in 36.4%

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

       7. metadata-eval 36.4%

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

   11. Simplified 36.4%

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

   if -8.5000000000000002e-124 < (*.f64 b c) < -4.8999999999999999e-281

   1. Initial program 92.2%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in j around 0 74.9%

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

   6. Taylor expanded in y around 0 71.0%

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

   7. Taylor expanded in a around inf 43.3%

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

      1. *-commutative 43.3%

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

   9. Simplified 43.3%

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

   if -4.8999999999999999e-281 < (*.f64 b c) < 1.05e-197

   1. Initial program 89.9%

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

   3. Simplified 87.9%

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

      1. pow1 87.9%

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

      2. associate-*l* 87.9%

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

      3. associate-*r* 87.8%

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

   6. Applied egg-rr 87.8%

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

      1. unpow1 87.8%

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

      2. *-commutative 87.8%

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

   8. Simplified 87.8%

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

   9. Taylor expanded in j around inf 33.3%

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

       1. *-commutative 33.3%

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

       2. associate-*r* 33.4%

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

   11. Simplified 33.4%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -35000000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -8.5 \cdot 10^{-124}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -4.9 \cdot 10^{-281}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{-197}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.4 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+67} \lor \neg \left(x \leq 5.5 \cdot 10^{+214}\right):\\ \;\;\;\;x \cdot \left(\left(-4 \cdot \frac{t \cdot a}{x} + \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -1.6e+67) (not (<= x 5.5e+214)))
   (*
    x
    (-
     (+ (* -4.0 (/ (* t a) x)) (+ (* 18.0 (* t (* y z))) (/ (* b c) x)))
     (* 4.0 i)))
   (-
    (+ (* b c) (* t (- (* x (* z (* 18.0 y))) (* 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -1.6e+67) || !(x <= 5.5e+214)) {
		tmp = x * (((-4.0 * ((t * a) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-1.6d+67)) .or. (.not. (x <= 5.5d+214))) then
        tmp = x * ((((-4.0d0) * ((t * a) / x)) + ((18.0d0 * (t * (y * z))) + ((b * c) / x))) - (4.0d0 * i))
    else
        tmp = ((b * c) + (t * ((x * (z * (18.0d0 * y))) - (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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -1.6e+67) || !(x <= 5.5e+214)) {
		tmp = x * (((-4.0 * ((t * a) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -1.6e+67) or not (x <= 5.5e+214):
		tmp = x * (((-4.0 * ((t * a) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x))) - (4.0 * i))
	else:
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -1.6e+67) || !(x <= 5.5e+214))
		tmp = Float64(x * Float64(Float64(Float64(-4.0 * Float64(Float64(t * a) / x)) + Float64(Float64(18.0 * Float64(t * Float64(y * z))) + Float64(Float64(b * c) / x))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(x * Float64(z * Float64(18.0 * y))) - 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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -1.6e+67) || ~((x <= 5.5e+214)))
		tmp = x * (((-4.0 * ((t * a) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x))) - (4.0 * i));
	else
		tmp = ((b * c) + (t * ((x * (z * (18.0 * y))) - (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.
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, -1.6e+67], N[Not[LessEqual[x, 5.5e+214]], $MachinePrecision]], N[(x * N[(N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.59999999999999991e67 or 5.5000000000000003e214 < x

   1. Initial program 65.0%

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

   3. Simplified 73.7%

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

   5. Taylor expanded in j around 0 80.5%

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

   6. Taylor expanded in x around inf 90.6%

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

   if -1.59999999999999991e67 < x < 5.5000000000000003e214

   1. Initial program 92.5%

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

   3. Simplified 90.1%

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

      1. pow1 90.1%

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

      2. associate-*l* 90.1%

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

      3. associate-*r* 90.1%

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

   6. Applied egg-rr 90.1%

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

      1. unpow1 90.1%

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

      2. *-commutative 90.1%

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

   8. Simplified 90.1%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+67} \lor \neg \left(x \leq 5.5 \cdot 10^{+214}\right):\\ \;\;\;\;x \cdot \left(\left(-4 \cdot \frac{t \cdot a}{x} + \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+55} \lor \neg \left(x \leq 0.0076\right):\\ \;\;\;\;x \cdot \left(\left(-4 \cdot \frac{t \cdot a}{x} + \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -8.2e+55) (not (<= x 0.0076)))
   (*
    x
    (-
     (+ (* -4.0 (/ (* t a) x)) (+ (* 18.0 (* t (* y z))) (/ (* b c) x)))
     (* 4.0 i)))
   (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -8.2e+55) || !(x <= 0.0076)) {
		tmp = x * (((-4.0 * ((t * a) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x))) - (4.0 * i));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-8.2d+55)) .or. (.not. (x <= 0.0076d0))) then
        tmp = x * ((((-4.0d0) * ((t * a) / x)) + ((18.0d0 * (t * (y * z))) + ((b * c) / x))) - (4.0d0 * i))
    else
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -8.2e+55) || !(x <= 0.0076)) {
		tmp = x * (((-4.0 * ((t * a) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x))) - (4.0 * i));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -8.2e+55) or not (x <= 0.0076):
		tmp = x * (((-4.0 * ((t * a) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x))) - (4.0 * i))
	else:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -8.2e+55) || !(x <= 0.0076))
		tmp = Float64(x * Float64(Float64(Float64(-4.0 * Float64(Float64(t * a) / x)) + Float64(Float64(18.0 * Float64(t * Float64(y * z))) + Float64(Float64(b * c) / x))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -8.2e+55) || ~((x <= 0.0076)))
		tmp = x * (((-4.0 * ((t * a) / x)) + ((18.0 * (t * (y * z))) + ((b * c) / x))) - (4.0 * i));
	else
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -8.2e+55], N[Not[LessEqual[x, 0.0076]], $MachinePrecision]], N[(x * N[(N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.19999999999999962e55 or 0.00759999999999999998 < x

   1. Initial program 74.8%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in j around 0 81.5%

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

   6. Taylor expanded in x around inf 88.4%

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

   if -8.19999999999999962e55 < x < 0.00759999999999999998

   1. Initial program 93.6%

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

   3. Taylor expanded in y around 0 87.5%

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

      1. distribute-lft-out 87.5%

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

      2. *-commutative 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+55} \lor \neg \left(x \leq 0.0076\right):\\ \;\;\;\;x \cdot \left(\left(-4 \cdot \frac{t \cdot a}{x} + \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{x}\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-53}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+168}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -5e+87)
     (- (* b c) (* 27.0 (* j k)))
     (if (<= t_1 1e-53)
       (+ (* b c) (* -4.0 (* t a)))
       (if (<= t_1 5e+168)
         (- (* b c) (* 4.0 (* x i)))
         (+ (* b c) (* j (* k -27.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e+87) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t_1 <= 1e-53) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t_1 <= 5e+168) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-5d+87)) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (t_1 <= 1d-53) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (t_1 <= 5d+168) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e+87) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t_1 <= 1e-53) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (t_1 <= 5e+168) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -5e+87:
		tmp = (b * c) - (27.0 * (j * k))
	elif t_1 <= 1e-53:
		tmp = (b * c) + (-4.0 * (t * a))
	elif t_1 <= 5e+168:
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -5e+87)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (t_1 <= 1e-53)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (t_1 <= 5e+168)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -5e+87)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (t_1 <= 1e-53)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (t_1 <= 5e+168)
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+87], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-53], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+168], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999998e87

   1. Initial program 77.3%

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

   3. Taylor expanded in t around 0 62.2%

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

   4. Taylor expanded in i around 0 61.0%

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

   if -4.9999999999999998e87 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000003e-53

   1. Initial program 89.2%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in j around 0 85.2%

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

   6. Taylor expanded in y around 0 85.2%

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

   7. Taylor expanded in x around 0 55.7%

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

   if 1.00000000000000003e-53 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999967e168

   1. Initial program 87.1%

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

   3. Taylor expanded in t around 0 71.5%

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

   4. Taylor expanded in j around 0 65.8%

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

   if 4.99999999999999967e168 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.9%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in b around inf 77.1%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-53}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+168}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;j \leq -7 \cdot 10^{+136}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-164}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{+54}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* x i)))))
   (if (<= j -7e+136)
     (+ (* b c) (* j (* k -27.0)))
     (if (<= j -1.75e-105)
       t_1
       (if (<= j 5.2e-164)
         (+ (* b c) (* -4.0 (* t a)))
         (if (<= j 1.5e+43)
           t_1
           (if (<= j 3.9e+54)
             (* 18.0 (* (* y z) (* x t)))
             (* -27.0 (* j k)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double tmp;
	if (j <= -7e+136) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (j <= -1.75e-105) {
		tmp = t_1;
	} else if (j <= 5.2e-164) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (j <= 1.5e+43) {
		tmp = t_1;
	} else if (j <= 3.9e+54) {
		tmp = 18.0 * ((y * z) * (x * t));
	} 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (x * i))
    if (j <= (-7d+136)) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (j <= (-1.75d-105)) then
        tmp = t_1
    else if (j <= 5.2d-164) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (j <= 1.5d+43) then
        tmp = t_1
    else if (j <= 3.9d+54) then
        tmp = 18.0d0 * ((y * z) * (x * t))
    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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double tmp;
	if (j <= -7e+136) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (j <= -1.75e-105) {
		tmp = t_1;
	} else if (j <= 5.2e-164) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (j <= 1.5e+43) {
		tmp = t_1;
	} else if (j <= 3.9e+54) {
		tmp = 18.0 * ((y * z) * (x * t));
	} 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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (x * i))
	tmp = 0
	if j <= -7e+136:
		tmp = (b * c) + (j * (k * -27.0))
	elif j <= -1.75e-105:
		tmp = t_1
	elif j <= 5.2e-164:
		tmp = (b * c) + (-4.0 * (t * a))
	elif j <= 1.5e+43:
		tmp = t_1
	elif j <= 3.9e+54:
		tmp = 18.0 * ((y * z) * (x * t))
	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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	tmp = 0.0
	if (j <= -7e+136)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (j <= -1.75e-105)
		tmp = t_1;
	elseif (j <= 5.2e-164)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (j <= 1.5e+43)
		tmp = t_1;
	elseif (j <= 3.9e+54)
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (x * i));
	tmp = 0.0;
	if (j <= -7e+136)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (j <= -1.75e-105)
		tmp = t_1;
	elseif (j <= 5.2e-164)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (j <= 1.5e+43)
		tmp = t_1;
	elseif (j <= 3.9e+54)
		tmp = 18.0 * ((y * z) * (x * t));
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7e+136], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.75e-105], t$95$1, If[LessEqual[j, 5.2e-164], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.5e+43], t$95$1, If[LessEqual[j, 3.9e+54], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -7.00000000000000002e136

   1. Initial program 82.7%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in b around inf 70.8%

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

   if -7.00000000000000002e136 < j < -1.75e-105 or 5.2000000000000003e-164 < j < 1.50000000000000008e43

   1. Initial program 78.5%

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

   3. Taylor expanded in t around 0 58.2%

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

   4. Taylor expanded in j around 0 50.5%

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

   if -1.75e-105 < j < 5.2000000000000003e-164

   1. Initial program 89.4%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in j around 0 84.9%

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

   6. Taylor expanded in y around 0 86.0%

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

   7. Taylor expanded in x around 0 61.6%

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

   if 1.50000000000000008e43 < j < 3.9000000000000003e54

   1. Initial program 80.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 80.3%

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

   6. Taylor expanded in t around inf 80.3%

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

      1. associate-*r* 80.3%

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

   8. Simplified 80.3%

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

   if 3.9000000000000003e54 < j

   1. Initial program 91.7%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in j around inf 38.8%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7 \cdot 10^{+136}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-105}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-164}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+43}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{+54}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -6.8 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -10200:\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;j \leq 5.9 \cdot 10^{-164}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a)))) (t_2 (+ (* b c) (* j (* k -27.0)))))
   (if (<= j -6.8e+55)
     t_2
     (if (<= j -10200.0)
       (* y (* 18.0 (* t (* x z))))
       (if (<= j -1.55e-43)
         t_1
         (if (<= j -9.5e-80)
           (* x (* i -4.0))
           (if (<= j 5.9e-164) t_1 t_2)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (j <= -6.8e+55) {
		tmp = t_2;
	} else if (j <= -10200.0) {
		tmp = y * (18.0 * (t * (x * z)));
	} else if (j <= -1.55e-43) {
		tmp = t_1;
	} else if (j <= -9.5e-80) {
		tmp = x * (i * -4.0);
	} else if (j <= 5.9e-164) {
		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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    t_2 = (b * c) + (j * (k * (-27.0d0)))
    if (j <= (-6.8d+55)) then
        tmp = t_2
    else if (j <= (-10200.0d0)) then
        tmp = y * (18.0d0 * (t * (x * z)))
    else if (j <= (-1.55d-43)) then
        tmp = t_1
    else if (j <= (-9.5d-80)) then
        tmp = x * (i * (-4.0d0))
    else if (j <= 5.9d-164) 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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (j <= -6.8e+55) {
		tmp = t_2;
	} else if (j <= -10200.0) {
		tmp = y * (18.0 * (t * (x * z)));
	} else if (j <= -1.55e-43) {
		tmp = t_1;
	} else if (j <= -9.5e-80) {
		tmp = x * (i * -4.0);
	} else if (j <= 5.9e-164) {
		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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	t_2 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if j <= -6.8e+55:
		tmp = t_2
	elif j <= -10200.0:
		tmp = y * (18.0 * (t * (x * z)))
	elif j <= -1.55e-43:
		tmp = t_1
	elif j <= -9.5e-80:
		tmp = x * (i * -4.0)
	elif j <= 5.9e-164:
		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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (j <= -6.8e+55)
		tmp = t_2;
	elseif (j <= -10200.0)
		tmp = Float64(y * Float64(18.0 * Float64(t * Float64(x * z))));
	elseif (j <= -1.55e-43)
		tmp = t_1;
	elseif (j <= -9.5e-80)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (j <= 5.9e-164)
		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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	t_2 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (j <= -6.8e+55)
		tmp = t_2;
	elseif (j <= -10200.0)
		tmp = y * (18.0 * (t * (x * z)));
	elseif (j <= -1.55e-43)
		tmp = t_1;
	elseif (j <= -9.5e-80)
		tmp = x * (i * -4.0);
	elseif (j <= 5.9e-164)
		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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.8e+55], t$95$2, If[LessEqual[j, -10200.0], N[(y * N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.55e-43], t$95$1, If[LessEqual[j, -9.5e-80], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.9e-164], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -6.7999999999999996e55 or 5.90000000000000018e-164 < j

   1. Initial program 83.2%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in b around inf 50.0%

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

   if -6.7999999999999996e55 < j < -10200

   1. Initial program 76.8%

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

   3. Simplified 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 52.6%

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

   6. Taylor expanded in y around inf 44.7%

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

   7. Taylor expanded in i around 0 36.8%

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

   if -10200 < j < -1.55e-43 or -9.5000000000000003e-80 < j < 5.90000000000000018e-164

   1. Initial program 89.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in j around 0 85.6%

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

   6. Taylor expanded in y around 0 86.5%

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

   7. Taylor expanded in x around 0 60.9%

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

   if -1.55e-43 < j < -9.5000000000000003e-80

   1. Initial program 80.0%

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

   3. Simplified 80.0%

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

      1. pow1 80.0%

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

      2. associate-*l* 79.7%

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

      3. associate-*r* 79.5%

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

   6. Applied egg-rr 79.5%

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

      1. unpow1 79.5%

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

      2. *-commutative 79.5%

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

   8. Simplified 79.5%

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

   9. Taylor expanded in i around inf 54.5%

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

       1. metadata-eval 54.5%

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

       2. distribute-lft-neg-in 54.5%

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

       3. associate-*r* 54.5%

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

       4. *-commutative 54.5%

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

       5. distribute-rgt-neg-in 54.5%

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

       6. distribute-lft-neg-in 54.5%

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

       7. metadata-eval 54.5%

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

   11. Simplified 54.5%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.8 \cdot 10^{+55}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -10200:\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-43}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;j \leq 5.9 \cdot 10^{-164}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(4 \cdot \left(-i\right) - \left(t \cdot -18\right) \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-211}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-62}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-8}:\\ \;\;\;\;t\_1 + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z \cdot \left(t \cdot \left(--18\right)\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -2.6e+55)
     (* x (- (* 4.0 (- i)) (* (* t -18.0) (* y z))))
     (if (<= x -4.2e-211)
       (+ (* b c) t_1)
       (if (<= x 4.7e-62)
         (+ (* b c) (* -4.0 (* t a)))
         (if (<= x 3.1e-8)
           (+ t_1 (* i (* x -4.0)))
           (* x (- (* y (* z (* t (- -18.0)))) (* 4.0 i)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -2.6e+55) {
		tmp = x * ((4.0 * -i) - ((t * -18.0) * (y * z)));
	} else if (x <= -4.2e-211) {
		tmp = (b * c) + t_1;
	} else if (x <= 4.7e-62) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 3.1e-8) {
		tmp = t_1 + (i * (x * -4.0));
	} else {
		tmp = x * ((y * (z * (t * -(-18.0)))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-2.6d+55)) then
        tmp = x * ((4.0d0 * -i) - ((t * (-18.0d0)) * (y * z)))
    else if (x <= (-4.2d-211)) then
        tmp = (b * c) + t_1
    else if (x <= 4.7d-62) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (x <= 3.1d-8) then
        tmp = t_1 + (i * (x * (-4.0d0)))
    else
        tmp = x * ((y * (z * (t * -(-18.0d0)))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -2.6e+55) {
		tmp = x * ((4.0 * -i) - ((t * -18.0) * (y * z)));
	} else if (x <= -4.2e-211) {
		tmp = (b * c) + t_1;
	} else if (x <= 4.7e-62) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 3.1e-8) {
		tmp = t_1 + (i * (x * -4.0));
	} else {
		tmp = x * ((y * (z * (t * -(-18.0)))) - (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -2.6e+55:
		tmp = x * ((4.0 * -i) - ((t * -18.0) * (y * z)))
	elif x <= -4.2e-211:
		tmp = (b * c) + t_1
	elif x <= 4.7e-62:
		tmp = (b * c) + (-4.0 * (t * a))
	elif x <= 3.1e-8:
		tmp = t_1 + (i * (x * -4.0))
	else:
		tmp = x * ((y * (z * (t * -(-18.0)))) - (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -2.6e+55)
		tmp = Float64(x * Float64(Float64(4.0 * Float64(-i)) - Float64(Float64(t * -18.0) * Float64(y * z))));
	elseif (x <= -4.2e-211)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= 4.7e-62)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 3.1e-8)
		tmp = Float64(t_1 + Float64(i * Float64(x * -4.0)));
	else
		tmp = Float64(x * Float64(Float64(y * Float64(z * Float64(t * Float64(-(-18.0))))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -2.6e+55)
		tmp = x * ((4.0 * -i) - ((t * -18.0) * (y * z)));
	elseif (x <= -4.2e-211)
		tmp = (b * c) + t_1;
	elseif (x <= 4.7e-62)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (x <= 3.1e-8)
		tmp = t_1 + (i * (x * -4.0));
	else
		tmp = x * ((y * (z * (t * -(-18.0)))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -2.6e+55], N[(x * N[(N[(4.0 * (-i)), $MachinePrecision] - N[(N[(t * -18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.2e-211], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 4.7e-62], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e-8], N[(t$95$1 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * N[(z * N[(t * (--18.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.6e55

   1. Initial program 64.6%

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

   3. Simplified 73.8%

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

      1. pow1 73.8%

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

      2. associate-*l* 73.8%

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

      3. associate-*r* 73.8%

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

   6. Applied egg-rr 73.8%

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

      1. unpow1 73.8%

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

      2. *-commutative 73.8%

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

   8. Simplified 73.8%

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

   9. Taylor expanded in x around -inf 76.4%

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

       1. associate-*r* 76.4%

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

       2. neg-mul-1 76.4%

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

       3. cancel-sign-sub-inv 76.4%

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

       4. metadata-eval 76.4%

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

       5. associate-*r* 76.4%

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

   11. Simplified 76.4%

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

   if -2.6e55 < x < -4.20000000000000015e-211

   1. Initial program 88.6%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in b around inf 61.8%

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

   if -4.20000000000000015e-211 < x < 4.69999999999999984e-62

   1. Initial program 98.3%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in j around 0 75.6%

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

   6. Taylor expanded in y around 0 75.6%

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

   7. Taylor expanded in x around 0 74.4%

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

   if 4.69999999999999984e-62 < x < 3.1e-8

   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 99.9%

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

   5. Taylor expanded in i around inf 74.2%

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

      1. associate-*r* 74.2%

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

      2. *-commutative 74.2%

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

      3. associate-*r* 74.2%

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

      4. *-commutative 74.2%

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

      5. *-commutative 74.2%

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

   7. Simplified 74.2%

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

   if 3.1e-8 < x

   1. Initial program 82.6%

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

   3. Simplified 84.2%

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

      1. pow1 84.2%

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

      2. associate-*l* 84.1%

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

      3. associate-*r* 84.1%

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

   6. Applied egg-rr 84.1%

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

      1. unpow1 84.1%

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

      2. *-commutative 84.1%

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

   8. Simplified 84.1%

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

   9. Taylor expanded in x around -inf 64.4%

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

       1. associate-*r* 64.4%

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

       2. neg-mul-1 64.4%

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

       3. cancel-sign-sub-inv 64.4%

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

       4. metadata-eval 64.4%

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

       5. associate-*r* 64.4%

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

   11. Simplified 64.4%

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

   12. Taylor expanded in t around 0 64.4%

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

       1. associate-*r* 64.4%

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

       2. *-commutative 64.4%

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

       3. *-commutative 64.4%

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

       4. associate-*l* 65.9%

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

   14. Simplified 65.9%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(4 \cdot \left(-i\right) - \left(t \cdot -18\right) \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-211}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-62}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-8}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z \cdot \left(t \cdot \left(--18\right)\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -1.62 \cdot 10^{-214}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-62}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-7}:\\ \;\;\;\;t\_1 + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z \cdot \left(t \cdot \left(--18\right)\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -2.15e+55)
     (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
     (if (<= x -1.62e-214)
       (+ (* b c) t_1)
       (if (<= x 6.4e-62)
         (+ (* b c) (* -4.0 (* t a)))
         (if (<= x 1.1e-7)
           (+ t_1 (* i (* x -4.0)))
           (* x (- (* y (* z (* t (- -18.0)))) (* 4.0 i)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -2.15e+55) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (x <= -1.62e-214) {
		tmp = (b * c) + t_1;
	} else if (x <= 6.4e-62) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 1.1e-7) {
		tmp = t_1 + (i * (x * -4.0));
	} else {
		tmp = x * ((y * (z * (t * -(-18.0)))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-2.15d+55)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (x <= (-1.62d-214)) then
        tmp = (b * c) + t_1
    else if (x <= 6.4d-62) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (x <= 1.1d-7) then
        tmp = t_1 + (i * (x * (-4.0d0)))
    else
        tmp = x * ((y * (z * (t * -(-18.0d0)))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -2.15e+55) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (x <= -1.62e-214) {
		tmp = (b * c) + t_1;
	} else if (x <= 6.4e-62) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 1.1e-7) {
		tmp = t_1 + (i * (x * -4.0));
	} else {
		tmp = x * ((y * (z * (t * -(-18.0)))) - (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -2.15e+55:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif x <= -1.62e-214:
		tmp = (b * c) + t_1
	elif x <= 6.4e-62:
		tmp = (b * c) + (-4.0 * (t * a))
	elif x <= 1.1e-7:
		tmp = t_1 + (i * (x * -4.0))
	else:
		tmp = x * ((y * (z * (t * -(-18.0)))) - (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -2.15e+55)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (x <= -1.62e-214)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= 6.4e-62)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 1.1e-7)
		tmp = Float64(t_1 + Float64(i * Float64(x * -4.0)));
	else
		tmp = Float64(x * Float64(Float64(y * Float64(z * Float64(t * Float64(-(-18.0))))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -2.15e+55)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (x <= -1.62e-214)
		tmp = (b * c) + t_1;
	elseif (x <= 6.4e-62)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (x <= 1.1e-7)
		tmp = t_1 + (i * (x * -4.0));
	else
		tmp = x * ((y * (z * (t * -(-18.0)))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -2.15e+55], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.62e-214], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 6.4e-62], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e-7], N[(t$95$1 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * N[(z * N[(t * (--18.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.1499999999999999e55

   1. Initial program 64.6%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in x around inf 76.4%

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

   if -2.1499999999999999e55 < x < -1.62e-214

   1. Initial program 88.6%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in b around inf 61.8%

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

   if -1.62e-214 < x < 6.40000000000000043e-62

   1. Initial program 98.3%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in j around 0 75.6%

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

   6. Taylor expanded in y around 0 75.6%

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

   7. Taylor expanded in x around 0 74.4%

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

   if 6.40000000000000043e-62 < x < 1.1000000000000001e-7

   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 99.9%

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

   5. Taylor expanded in i around inf 74.2%

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

      1. associate-*r* 74.2%

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

      2. *-commutative 74.2%

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

      3. associate-*r* 74.2%

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

      4. *-commutative 74.2%

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

      5. *-commutative 74.2%

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

   7. Simplified 74.2%

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

   if 1.1000000000000001e-7 < x

   1. Initial program 82.6%

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

   3. Simplified 84.2%

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

      1. pow1 84.2%

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

      2. associate-*l* 84.1%

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

      3. associate-*r* 84.1%

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

   6. Applied egg-rr 84.1%

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

      1. unpow1 84.1%

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

      2. *-commutative 84.1%

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

   8. Simplified 84.1%

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

   9. Taylor expanded in x around -inf 64.4%

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

       1. associate-*r* 64.4%

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

       2. neg-mul-1 64.4%

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

       3. cancel-sign-sub-inv 64.4%

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

       4. metadata-eval 64.4%

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

       5. associate-*r* 64.4%

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

   11. Simplified 64.4%

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

   12. Taylor expanded in t around 0 64.4%

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

       1. associate-*r* 64.4%

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

       2. *-commutative 64.4%

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

       3. *-commutative 64.4%

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

       4. associate-*l* 65.9%

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

   14. Simplified 65.9%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -1.62 \cdot 10^{-214}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-62}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-7}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z \cdot \left(t \cdot \left(--18\right)\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -2.35 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-214}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-62}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-8}:\\ \;\;\;\;t\_1 + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<= x -2.35e+55)
     t_2
     (if (<= x -6.2e-214)
       (+ (* b c) t_1)
       (if (<= x 4.2e-62)
         (+ (* b c) (* -4.0 (* t a)))
         (if (<= x 3.1e-8) (+ t_1 (* i (* x -4.0))) t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -2.35e+55) {
		tmp = t_2;
	} else if (x <= -6.2e-214) {
		tmp = (b * c) + t_1;
	} else if (x <= 4.2e-62) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 3.1e-8) {
		tmp = t_1 + (i * (x * -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.
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 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (x <= (-2.35d+55)) then
        tmp = t_2
    else if (x <= (-6.2d-214)) then
        tmp = (b * c) + t_1
    else if (x <= 4.2d-62) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (x <= 3.1d-8) then
        tmp = t_1 + (i * (x * (-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;
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 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -2.35e+55) {
		tmp = t_2;
	} else if (x <= -6.2e-214) {
		tmp = (b * c) + t_1;
	} else if (x <= 4.2e-62) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 3.1e-8) {
		tmp = t_1 + (i * (x * -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])
[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 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if x <= -2.35e+55:
		tmp = t_2
	elif x <= -6.2e-214:
		tmp = (b * c) + t_1
	elif x <= 4.2e-62:
		tmp = (b * c) + (-4.0 * (t * a))
	elif x <= 3.1e-8:
		tmp = t_1 + (i * (x * -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])
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(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -2.35e+55)
		tmp = t_2;
	elseif (x <= -6.2e-214)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= 4.2e-62)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 3.1e-8)
		tmp = Float64(t_1 + Float64(i * Float64(x * -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])){:}
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 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (x <= -2.35e+55)
		tmp = t_2;
	elseif (x <= -6.2e-214)
		tmp = (b * c) + t_1;
	elseif (x <= 4.2e-62)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (x <= 3.1e-8)
		tmp = t_1 + (i * (x * -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.
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[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.35e+55], t$95$2, If[LessEqual[x, -6.2e-214], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 4.2e-62], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e-8], N[(t$95$1 + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.35e55 or 3.1e-8 < 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 79.4%

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

   5. Taylor expanded in x around inf 69.9%

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

   if -2.35e55 < x < -6.20000000000000008e-214

   1. Initial program 88.6%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in b around inf 61.8%

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

   if -6.20000000000000008e-214 < x < 4.1999999999999998e-62

   1. Initial program 98.3%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in j around 0 75.6%

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

   6. Taylor expanded in y around 0 75.6%

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

   7. Taylor expanded in x around 0 74.4%

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

   if 4.1999999999999998e-62 < x < 3.1e-8

   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 99.9%

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

   5. Taylor expanded in i around inf 74.2%

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

      1. associate-*r* 74.2%

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

      2. *-commutative 74.2%

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

      3. associate-*r* 74.2%

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

      4. *-commutative 74.2%

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

      5. *-commutative 74.2%

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

   7. Simplified 74.2%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-214}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-62}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-8}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -2.2 \cdot 10^{+25}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -4.6 \cdot 10^{-263}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{-248}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t a))))
   (if (<= (* b c) -2.2e+25)
     (* b c)
     (if (<= (* b c) -4.6e-263)
       t_1
       (if (<= (* b c) 4.2e-248)
         (* j (* k -27.0))
         (if (<= (* b c) 4e+135) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -2.2e+25) {
		tmp = b * c;
	} else if ((b * c) <= -4.6e-263) {
		tmp = t_1;
	} else if ((b * c) <= 4.2e-248) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 4e+135) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) * (t * a)
    if ((b * c) <= (-2.2d+25)) then
        tmp = b * c
    else if ((b * c) <= (-4.6d-263)) then
        tmp = t_1
    else if ((b * c) <= 4.2d-248) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 4d+135) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -2.2e+25) {
		tmp = b * c;
	} else if ((b * c) <= -4.6e-263) {
		tmp = t_1;
	} else if ((b * c) <= 4.2e-248) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 4e+135) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (t * a)
	tmp = 0
	if (b * c) <= -2.2e+25:
		tmp = b * c
	elif (b * c) <= -4.6e-263:
		tmp = t_1
	elif (b * c) <= 4.2e-248:
		tmp = j * (k * -27.0)
	elif (b * c) <= 4e+135:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(t * a))
	tmp = 0.0
	if (Float64(b * c) <= -2.2e+25)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -4.6e-263)
		tmp = t_1;
	elseif (Float64(b * c) <= 4.2e-248)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 4e+135)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (t * a);
	tmp = 0.0;
	if ((b * c) <= -2.2e+25)
		tmp = b * c;
	elseif ((b * c) <= -4.6e-263)
		tmp = t_1;
	elseif ((b * c) <= 4.2e-248)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 4e+135)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.2e+25], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -4.6e-263], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 4.2e-248], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4e+135], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.2000000000000001e25 or 3.99999999999999985e135 < (*.f64 b c)

   1. Initial program 80.3%

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

   3. Simplified 81.3%

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

      1. pow1 81.3%

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

      2. associate-*l* 81.3%

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

      3. associate-*r* 81.3%

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

   6. Applied egg-rr 81.3%

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

      1. unpow1 81.3%

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

      2. *-commutative 81.3%

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

   8. Simplified 81.3%

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

   9. Taylor expanded in b around inf 60.0%

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

   if -2.2000000000000001e25 < (*.f64 b c) < -4.60000000000000006e-263 or 4.2e-248 < (*.f64 b c) < 3.99999999999999985e135

   1. Initial program 87.8%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in j around 0 79.1%

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

   6. Taylor expanded in y around 0 77.3%

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

   7. Taylor expanded in a around inf 29.6%

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

      1. *-commutative 29.6%

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

   9. Simplified 29.6%

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

   if -4.60000000000000006e-263 < (*.f64 b c) < 4.2e-248

   1. Initial program 89.1%

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

   3. Simplified 86.9%

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

      1. pow1 86.9%

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

      2. associate-*l* 86.9%

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

      3. associate-*r* 86.9%

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

   6. Applied egg-rr 86.9%

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

      1. unpow1 86.9%

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

      2. *-commutative 86.9%

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

   8. Simplified 86.9%

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

   9. Taylor expanded in j around inf 35.0%

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

       1. *-commutative 35.0%

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

       2. associate-*r* 35.0%

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

   11. Simplified 35.0%

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

Alternative 15: 35.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -9.4 \cdot 10^{+20}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 3.6 \cdot 10^{-245}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 8.5 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t a))))
   (if (<= (* b c) -9.4e+20)
     (* b c)
     (if (<= (* b c) -3e-272)
       t_1
       (if (<= (* b c) 3.6e-245)
         (* -27.0 (* j k))
         (if (<= (* b c) 8.5e+134) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -9.4e+20) {
		tmp = b * c;
	} else if ((b * c) <= -3e-272) {
		tmp = t_1;
	} else if ((b * c) <= 3.6e-245) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 8.5e+134) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) * (t * a)
    if ((b * c) <= (-9.4d+20)) then
        tmp = b * c
    else if ((b * c) <= (-3d-272)) then
        tmp = t_1
    else if ((b * c) <= 3.6d-245) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 8.5d+134) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -9.4e+20) {
		tmp = b * c;
	} else if ((b * c) <= -3e-272) {
		tmp = t_1;
	} else if ((b * c) <= 3.6e-245) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 8.5e+134) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (t * a)
	tmp = 0
	if (b * c) <= -9.4e+20:
		tmp = b * c
	elif (b * c) <= -3e-272:
		tmp = t_1
	elif (b * c) <= 3.6e-245:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 8.5e+134:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(t * a))
	tmp = 0.0
	if (Float64(b * c) <= -9.4e+20)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3e-272)
		tmp = t_1;
	elseif (Float64(b * c) <= 3.6e-245)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 8.5e+134)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (t * a);
	tmp = 0.0;
	if ((b * c) <= -9.4e+20)
		tmp = b * c;
	elseif ((b * c) <= -3e-272)
		tmp = t_1;
	elseif ((b * c) <= 3.6e-245)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 8.5e+134)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -9.4e+20], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3e-272], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 3.6e-245], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 8.5e+134], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -9.4e20 or 8.50000000000000024e134 < (*.f64 b c)

   1. Initial program 80.3%

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

   3. Simplified 81.3%

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

      1. pow1 81.3%

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

      2. associate-*l* 81.3%

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

      3. associate-*r* 81.3%

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

   6. Applied egg-rr 81.3%

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

      1. unpow1 81.3%

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

      2. *-commutative 81.3%

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

   8. Simplified 81.3%

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

   9. Taylor expanded in b around inf 60.0%

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

   if -9.4e20 < (*.f64 b c) < -3.0000000000000003e-272 or 3.59999999999999999e-245 < (*.f64 b c) < 8.50000000000000024e134

   1. Initial program 87.8%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in j around 0 79.1%

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

   6. Taylor expanded in y around 0 77.3%

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

   7. Taylor expanded in a around inf 29.6%

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

      1. *-commutative 29.6%

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

   9. Simplified 29.6%

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

   if -3.0000000000000003e-272 < (*.f64 b c) < 3.59999999999999999e-245

   1. Initial program 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in j around inf 35.0%

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

Alternative 16: 81.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-29} \lor \neg \left(t \leq 40000\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -8.8e-29) (not (<= t 40000.0)))
   (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) (* 4.0 (* x i)))
   (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -8.8e-29) || !(t <= 40000.0)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-8.8d-29)) .or. (.not. (t <= 40000.0d0))) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (4.0d0 * (x * i))
    else
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -8.8e-29) || !(t <= 40000.0)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -8.8e-29) or not (t <= 40000.0):
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i))
	else:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -8.8e-29) || !(t <= 40000.0))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -8.8e-29) || ~((t <= 40000.0)))
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	else
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -8.8e-29], N[Not[LessEqual[t, 40000.0]], $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] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.79999999999999961e-29 or 4e4 < t

   1. Initial program 86.6%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in j around 0 86.6%

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

   if -8.79999999999999961e-29 < t < 4e4

   1. Initial program 83.8%

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

   3. Taylor expanded in y around 0 85.4%

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

      1. distribute-lft-out 85.4%

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

      2. *-commutative 85.4%

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

   5. Simplified 85.4%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-29} \lor \neg \left(t \leq 40000\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 68.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+76}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+195}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -1e+76)
     (- (* b c) (* 27.0 (* j k)))
     (if (<= t_1 4e+195)
       (- (+ (* b c) (* -4.0 (* t a))) (* 4.0 (* x i)))
       (+ (* j (* k -27.0)) (* i (* x -4.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+76) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t_1 <= 4e+195) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i));
	} else {
		tmp = (j * (k * -27.0)) + (i * (x * -4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-1d+76)) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (t_1 <= 4d+195) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (4.0d0 * (x * i))
    else
        tmp = (j * (k * (-27.0d0))) + (i * (x * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+76) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t_1 <= 4e+195) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i));
	} else {
		tmp = (j * (k * -27.0)) + (i * (x * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -1e+76:
		tmp = (b * c) - (27.0 * (j * k))
	elif t_1 <= 4e+195:
		tmp = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i))
	else:
		tmp = (j * (k * -27.0)) + (i * (x * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -1e+76)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (t_1 <= 4e+195)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(i * Float64(x * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -1e+76)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (t_1 <= 4e+195)
		tmp = ((b * c) + (-4.0 * (t * a))) - (4.0 * (x * i));
	else
		tmp = (j * (k * -27.0)) + (i * (x * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+76], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+195], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e76

   1. Initial program 76.0%

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

   3. Taylor expanded in t around 0 61.1%

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

   4. Taylor expanded in i around 0 60.0%

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

   if -1e76 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.99999999999999991e195

   1. Initial program 89.1%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in j around 0 84.8%

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

   6. Taylor expanded in y around 0 73.9%

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

   if 3.99999999999999991e195 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in i around inf 80.5%

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

      1. associate-*r* 80.5%

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

      2. *-commutative 80.5%

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

      3. associate-*r* 80.5%

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

      4. *-commutative 80.5%

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

      5. *-commutative 80.5%

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

   7. Simplified 80.5%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+76}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 4 \cdot 10^{+195}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-9}:\\ \;\;\;\;t\_1 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+145}:\\ \;\;\;\;t\_1 - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-4 \cdot \frac{i}{z} + 18 \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a)))))
   (if (<= x -5.8e+55)
     (+ (* x (+ (* 18.0 (* t (* y z))) (* i -4.0))) (* j (* k -27.0)))
     (if (<= x 3.4e-9)
       (- t_1 (* 27.0 (* j k)))
       (if (<= x 4.2e+145)
         (- t_1 (* 4.0 (* x i)))
         (* x (* z (+ (* -4.0 (/ i z)) (* 18.0 (* y t))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if (x <= -5.8e+55) {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	} else if (x <= 3.4e-9) {
		tmp = t_1 - (27.0 * (j * k));
	} else if (x <= 4.2e+145) {
		tmp = t_1 - (4.0 * (x * i));
	} else {
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    if (x <= (-5.8d+55)) then
        tmp = (x * ((18.0d0 * (t * (y * z))) + (i * (-4.0d0)))) + (j * (k * (-27.0d0)))
    else if (x <= 3.4d-9) then
        tmp = t_1 - (27.0d0 * (j * k))
    else if (x <= 4.2d+145) then
        tmp = t_1 - (4.0d0 * (x * i))
    else
        tmp = x * (z * (((-4.0d0) * (i / z)) + (18.0d0 * (y * t))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if (x <= -5.8e+55) {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	} else if (x <= 3.4e-9) {
		tmp = t_1 - (27.0 * (j * k));
	} else if (x <= 4.2e+145) {
		tmp = t_1 - (4.0 * (x * i));
	} else {
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	tmp = 0
	if x <= -5.8e+55:
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0))
	elif x <= 3.4e-9:
		tmp = t_1 - (27.0 * (j * k))
	elif x <= 4.2e+145:
		tmp = t_1 - (4.0 * (x * i))
	else:
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (x <= -5.8e+55)
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) + Float64(i * -4.0))) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 3.4e-9)
		tmp = Float64(t_1 - Float64(27.0 * Float64(j * k)));
	elseif (x <= 4.2e+145)
		tmp = Float64(t_1 - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(x * Float64(z * Float64(Float64(-4.0 * Float64(i / z)) + Float64(18.0 * Float64(y * t)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	tmp = 0.0;
	if (x <= -5.8e+55)
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	elseif (x <= 3.4e-9)
		tmp = t_1 - (27.0 * (j * k));
	elseif (x <= 4.2e+145)
		tmp = t_1 - (4.0 * (x * i));
	else
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e+55], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e-9], N[(t$95$1 - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+145], N[(t$95$1 - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * N[(N[(-4.0 * N[(i / z), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.7999999999999997e55

   1. Initial program 64.6%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in x around inf 76.9%

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

   if -5.7999999999999997e55 < x < 3.3999999999999998e-9

   1. Initial program 94.2%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around 0 80.6%

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

   if 3.3999999999999998e-9 < x < 4.19999999999999979e145

   1. Initial program 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in j around 0 96.4%

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

   6. Taylor expanded in y around 0 79.4%

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

   if 4.19999999999999979e145 < x

   1. Initial program 71.5%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in x around inf 71.9%

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

   6. Taylor expanded in z around inf 74.6%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-9}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+145}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-4 \cdot \frac{i}{z} + 18 \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 72.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(4 \cdot \left(-i\right) - \left(t \cdot -18\right) \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-7}:\\ \;\;\;\;t\_1 - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+141}:\\ \;\;\;\;t\_1 - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-4 \cdot \frac{i}{z} + 18 \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a)))))
   (if (<= x -6e+55)
     (* x (- (* 4.0 (- i)) (* (* t -18.0) (* y z))))
     (if (<= x 3.6e-7)
       (- t_1 (* 27.0 (* j k)))
       (if (<= x 3.7e+141)
         (- t_1 (* 4.0 (* x i)))
         (* x (* z (+ (* -4.0 (/ i z)) (* 18.0 (* y t))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if (x <= -6e+55) {
		tmp = x * ((4.0 * -i) - ((t * -18.0) * (y * z)));
	} else if (x <= 3.6e-7) {
		tmp = t_1 - (27.0 * (j * k));
	} else if (x <= 3.7e+141) {
		tmp = t_1 - (4.0 * (x * i));
	} else {
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    if (x <= (-6d+55)) then
        tmp = x * ((4.0d0 * -i) - ((t * (-18.0d0)) * (y * z)))
    else if (x <= 3.6d-7) then
        tmp = t_1 - (27.0d0 * (j * k))
    else if (x <= 3.7d+141) then
        tmp = t_1 - (4.0d0 * (x * i))
    else
        tmp = x * (z * (((-4.0d0) * (i / z)) + (18.0d0 * (y * t))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if (x <= -6e+55) {
		tmp = x * ((4.0 * -i) - ((t * -18.0) * (y * z)));
	} else if (x <= 3.6e-7) {
		tmp = t_1 - (27.0 * (j * k));
	} else if (x <= 3.7e+141) {
		tmp = t_1 - (4.0 * (x * i));
	} else {
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	tmp = 0
	if x <= -6e+55:
		tmp = x * ((4.0 * -i) - ((t * -18.0) * (y * z)))
	elif x <= 3.6e-7:
		tmp = t_1 - (27.0 * (j * k))
	elif x <= 3.7e+141:
		tmp = t_1 - (4.0 * (x * i))
	else:
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (x <= -6e+55)
		tmp = Float64(x * Float64(Float64(4.0 * Float64(-i)) - Float64(Float64(t * -18.0) * Float64(y * z))));
	elseif (x <= 3.6e-7)
		tmp = Float64(t_1 - Float64(27.0 * Float64(j * k)));
	elseif (x <= 3.7e+141)
		tmp = Float64(t_1 - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(x * Float64(z * Float64(Float64(-4.0 * Float64(i / z)) + Float64(18.0 * Float64(y * t)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	tmp = 0.0;
	if (x <= -6e+55)
		tmp = x * ((4.0 * -i) - ((t * -18.0) * (y * z)));
	elseif (x <= 3.6e-7)
		tmp = t_1 - (27.0 * (j * k));
	elseif (x <= 3.7e+141)
		tmp = t_1 - (4.0 * (x * i));
	else
		tmp = x * (z * ((-4.0 * (i / z)) + (18.0 * (y * t))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+55], N[(x * N[(N[(4.0 * (-i)), $MachinePrecision] - N[(N[(t * -18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e-7], N[(t$95$1 - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e+141], N[(t$95$1 - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * N[(N[(-4.0 * N[(i / z), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.00000000000000033e55

   1. Initial program 64.6%

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

   3. Simplified 73.8%

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

      1. pow1 73.8%

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

      2. associate-*l* 73.8%

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

      3. associate-*r* 73.8%

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

   6. Applied egg-rr 73.8%

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

      1. unpow1 73.8%

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

      2. *-commutative 73.8%

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

   8. Simplified 73.8%

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

   9. Taylor expanded in x around -inf 76.4%

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

       1. associate-*r* 76.4%

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

       2. neg-mul-1 76.4%

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

       3. cancel-sign-sub-inv 76.4%

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

       4. metadata-eval 76.4%

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

       5. associate-*r* 76.4%

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

   11. Simplified 76.4%

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

   if -6.00000000000000033e55 < x < 3.59999999999999994e-7

   1. Initial program 94.2%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around 0 80.6%

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

   if 3.59999999999999994e-7 < x < 3.7000000000000003e141

   1. Initial program 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in j around 0 96.4%

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

   6. Taylor expanded in y around 0 79.4%

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

   if 3.7000000000000003e141 < x

   1. Initial program 71.5%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in x around inf 71.9%

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

   6. Taylor expanded in z around inf 74.6%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(4 \cdot \left(-i\right) - \left(t \cdot -18\right) \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-7}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+141}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-4 \cdot \frac{i}{z} + 18 \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 44.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{-93}:\\ \;\;\;\;x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a)))))
   (if (<= z -3.4e-93)
     (* x (* t (* 18.0 (* y z))))
     (if (<= z -5.8e-174)
       t_1
       (if (<= z -5.5e-232)
         (* x (* i -4.0))
         (if (<= z 8e+200) t_1 (* 18.0 (* (* y z) (* x t)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if (z <= -3.4e-93) {
		tmp = x * (t * (18.0 * (y * z)));
	} else if (z <= -5.8e-174) {
		tmp = t_1;
	} else if (z <= -5.5e-232) {
		tmp = x * (i * -4.0);
	} else if (z <= 8e+200) {
		tmp = t_1;
	} else {
		tmp = 18.0 * ((y * z) * (x * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    if (z <= (-3.4d-93)) then
        tmp = x * (t * (18.0d0 * (y * z)))
    else if (z <= (-5.8d-174)) then
        tmp = t_1
    else if (z <= (-5.5d-232)) then
        tmp = x * (i * (-4.0d0))
    else if (z <= 8d+200) then
        tmp = t_1
    else
        tmp = 18.0d0 * ((y * z) * (x * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if (z <= -3.4e-93) {
		tmp = x * (t * (18.0 * (y * z)));
	} else if (z <= -5.8e-174) {
		tmp = t_1;
	} else if (z <= -5.5e-232) {
		tmp = x * (i * -4.0);
	} else if (z <= 8e+200) {
		tmp = t_1;
	} else {
		tmp = 18.0 * ((y * z) * (x * t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	tmp = 0
	if z <= -3.4e-93:
		tmp = x * (t * (18.0 * (y * z)))
	elif z <= -5.8e-174:
		tmp = t_1
	elif z <= -5.5e-232:
		tmp = x * (i * -4.0)
	elif z <= 8e+200:
		tmp = t_1
	else:
		tmp = 18.0 * ((y * z) * (x * t))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (z <= -3.4e-93)
		tmp = Float64(x * Float64(t * Float64(18.0 * Float64(y * z))));
	elseif (z <= -5.8e-174)
		tmp = t_1;
	elseif (z <= -5.5e-232)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (z <= 8e+200)
		tmp = t_1;
	else
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	tmp = 0.0;
	if (z <= -3.4e-93)
		tmp = x * (t * (18.0 * (y * z)));
	elseif (z <= -5.8e-174)
		tmp = t_1;
	elseif (z <= -5.5e-232)
		tmp = x * (i * -4.0);
	elseif (z <= 8e+200)
		tmp = t_1;
	else
		tmp = 18.0 * ((y * z) * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e-93], N[(x * N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8e-174], t$95$1, If[LessEqual[z, -5.5e-232], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+200], t$95$1, N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.40000000000000001e-93

   1. Initial program 85.5%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in x around inf 53.7%

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

   6. Taylor expanded in t around inf 39.8%

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

      1. *-commutative 39.8%

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

      2. associate-*l* 39.8%

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

      3. *-commutative 39.8%

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

   8. Simplified 39.8%

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

   if -3.40000000000000001e-93 < z < -5.8000000000000002e-174 or -5.50000000000000023e-232 < z < 7.9999999999999998e200

   1. Initial program 86.3%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in j around 0 76.2%

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

   6. Taylor expanded in y around 0 76.9%

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

   7. Taylor expanded in x around 0 54.1%

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

   if -5.8000000000000002e-174 < z < -5.50000000000000023e-232

   1. Initial program 93.1%

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

   3. Simplified 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. Step-by-step derivation

      1. pow1 99.8%

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

      2. associate-*l* 99.8%

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

      3. associate-*r* 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. unpow1 99.8%

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

      2. *-commutative 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in i around inf 37.1%

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

       1. metadata-eval 37.1%

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

       2. distribute-lft-neg-in 37.1%

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

       3. associate-*r* 37.1%

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

       4. *-commutative 37.1%

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

       5. distribute-rgt-neg-in 37.1%

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

       6. distribute-lft-neg-in 37.1%

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

       7. metadata-eval 37.1%

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

   11. Simplified 37.1%

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

   if 7.9999999999999998e200 < z

   1. Initial program 71.7%

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

   3. Simplified 73.0%

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

   5. Taylor expanded in x around inf 78.3%

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

   6. Taylor expanded in t around inf 66.4%

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

      1. associate-*r* 70.8%

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

   8. Simplified 70.8%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-93}:\\ \;\;\;\;x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-174}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+200}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 79.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+135}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -2.5e+55)
   (+ (* x (+ (* 18.0 (* t (* y z))) (* i -4.0))) (* j (* k -27.0)))
   (if (<= x 1.1e+135)
     (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) (* (* j 27.0) k))
     (- (+ (* b c) (* 18.0 (* t (* x (* y z))))) (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -2.5e+55) {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	} else if (x <= 1.1e+135) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-2.5d+55)) then
        tmp = (x * ((18.0d0 * (t * (y * z))) + (i * (-4.0d0)))) + (j * (k * (-27.0d0)))
    else if (x <= 1.1d+135) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - ((j * 27.0d0) * k)
    else
        tmp = ((b * c) + (18.0d0 * (t * (x * (y * z))))) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -2.5e+55) {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	} else if (x <= 1.1e+135) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -2.5e+55:
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0))
	elif x <= 1.1e+135:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k)
	else:
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -2.5e+55)
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) + Float64(i * -4.0))) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 1.1e+135)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -2.5e+55)
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	elseif (x <= 1.1e+135)
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	else
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -2.5e+55], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+135], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.50000000000000023e55

   1. Initial program 64.6%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in x around inf 76.9%

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

   if -2.50000000000000023e55 < x < 1.1e135

   1. Initial program 94.4%

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

   3. Taylor expanded in y around 0 86.7%

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

      1. distribute-lft-out 86.7%

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

      2. *-commutative 86.7%

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

   5. Simplified 86.7%

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

   if 1.1e135 < x

   1. Initial program 75.1%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in j around 0 80.2%

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

   6. Taylor expanded in a around 0 77.8%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+135}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 74.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-7}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -2.1e+55)
   (+ (* x (+ (* 18.0 (* t (* y z))) (* i -4.0))) (* j (* k -27.0)))
   (if (<= x 1.4e-7)
     (- (+ (* b c) (* -4.0 (* t a))) (* 27.0 (* j k)))
     (- (+ (* b c) (* 18.0 (* t (* x (* y z))))) (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -2.1e+55) {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	} else if (x <= 1.4e-7) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-2.1d+55)) then
        tmp = (x * ((18.0d0 * (t * (y * z))) + (i * (-4.0d0)))) + (j * (k * (-27.0d0)))
    else if (x <= 1.4d-7) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (27.0d0 * (j * k))
    else
        tmp = ((b * c) + (18.0d0 * (t * (x * (y * z))))) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -2.1e+55) {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	} else if (x <= 1.4e-7) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -2.1e+55:
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0))
	elif x <= 1.4e-7:
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k))
	else:
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -2.1e+55)
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) + Float64(i * -4.0))) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 1.4e-7)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -2.1e+55)
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	elseif (x <= 1.4e-7)
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	else
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -2.1e+55], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e-7], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1000000000000001e55

   1. Initial program 64.6%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in x around inf 76.9%

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

   if -2.1000000000000001e55 < x < 1.4000000000000001e-7

   1. Initial program 94.2%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around 0 80.6%

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

   if 1.4000000000000001e-7 < x

   1. Initial program 82.6%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in j around 0 85.9%

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

   6. Taylor expanded in a around 0 74.9%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-7}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 73.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 160:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -4.3e+55)
   (+ (* x (+ (* 18.0 (* t (* y z))) (* i -4.0))) (* j (* k -27.0)))
   (if (<= x 160.0)
     (- (+ (* b c) (* -4.0 (* t a))) (* 27.0 (* j k)))
     (- (* t (- (* 18.0 (* x (* y z))) (* a 4.0))) (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -4.3e+55) {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	} else if (x <= 160.0) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} else {
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-4.3d+55)) then
        tmp = (x * ((18.0d0 * (t * (y * z))) + (i * (-4.0d0)))) + (j * (k * (-27.0d0)))
    else if (x <= 160.0d0) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (27.0d0 * (j * k))
    else
        tmp = (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -4.3e+55) {
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	} else if (x <= 160.0) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} else {
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -4.3e+55:
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0))
	elif x <= 160.0:
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k))
	else:
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -4.3e+55)
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) + Float64(i * -4.0))) + Float64(j * Float64(k * -27.0)));
	elseif (x <= 160.0)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -4.3e+55)
		tmp = (x * ((18.0 * (t * (y * z))) + (i * -4.0))) + (j * (k * -27.0));
	elseif (x <= 160.0)
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	else
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -4.3e+55], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 160.0], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2999999999999999e55

   1. Initial program 64.6%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in x around inf 76.9%

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

   if -4.2999999999999999e55 < x < 160

   1. Initial program 94.2%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around 0 80.4%

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

   if 160 < x

   1. Initial program 82.3%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in j around 0 85.6%

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

   6. Taylor expanded in b around 0 74.7%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 160:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 36.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8 \cdot 10^{-45} \lor \neg \left(b \cdot c \leq 3.1 \cdot 10^{+125}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) -8e-45) (not (<= (* b c) 3.1e+125)))
   (* 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);
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) <= -8e-45) || !((b * c) <= 3.1e+125)) {
		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.
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) <= (-8d-45)) .or. (.not. ((b * c) <= 3.1d+125))) 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;
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) <= -8e-45) || !((b * c) <= 3.1e+125)) {
		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])
[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) <= -8e-45) or not ((b * c) <= 3.1e+125):
		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])
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) <= -8e-45) || !(Float64(b * c) <= 3.1e+125))
		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])){:}
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) <= -8e-45) || ~(((b * c) <= 3.1e+125)))
		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.
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], -8e-45], N[Not[LessEqual[N[(b * c), $MachinePrecision], 3.1e+125]], $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) < -7.99999999999999987e-45 or 3.1e125 < (*.f64 b c)

   1. Initial program 81.8%

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

   3. Simplified 81.9%

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

      1. pow1 81.9%

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

      2. associate-*l* 81.9%

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

      3. associate-*r* 81.8%

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

   6. Applied egg-rr 81.8%

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

      1. unpow1 81.8%

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

      2. *-commutative 81.8%

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

   8. Simplified 81.8%

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

   9. Taylor expanded in b around inf 57.0%

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

   if -7.99999999999999987e-45 < (*.f64 b c) < 3.1e125

   1. Initial program 87.5%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in j around inf 25.1%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8 \cdot 10^{-45} \lor \neg \left(b \cdot c \leq 3.1 \cdot 10^{+125}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 23.6% accurate, 10.3× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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);
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.
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;
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])
[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])
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])){:}
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.
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 85.2%

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

3. Simplified 85.7%

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

   1. pow1 85.7%

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

   2. associate-*l* 85.7%

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

   3. associate-*r* 85.7%

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

6. Applied egg-rr 85.7%

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

   1. unpow1 85.7%

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

   2. *-commutative 85.7%

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

8. Simplified 85.7%

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

9. Taylor expanded in b around inf 26.3%

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

Developer target: 89.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024094 
(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)))