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

Percentage Accurate: 84.4% → 91.9%

Time: 25.9s

Alternatives: 25

Speedup: 0.8×

• 50.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 4\right) \cdot i\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := t \cdot \left(a \cdot 4\right)\\ t_4 := \left(\left(\left(\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right) \cdot t - t\_3\right) + b \cdot c\right) - t\_1\right) - t\_2\\ \mathbf{if}\;t\_4 \leq 4 \cdot 10^{+208}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;\left(\left(b \cdot c + \left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right) - t\_3\right)\right) - t\_1\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* x 4.0) i))
        (t_2 (* (* j 27.0) k))
        (t_3 (* t (* a 4.0)))
        (t_4 (- (- (+ (- (* (* z (* (* x 18.0) y)) t) t_3) (* b c)) t_1) t_2)))
   (if (<= t_4 4e+208)
     t_4
     (if (<= t_4 INFINITY)
       (- (- (+ (* b c) (- (* y (* (* x 18.0) (* z t))) t_3)) t_1) t_2)
       (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * 4.0) * i;
	double t_2 = (j * 27.0) * k;
	double t_3 = t * (a * 4.0);
	double t_4 = (((((z * ((x * 18.0) * y)) * t) - t_3) + (b * c)) - t_1) - t_2;
	double tmp;
	if (t_4 <= 4e+208) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - t_3)) - t_1) - t_2;
	} else {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * 4.0) * i;
	double t_2 = (j * 27.0) * k;
	double t_3 = t * (a * 4.0);
	double t_4 = (((((z * ((x * 18.0) * y)) * t) - t_3) + (b * c)) - t_1) - t_2;
	double tmp;
	if (t_4 <= 4e+208) {
		tmp = t_4;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - t_3)) - t_1) - t_2;
	} else {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * 4.0) * i
	t_2 = (j * 27.0) * k
	t_3 = t * (a * 4.0)
	t_4 = (((((z * ((x * 18.0) * y)) * t) - t_3) + (b * c)) - t_1) - t_2
	tmp = 0
	if t_4 <= 4e+208:
		tmp = t_4
	elif t_4 <= math.inf:
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - t_3)) - t_1) - t_2
	else:
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * 4.0) * i)
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(t * Float64(a * 4.0))
	t_4 = Float64(Float64(Float64(Float64(Float64(Float64(z * Float64(Float64(x * 18.0) * y)) * t) - t_3) + Float64(b * c)) - t_1) - t_2)
	tmp = 0.0
	if (t_4 <= 4e+208)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(y * Float64(Float64(x * 18.0) * Float64(z * t))) - t_3)) - t_1) - t_2);
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * 4.0) * i;
	t_2 = (j * 27.0) * k;
	t_3 = t * (a * 4.0);
	t_4 = (((((z * ((x * 18.0) * y)) * t) - t_3) + (b * c)) - t_1) - t_2;
	tmp = 0.0;
	if (t_4 <= 4e+208)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - t_3)) - t_1) - t_2;
	else
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(N[(N[(z * N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - t$95$3), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, 4e+208], t$95$4, If[LessEqual[t$95$4, Infinity], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < 3.9999999999999999e208

   1. Initial program 98.5%

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

   if 3.9999999999999999e208 < (-.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 83.7%

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

      1. pow1 83.7%

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

      2. associate-*l* 90.3%

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

      3. *-commutative 90.3%

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

   4. Applied egg-rr 90.3%

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

      1. unpow1 90.3%

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

      2. associate-*l* 98.4%

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

      3. *-commutative 98.4%

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

   6. Simplified 98.4%

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

   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 25.8%

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

   5. Taylor expanded in x around inf 64.6%

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

      1. pow1 64.6%

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

   7. Applied egg-rr 64.6%

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

      1. unpow1 64.6%

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

      2. *-commutative 64.6%

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

      3. associate-*r* 67.8%

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

   9. Simplified 67.8%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq 4 \cdot 10^{+208}:\\ \;\;\;\;\left(\left(\left(\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\left(\left(b \cdot c + \left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -0.125:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27 + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-137}:\\ \;\;\;\;b \cdot c - \left(t\_1 + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-61}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+73}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* j k)))
        (t_2 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))))
   (if (<= t -3.7e+37)
     t_2
     (if (<= t -0.125)
       (+ (* (* j k) -27.0) (* 18.0 (* t (* y (* x z)))))
       (if (<= t 4.6e-137)
         (- (* b c) (+ t_1 (* 4.0 (* x i))))
         (if (<= t 4.5e-87)
           t_2
           (if (<= t 8.2e-61)
             (- (* b c) (* (* x 4.0) i))
             (if (<= t 4e+73) (- (+ (* b c) (* -4.0 (* t a))) t_1) t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -3.7e+37) {
		tmp = t_2;
	} else if (t <= -0.125) {
		tmp = ((j * k) * -27.0) + (18.0 * (t * (y * (x * z))));
	} else if (t <= 4.6e-137) {
		tmp = (b * c) - (t_1 + (4.0 * (x * i)));
	} else if (t <= 4.5e-87) {
		tmp = t_2;
	} else if (t <= 8.2e-61) {
		tmp = (b * c) - ((x * 4.0) * i);
	} else if (t <= 4e+73) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (j * k)
    t_2 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    if (t <= (-3.7d+37)) then
        tmp = t_2
    else if (t <= (-0.125d0)) then
        tmp = ((j * k) * (-27.0d0)) + (18.0d0 * (t * (y * (x * z))))
    else if (t <= 4.6d-137) then
        tmp = (b * c) - (t_1 + (4.0d0 * (x * i)))
    else if (t <= 4.5d-87) then
        tmp = t_2
    else if (t <= 8.2d-61) then
        tmp = (b * c) - ((x * 4.0d0) * i)
    else if (t <= 4d+73) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -3.7e+37) {
		tmp = t_2;
	} else if (t <= -0.125) {
		tmp = ((j * k) * -27.0) + (18.0 * (t * (y * (x * z))));
	} else if (t <= 4.6e-137) {
		tmp = (b * c) - (t_1 + (4.0 * (x * i)));
	} else if (t <= 4.5e-87) {
		tmp = t_2;
	} else if (t <= 8.2e-61) {
		tmp = (b * c) - ((x * 4.0) * i);
	} else if (t <= 4e+73) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	tmp = 0
	if t <= -3.7e+37:
		tmp = t_2
	elif t <= -0.125:
		tmp = ((j * k) * -27.0) + (18.0 * (t * (y * (x * z))))
	elif t <= 4.6e-137:
		tmp = (b * c) - (t_1 + (4.0 * (x * i)))
	elif t <= 4.5e-87:
		tmp = t_2
	elif t <= 8.2e-61:
		tmp = (b * c) - ((x * 4.0) * i)
	elif t <= 4e+73:
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	t_2 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))))
	tmp = 0.0
	if (t <= -3.7e+37)
		tmp = t_2;
	elseif (t <= -0.125)
		tmp = Float64(Float64(Float64(j * k) * -27.0) + Float64(18.0 * Float64(t * Float64(y * Float64(x * z)))));
	elseif (t <= 4.6e-137)
		tmp = Float64(Float64(b * c) - Float64(t_1 + Float64(4.0 * Float64(x * i))));
	elseif (t <= 4.5e-87)
		tmp = t_2;
	elseif (t <= 8.2e-61)
		tmp = Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i));
	elseif (t <= 4e+73)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 27.0 * (j * k);
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	tmp = 0.0;
	if (t <= -3.7e+37)
		tmp = t_2;
	elseif (t <= -0.125)
		tmp = ((j * k) * -27.0) + (18.0 * (t * (y * (x * z))));
	elseif (t <= 4.6e-137)
		tmp = (b * c) - (t_1 + (4.0 * (x * i)));
	elseif (t <= 4.5e-87)
		tmp = t_2;
	elseif (t <= 8.2e-61)
		tmp = (b * c) - ((x * 4.0) * i);
	elseif (t <= 4e+73)
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+37], t$95$2, If[LessEqual[t, -0.125], N[(N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision] + N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-137], N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-87], t$95$2, If[LessEqual[t, 8.2e-61], N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+73], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.6999999999999999e37 or 4.60000000000000016e-137 < t < 4.49999999999999958e-87 or 3.99999999999999993e73 < t

   1. Initial program 80.9%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in i around 0 84.3%

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

   6. Taylor expanded in j around 0 82.0%

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

   if -3.6999999999999999e37 < t < -0.125

   1. Initial program 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in t around inf 92.3%

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

   6. Taylor expanded in a around 0 85.7%

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

      1. pow1 85.7%

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

   8. Applied egg-rr 85.7%

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

      1. unpow1 85.7%

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

      2. *-commutative 85.7%

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

      3. associate-*r* 85.7%

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

   10. Simplified 85.7%

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

   if -0.125 < t < 4.60000000000000016e-137

   1. Initial program 79.3%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in t around 0 83.3%

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

   if 4.49999999999999958e-87 < t < 8.19999999999999998e-61

   1. Initial program 100.0%

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

   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 t around 0 100.0%

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

   6. Taylor expanded in i around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 100.0%

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

   8. Simplified 100.0%

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

   if 8.19999999999999998e-61 < t < 3.99999999999999993e73

   1. Initial program 95.8%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in x around 0 80.6%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+37}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -0.125:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27 + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-137}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-87}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-61}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+73}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -2.2 \cdot 10^{+71}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;b \cdot c \leq -3.8 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \left(x \cdot \left(t \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -1.5 \cdot 10^{-276}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 5.6 \cdot 10^{-224}:\\ \;\;\;\;t\_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{+160}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ t_1 (* t (* a -4.0)))))
   (if (<= (* b c) -2.2e+71)
     (+ (* b c) t_1)
     (if (<= (* b c) -3.8e-31)
       (* y (* x (* t (* 18.0 z))))
       (if (<= (* b c) -1.5e-276)
         t_2
         (if (<= (* b c) 5.6e-224)
           (+ t_1 (* -4.0 (* x i)))
           (if (<= (* b c) 1.9e+160) t_2 (- (* b c) (* (* x 4.0) i)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (t * (a * -4.0));
	double tmp;
	if ((b * c) <= -2.2e+71) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= -3.8e-31) {
		tmp = y * (x * (t * (18.0 * z)));
	} else if ((b * c) <= -1.5e-276) {
		tmp = t_2;
	} else if ((b * c) <= 5.6e-224) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if ((b * c) <= 1.9e+160) {
		tmp = t_2;
	} else {
		tmp = (b * c) - ((x * 4.0) * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + (t * (a * (-4.0d0)))
    if ((b * c) <= (-2.2d+71)) then
        tmp = (b * c) + t_1
    else if ((b * c) <= (-3.8d-31)) then
        tmp = y * (x * (t * (18.0d0 * z)))
    else if ((b * c) <= (-1.5d-276)) then
        tmp = t_2
    else if ((b * c) <= 5.6d-224) then
        tmp = t_1 + ((-4.0d0) * (x * i))
    else if ((b * c) <= 1.9d+160) then
        tmp = t_2
    else
        tmp = (b * c) - ((x * 4.0d0) * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (t * (a * -4.0));
	double tmp;
	if ((b * c) <= -2.2e+71) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= -3.8e-31) {
		tmp = y * (x * (t * (18.0 * z)));
	} else if ((b * c) <= -1.5e-276) {
		tmp = t_2;
	} else if ((b * c) <= 5.6e-224) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if ((b * c) <= 1.9e+160) {
		tmp = t_2;
	} else {
		tmp = (b * c) - ((x * 4.0) * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (t * (a * -4.0))
	tmp = 0
	if (b * c) <= -2.2e+71:
		tmp = (b * c) + t_1
	elif (b * c) <= -3.8e-31:
		tmp = y * (x * (t * (18.0 * z)))
	elif (b * c) <= -1.5e-276:
		tmp = t_2
	elif (b * c) <= 5.6e-224:
		tmp = t_1 + (-4.0 * (x * i))
	elif (b * c) <= 1.9e+160:
		tmp = t_2
	else:
		tmp = (b * c) - ((x * 4.0) * i)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(t * Float64(a * -4.0)))
	tmp = 0.0
	if (Float64(b * c) <= -2.2e+71)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (Float64(b * c) <= -3.8e-31)
		tmp = Float64(y * Float64(x * Float64(t * Float64(18.0 * z))));
	elseif (Float64(b * c) <= -1.5e-276)
		tmp = t_2;
	elseif (Float64(b * c) <= 5.6e-224)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= 1.9e+160)
		tmp = t_2;
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (t * (a * -4.0));
	tmp = 0.0;
	if ((b * c) <= -2.2e+71)
		tmp = (b * c) + t_1;
	elseif ((b * c) <= -3.8e-31)
		tmp = y * (x * (t * (18.0 * z)));
	elseif ((b * c) <= -1.5e-276)
		tmp = t_2;
	elseif ((b * c) <= 5.6e-224)
		tmp = t_1 + (-4.0 * (x * i));
	elseif ((b * c) <= 1.9e+160)
		tmp = t_2;
	else
		tmp = (b * c) - ((x * 4.0) * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.2e+71], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.8e-31], N[(y * N[(x * N[(t * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.5e-276], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 5.6e-224], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.9e+160], t$95$2, N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -2.19999999999999995e71

   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 80.2%

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

   5. Taylor expanded in b around inf 78.7%

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

   if -2.19999999999999995e71 < (*.f64 b c) < -3.8e-31

   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 80.4%

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

   5. Taylor expanded in x around inf 61.2%

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

   6. Taylor expanded in y around inf 60.8%

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

   7. Taylor expanded in i around 0 58.2%

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

      1. *-commutative 58.2%

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

      2. *-commutative 58.2%

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

      3. associate-*l* 62.2%

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

      4. *-commutative 62.2%

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

      5. associate-*r* 62.2%

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

      6. *-commutative 62.2%

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

      7. associate-*r* 62.2%

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

      8. *-commutative 62.2%

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

      9. associate-*l* 62.1%

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

   9. Simplified 62.1%

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

   if -3.8e-31 < (*.f64 b c) < -1.49999999999999994e-276 or 5.5999999999999995e-224 < (*.f64 b c) < 1.90000000000000006e160

   1. Initial program 84.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in a around inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. metadata-eval 57.1%

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

      4. distribute-rgt-neg-in 57.1%

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

      5. *-commutative 57.1%

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

      6. distribute-rgt-neg-in 57.1%

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

      7. metadata-eval 57.1%

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

      8. *-commutative 57.1%

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

   7. Simplified 57.1%

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

   if -1.49999999999999994e-276 < (*.f64 b c) < 5.5999999999999995e-224

   1. Initial program 79.4%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in i around inf 62.7%

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

   if 1.90000000000000006e160 < (*.f64 b c)

   1. Initial program 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in t around 0 80.2%

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

   6. Taylor expanded in i around inf 74.0%

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

      1. associate-*r* 74.0%

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

      2. *-commutative 74.0%

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

      3. associate-*r* 74.0%

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

   8. Simplified 74.0%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.2 \cdot 10^{+71}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -3.8 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \left(x \cdot \left(t \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -1.5 \cdot 10^{-276}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 5.6 \cdot 10^{-224}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{+160}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := t \cdot \left(18 \cdot t\_1 + a \cdot -4\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -135000000000:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27 + 18 \cdot \left(t \cdot t\_1\right)\\ \mathbf{elif}\;t \leq -2.6:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-138}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+17}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* t (+ (* 18.0 t_1) (* a -4.0)))))
   (if (<= t -2.4e+38)
     t_2
     (if (<= t -135000000000.0)
       (+ (* (* j k) -27.0) (* 18.0 (* t t_1)))
       (if (<= t -2.6)
         t_2
         (if (<= t 8e-138)
           (- (* b c) (* (* j 27.0) k))
           (if (<= t 6.6e-25)
             (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
             (if (<= t 8.8e+17) (+ (* b c) (* j (* k -27.0))) t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double t_2 = t * ((18.0 * t_1) + (a * -4.0));
	double tmp;
	if (t <= -2.4e+38) {
		tmp = t_2;
	} else if (t <= -135000000000.0) {
		tmp = ((j * k) * -27.0) + (18.0 * (t * t_1));
	} else if (t <= -2.6) {
		tmp = t_2;
	} else if (t <= 8e-138) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (t <= 6.6e-25) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (t <= 8.8e+17) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = t * ((18.0d0 * t_1) + (a * (-4.0d0)))
    if (t <= (-2.4d+38)) then
        tmp = t_2
    else if (t <= (-135000000000.0d0)) then
        tmp = ((j * k) * (-27.0d0)) + (18.0d0 * (t * t_1))
    else if (t <= (-2.6d0)) then
        tmp = t_2
    else if (t <= 8d-138) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else if (t <= 6.6d-25) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    else if (t <= 8.8d+17) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double t_2 = t * ((18.0 * t_1) + (a * -4.0));
	double tmp;
	if (t <= -2.4e+38) {
		tmp = t_2;
	} else if (t <= -135000000000.0) {
		tmp = ((j * k) * -27.0) + (18.0 * (t * t_1));
	} else if (t <= -2.6) {
		tmp = t_2;
	} else if (t <= 8e-138) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (t <= 6.6e-25) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (t <= 8.8e+17) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (y * z)
	t_2 = t * ((18.0 * t_1) + (a * -4.0))
	tmp = 0
	if t <= -2.4e+38:
		tmp = t_2
	elif t <= -135000000000.0:
		tmp = ((j * k) * -27.0) + (18.0 * (t * t_1))
	elif t <= -2.6:
		tmp = t_2
	elif t <= 8e-138:
		tmp = (b * c) - ((j * 27.0) * k)
	elif t <= 6.6e-25:
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	elif t <= 8.8e+17:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(t * Float64(Float64(18.0 * t_1) + Float64(a * -4.0)))
	tmp = 0.0
	if (t <= -2.4e+38)
		tmp = t_2;
	elseif (t <= -135000000000.0)
		tmp = Float64(Float64(Float64(j * k) * -27.0) + Float64(18.0 * Float64(t * t_1)));
	elseif (t <= -2.6)
		tmp = t_2;
	elseif (t <= 8e-138)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 6.6e-25)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	elseif (t <= 8.8e+17)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (y * z);
	t_2 = t * ((18.0 * t_1) + (a * -4.0));
	tmp = 0.0;
	if (t <= -2.4e+38)
		tmp = t_2;
	elseif (t <= -135000000000.0)
		tmp = ((j * k) * -27.0) + (18.0 * (t * t_1));
	elseif (t <= -2.6)
		tmp = t_2;
	elseif (t <= 8e-138)
		tmp = (b * c) - ((j * 27.0) * k);
	elseif (t <= 6.6e-25)
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	elseif (t <= 8.8e+17)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * t$95$1), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+38], t$95$2, If[LessEqual[t, -135000000000.0], N[(N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision] + N[(18.0 * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.6], t$95$2, If[LessEqual[t, 8e-138], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e-25], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e+17], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.40000000000000017e38 or -1.35e11 < t < -2.60000000000000009 or 8.8e17 < t

   1. Initial program 82.0%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in t around inf 75.8%

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

   6. Taylor expanded in t around inf 72.8%

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

   if -2.40000000000000017e38 < t < -1.35e11

   1. Initial program 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around inf 90.4%

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

   6. Taylor expanded in a around 0 90.4%

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

   if -2.60000000000000009 < t < 8.00000000000000054e-138

   1. Initial program 80.1%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in t around 0 83.1%

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

   6. Taylor expanded in i around 0 66.0%

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

      1. associate-*r* 65.9%

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

   8. Simplified 65.9%

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

   if 8.00000000000000054e-138 < t < 6.5999999999999997e-25

   1. Initial program 91.5%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in x around inf 53.9%

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

      1. pow1 53.9%

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

   7. Applied egg-rr 53.9%

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

      1. unpow1 53.9%

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

      2. *-commutative 53.9%

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

      3. associate-*r* 57.9%

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

   9. Simplified 57.9%

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

   if 6.5999999999999997e-25 < t < 8.8e17

   1. Initial program 83.1%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in b around inf 99.7%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -135000000000:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27 + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -2.6:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-138}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+17}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ t_3 := 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;t \leq -0.0047:\\ \;\;\;\;t\_2 - t\_3\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.07 \cdot 10^{-91}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot z\right) \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right) - t\_3\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (- (- (+ (* b c) (* -4.0 (* t a))) (* (* x 4.0) i)) (* (* j 27.0) k)))
        (t_2 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
        (t_3 (* 27.0 (* j k))))
   (if (<= t -0.0047)
     (- t_2 t_3)
     (if (<= t 2.2e-196)
       t_1
       (if (<= t 1.07e-91)
         (- (+ (* b c) (* (* x z) (* y (* 18.0 t)))) t_3)
         (if (<= t 4.6e+77) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((b * c) + (-4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double t_3 = 27.0 * (j * k);
	double tmp;
	if (t <= -0.0047) {
		tmp = t_2 - t_3;
	} else if (t <= 2.2e-196) {
		tmp = t_1;
	} else if (t <= 1.07e-91) {
		tmp = ((b * c) + ((x * z) * (y * (18.0 * t)))) - t_3;
	} else if (t <= 4.6e+77) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (((b * c) + ((-4.0d0) * (t * a))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    t_2 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    t_3 = 27.0d0 * (j * k)
    if (t <= (-0.0047d0)) then
        tmp = t_2 - t_3
    else if (t <= 2.2d-196) then
        tmp = t_1
    else if (t <= 1.07d-91) then
        tmp = ((b * c) + ((x * z) * (y * (18.0d0 * t)))) - t_3
    else if (t <= 4.6d+77) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((b * c) + (-4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double t_3 = 27.0 * (j * k);
	double tmp;
	if (t <= -0.0047) {
		tmp = t_2 - t_3;
	} else if (t <= 2.2e-196) {
		tmp = t_1;
	} else if (t <= 1.07e-91) {
		tmp = ((b * c) + ((x * z) * (y * (18.0 * t)))) - t_3;
	} else if (t <= 4.6e+77) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (((b * c) + (-4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	t_3 = 27.0 * (j * k)
	tmp = 0
	if t <= -0.0047:
		tmp = t_2 - t_3
	elif t <= 2.2e-196:
		tmp = t_1
	elif t <= 1.07e-91:
		tmp = ((b * c) + ((x * z) * (y * (18.0 * t)))) - t_3
	elif t <= 4.6e+77:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	t_2 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))))
	t_3 = Float64(27.0 * Float64(j * k))
	tmp = 0.0
	if (t <= -0.0047)
		tmp = Float64(t_2 - t_3);
	elseif (t <= 2.2e-196)
		tmp = t_1;
	elseif (t <= 1.07e-91)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(x * z) * Float64(y * Float64(18.0 * t)))) - t_3);
	elseif (t <= 4.6e+77)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (((b * c) + (-4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	t_3 = 27.0 * (j * k);
	tmp = 0.0;
	if (t <= -0.0047)
		tmp = t_2 - t_3;
	elseif (t <= 2.2e-196)
		tmp = t_1;
	elseif (t <= 1.07e-91)
		tmp = ((b * c) + ((x * z) * (y * (18.0 * t)))) - t_3;
	elseif (t <= 4.6e+77)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.0047], N[(t$95$2 - t$95$3), $MachinePrecision], If[LessEqual[t, 2.2e-196], t$95$1, If[LessEqual[t, 1.07e-91], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] * N[(y * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[t, 4.6e+77], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -0.00470000000000000018

   1. Initial program 82.0%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in i around 0 85.8%

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

   if -0.00470000000000000018 < t < 2.20000000000000015e-196 or 1.07000000000000002e-91 < t < 4.5999999999999999e77

   1. Initial program 84.3%

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

      1. pow1 84.3%

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

      2. associate-*l* 92.8%

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

      3. *-commutative 92.8%

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

   4. Applied egg-rr 92.8%

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

      1. unpow1 92.8%

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

      2. associate-*l* 94.6%

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

      3. *-commutative 94.6%

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

   6. Simplified 94.6%

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

   7. Taylor expanded in y around 0 90.7%

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

      1. *-commutative 90.7%

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

   9. Simplified 90.7%

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

   if 2.20000000000000015e-196 < t < 1.07000000000000002e-91

   1. Initial program 79.4%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in i around 0 72.7%

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

   6. Taylor expanded in x around inf 65.8%

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

      1. associate-*r* 65.8%

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

      2. *-commutative 65.8%

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

      3. associate-*r* 66.0%

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

      4. associate-*l* 79.5%

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

      5. *-commutative 79.5%

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

      6. associate-*l* 79.1%

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

      7. *-commutative 79.1%

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

   8. Simplified 79.1%

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

   if 4.5999999999999999e77 < t

   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 85.3%

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

   5. Taylor expanded in i around 0 82.9%

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

   6. Taylor expanded in j around 0 85.2%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0047:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-196}:\\ \;\;\;\;\left(\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.07 \cdot 10^{-91}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot z\right) \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+77}:\\ \;\;\;\;\left(\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t \leq -1.36 \cdot 10^{+94}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-10}:\\ \;\;\;\;\left(\left(b \cdot c + \left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(t\_1 + \frac{b \cdot c}{t}\right) - a \cdot 4\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z)))))
   (if (<= t -1.36e+94)
     (- (+ (* b c) (* t (- t_1 (* a 4.0)))) (* 27.0 (* j k)))
     (if (<= t 1.02e-10)
       (-
        (-
         (+ (* b c) (- (* y (* (* x 18.0) (* z t))) (* t (* a 4.0))))
         (* (* x 4.0) i))
        (* (* j 27.0) k))
       (-
        (* t (- (+ t_1 (/ (* b c) t)) (* a 4.0)))
        (+ (* x (* 4.0 i)) (* j (* 27.0 k))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -1.36e+94) {
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (27.0 * (j * k));
	} else if (t <= 1.02e-10) {
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = (t * ((t_1 + ((b * c) / t)) - (a * 4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    if (t <= (-1.36d+94)) then
        tmp = ((b * c) + (t * (t_1 - (a * 4.0d0)))) - (27.0d0 * (j * k))
    else if (t <= 1.02d-10) then
        tmp = (((b * c) + ((y * ((x * 18.0d0) * (z * t))) - (t * (a * 4.0d0)))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    else
        tmp = (t * ((t_1 + ((b * c) / t)) - (a * 4.0d0))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -1.36e+94) {
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (27.0 * (j * k));
	} else if (t <= 1.02e-10) {
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = (t * ((t_1 + ((b * c) / t)) - (a * 4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	tmp = 0
	if t <= -1.36e+94:
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (27.0 * (j * k))
	elif t <= 1.02e-10:
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	else:
		tmp = (t * ((t_1 + ((b * c) / t)) - (a * 4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	tmp = 0.0
	if (t <= -1.36e+94)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(t_1 - Float64(a * 4.0)))) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 1.02e-10)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(y * Float64(Float64(x * 18.0) * Float64(z * t))) - Float64(t * Float64(a * 4.0)))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(t * Float64(Float64(t_1 + Float64(Float64(b * c) / t)) - Float64(a * 4.0))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	tmp = 0.0;
	if (t <= -1.36e+94)
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (27.0 * (j * k));
	elseif (t <= 1.02e-10)
		tmp = (((b * c) + ((y * ((x * 18.0) * (z * t))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	else
		tmp = (t * ((t_1 + ((b * c) / t)) - (a * 4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.36e+94], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e-10], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(t$95$1 + N[(N[(b * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $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 3 regimes

2. if t < -1.36e94

   1. Initial program 78.6%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in i around 0 89.5%

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

   if -1.36e94 < t < 1.01999999999999997e-10

   1. Initial program 83.0%

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

      1. pow1 83.0%

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

      2. associate-*l* 90.4%

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

      3. *-commutative 90.4%

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

   4. Applied egg-rr 90.4%

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

      1. unpow1 90.4%

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

      2. associate-*l* 95.4%

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

      3. *-commutative 95.4%

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

   6. Simplified 95.4%

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

   if 1.01999999999999997e-10 < t

   1. Initial program 84.5%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in t around inf 90.3%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{+94}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-10}:\\ \;\;\;\;\left(\left(b \cdot c + \left(y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - a \cdot 4\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t \leq -1.28 \cdot 10^{+98}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-15}:\\ \;\;\;\;\left(\left(b \cdot c + \left(18 \cdot \left(y \cdot \left(x \cdot \left(z \cdot t\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(t\_1 + \frac{b \cdot c}{t}\right) - a \cdot 4\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z)))))
   (if (<= t -1.28e+98)
     (- (+ (* b c) (* t (- t_1 (* a 4.0)))) (* 27.0 (* j k)))
     (if (<= t 9e-15)
       (-
        (-
         (+ (* b c) (- (* 18.0 (* y (* x (* z t)))) (* t (* a 4.0))))
         (* (* x 4.0) i))
        (* (* j 27.0) k))
       (-
        (* t (- (+ t_1 (/ (* b c) t)) (* a 4.0)))
        (+ (* x (* 4.0 i)) (* j (* 27.0 k))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -1.28e+98) {
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (27.0 * (j * k));
	} else if (t <= 9e-15) {
		tmp = (((b * c) + ((18.0 * (y * (x * (z * t)))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = (t * ((t_1 + ((b * c) / t)) - (a * 4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    if (t <= (-1.28d+98)) then
        tmp = ((b * c) + (t * (t_1 - (a * 4.0d0)))) - (27.0d0 * (j * k))
    else if (t <= 9d-15) then
        tmp = (((b * c) + ((18.0d0 * (y * (x * (z * t)))) - (t * (a * 4.0d0)))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    else
        tmp = (t * ((t_1 + ((b * c) / t)) - (a * 4.0d0))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -1.28e+98) {
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (27.0 * (j * k));
	} else if (t <= 9e-15) {
		tmp = (((b * c) + ((18.0 * (y * (x * (z * t)))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = (t * ((t_1 + ((b * c) / t)) - (a * 4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	tmp = 0
	if t <= -1.28e+98:
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (27.0 * (j * k))
	elif t <= 9e-15:
		tmp = (((b * c) + ((18.0 * (y * (x * (z * t)))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	else:
		tmp = (t * ((t_1 + ((b * c) / t)) - (a * 4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	tmp = 0.0
	if (t <= -1.28e+98)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(t_1 - Float64(a * 4.0)))) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 9e-15)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(18.0 * Float64(y * Float64(x * Float64(z * t)))) - Float64(t * Float64(a * 4.0)))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(t * Float64(Float64(t_1 + Float64(Float64(b * c) / t)) - Float64(a * 4.0))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	tmp = 0.0;
	if (t <= -1.28e+98)
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (27.0 * (j * k));
	elseif (t <= 9e-15)
		tmp = (((b * c) + ((18.0 * (y * (x * (z * t)))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	else
		tmp = (t * ((t_1 + ((b * c) / t)) - (a * 4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.28e+98], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e-15], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(18.0 * N[(y * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(t$95$1 + N[(N[(b * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $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 3 regimes

2. if t < -1.28000000000000006e98

   1. Initial program 78.6%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in i around 0 89.5%

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

   if -1.28000000000000006e98 < t < 8.9999999999999995e-15

   1. Initial program 83.0%

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

      1. pow1 83.0%

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

      2. associate-*l* 90.4%

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

      3. *-commutative 90.4%

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

   4. Applied egg-rr 90.4%

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

      1. unpow1 90.4%

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

      2. associate-*l* 95.4%

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

      3. *-commutative 95.4%

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

   6. Simplified 95.4%

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

   7. Taylor expanded in y around 0 82.4%

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

      1. associate-*r* 86.7%

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

      2. *-commutative 86.7%

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

      3. associate-*r* 93.1%

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

      4. associate-*r* 92.2%

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

      5. *-commutative 92.2%

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

      6. associate-*r* 95.3%

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

   9. Simplified 95.3%

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

   if 8.9999999999999995e-15 < t

   1. Initial program 84.5%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in t around inf 90.3%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.28 \cdot 10^{+98}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-15}:\\ \;\;\;\;\left(\left(b \cdot c + \left(18 \cdot \left(y \cdot \left(x \cdot \left(z \cdot t\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \frac{b \cdot c}{t}\right) - a \cdot 4\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+96}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-222}:\\ \;\;\;\;\left(b \cdot c + \left(\left(z \cdot t\right) \cdot \left(\left(x \cdot 18\right) \cdot y\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - t \cdot \left(a \cdot 4 + \left(y \cdot z\right) \cdot \left(x \cdot -18\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -7.8e+96)
   (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) (* 27.0 (* j k)))
   (if (<= t 5e-222)
     (-
      (+ (* b c) (- (* (* z t) (* (* x 18.0) y)) (* t (* a 4.0))))
      (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
     (-
      (-
       (- (* b c) (* t (+ (* a 4.0) (* (* y z) (* x -18.0)))))
       (* (* x 4.0) i))
      (* (* j 27.0) k)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -7.8e+96) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	} else if (t <= 5e-222) {
		tmp = ((b * c) + (((z * t) * ((x * 18.0) * y)) - (t * (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (((b * c) - (t * ((a * 4.0) + ((y * z) * (x * -18.0))))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-7.8d+96)) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (27.0d0 * (j * k))
    else if (t <= 5d-222) then
        tmp = ((b * c) + (((z * t) * ((x * 18.0d0) * y)) - (t * (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = (((b * c) - (t * ((a * 4.0d0) + ((y * z) * (x * (-18.0d0)))))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -7.8e+96) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	} else if (t <= 5e-222) {
		tmp = ((b * c) + (((z * t) * ((x * 18.0) * y)) - (t * (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (((b * c) - (t * ((a * 4.0) + ((y * z) * (x * -18.0))))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -7.8e+96:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k))
	elif t <= 5e-222:
		tmp = ((b * c) + (((z * t) * ((x * 18.0) * y)) - (t * (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = (((b * c) - (t * ((a * 4.0) + ((y * z) * (x * -18.0))))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -7.8e+96)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 5e-222)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(Float64(z * t) * Float64(Float64(x * 18.0) * y)) - Float64(t * Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) + Float64(Float64(y * z) * Float64(x * -18.0))))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -7.8e+96)
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	elseif (t <= 5e-222)
		tmp = ((b * c) + (((z * t) * ((x * 18.0) * y)) - (t * (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = (((b * c) - (t * ((a * 4.0) + ((y * z) * (x * -18.0))))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -7.8e+96], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-222], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] * N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] * N[(x * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.8e96

   1. Initial program 78.6%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in i around 0 89.5%

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

   if -7.8e96 < t < 5.00000000000000008e-222

   1. Initial program 82.8%

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

   3. Simplified 81.1%

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

      1. associate-*r* 82.8%

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

      2. distribute-rgt-out-- 82.8%

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

      3. associate-*l* 92.1%

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

      4. *-commutative 92.1%

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

      5. *-commutative 92.1%

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

   6. Applied egg-rr 92.1%

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

   if 5.00000000000000008e-222 < t

   1. Initial program 83.9%

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

   3. Taylor expanded in t around -inf 86.8%

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

      1. associate-*r* 86.8%

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

      2. neg-mul-1 86.8%

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

      3. cancel-sign-sub-inv 86.8%

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

      4. metadata-eval 86.8%

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

      5. associate-*r* 86.8%

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

      6. *-commutative 86.8%

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

   5. Simplified 86.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+96}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-222}:\\ \;\;\;\;\left(b \cdot c + \left(\left(z \cdot t\right) \cdot \left(\left(x \cdot 18\right) \cdot y\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - t \cdot \left(a \cdot 4 + \left(y \cdot z\right) \cdot \left(x \cdot -18\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+119} \lor \neg \left(z \leq 7.5 \cdot 10^{+179}\right):\\ \;\;\;\;z \cdot \left(-4 \cdot \frac{t \cdot a}{z} + \left(18 \cdot \left(t \cdot \left(x \cdot y\right)\right) + \frac{b \cdot c}{z}\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - t \cdot \left(a \cdot 4 + \left(y \cdot z\right) \cdot \left(x \cdot -18\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= z -5e+119) (not (<= z 7.5e+179)))
   (-
    (* z (+ (* -4.0 (/ (* t a) z)) (+ (* 18.0 (* t (* x y))) (/ (* b c) z))))
    (* 27.0 (* j k)))
   (-
    (- (- (* b c) (* t (+ (* a 4.0) (* (* y z) (* x -18.0))))) (* (* x 4.0) i))
    (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((z <= -5e+119) || !(z <= 7.5e+179)) {
		tmp = (z * ((-4.0 * ((t * a) / z)) + ((18.0 * (t * (x * y))) + ((b * c) / z)))) - (27.0 * (j * k));
	} else {
		tmp = (((b * c) - (t * ((a * 4.0) + ((y * z) * (x * -18.0))))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((z <= (-5d+119)) .or. (.not. (z <= 7.5d+179))) then
        tmp = (z * (((-4.0d0) * ((t * a) / z)) + ((18.0d0 * (t * (x * y))) + ((b * c) / z)))) - (27.0d0 * (j * k))
    else
        tmp = (((b * c) - (t * ((a * 4.0d0) + ((y * z) * (x * (-18.0d0)))))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((z <= -5e+119) || !(z <= 7.5e+179)) {
		tmp = (z * ((-4.0 * ((t * a) / z)) + ((18.0 * (t * (x * y))) + ((b * c) / z)))) - (27.0 * (j * k));
	} else {
		tmp = (((b * c) - (t * ((a * 4.0) + ((y * z) * (x * -18.0))))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (z <= -5e+119) or not (z <= 7.5e+179):
		tmp = (z * ((-4.0 * ((t * a) / z)) + ((18.0 * (t * (x * y))) + ((b * c) / z)))) - (27.0 * (j * k))
	else:
		tmp = (((b * c) - (t * ((a * 4.0) + ((y * z) * (x * -18.0))))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((z <= -5e+119) || !(z <= 7.5e+179))
		tmp = Float64(Float64(z * Float64(Float64(-4.0 * Float64(Float64(t * a) / z)) + Float64(Float64(18.0 * Float64(t * Float64(x * y))) + Float64(Float64(b * c) / z)))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) + Float64(Float64(y * z) * Float64(x * -18.0))))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((z <= -5e+119) || ~((z <= 7.5e+179)))
		tmp = (z * ((-4.0 * ((t * a) / z)) + ((18.0 * (t * (x * y))) + ((b * c) / z)))) - (27.0 * (j * k));
	else
		tmp = (((b * c) - (t * ((a * 4.0) + ((y * z) * (x * -18.0))))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[z, -5e+119], N[Not[LessEqual[z, 7.5e+179]], $MachinePrecision]], N[(N[(z * N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(N[(18.0 * N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] * N[(x * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999999e119 or 7.50000000000000007e179 < z

   1. Initial program 71.2%

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

   3. Simplified 64.4%

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

   5. Taylor expanded in i around 0 67.6%

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

   6. Taylor expanded in z around inf 84.3%

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

   if -4.9999999999999999e119 < z < 7.50000000000000007e179

   1. Initial program 86.6%

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

   3. Taylor expanded in t around -inf 91.4%

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

      1. associate-*r* 91.4%

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

      2. neg-mul-1 91.4%

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

      3. cancel-sign-sub-inv 91.4%

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

      4. metadata-eval 91.4%

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

      5. associate-*r* 91.4%

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

      6. *-commutative 91.4%

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

   5. Simplified 91.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+119} \lor \neg \left(z \leq 7.5 \cdot 10^{+179}\right):\\ \;\;\;\;z \cdot \left(-4 \cdot \frac{t \cdot a}{z} + \left(18 \cdot \left(t \cdot \left(x \cdot y\right)\right) + \frac{b \cdot c}{z}\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - t \cdot \left(a \cdot 4 + \left(y \cdot z\right) \cdot \left(x \cdot -18\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+109} \lor \neg \left(z \leq 3.1 \cdot 10^{+180}\right):\\ \;\;\;\;z \cdot \left(-4 \cdot \frac{t \cdot a}{z} + \left(18 \cdot \left(t \cdot \left(x \cdot y\right)\right) + \frac{b \cdot c}{z}\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= z -1.25e+109) (not (<= z 3.1e+180)))
   (-
    (* z (+ (* -4.0 (/ (* t a) z)) (+ (* 18.0 (* t (* x y))) (/ (* b c) z))))
    (* 27.0 (* j k)))
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((z <= -1.25e+109) || !(z <= 3.1e+180)) {
		tmp = (z * ((-4.0 * ((t * a) / z)) + ((18.0 * (t * (x * y))) + ((b * c) / z)))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((z <= (-1.25d+109)) .or. (.not. (z <= 3.1d+180))) then
        tmp = (z * (((-4.0d0) * ((t * a) / z)) + ((18.0d0 * (t * (x * y))) + ((b * c) / z)))) - (27.0d0 * (j * k))
    else
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((z <= -1.25e+109) || !(z <= 3.1e+180)) {
		tmp = (z * ((-4.0 * ((t * a) / z)) + ((18.0 * (t * (x * y))) + ((b * c) / z)))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (z <= -1.25e+109) or not (z <= 3.1e+180):
		tmp = (z * ((-4.0 * ((t * a) / z)) + ((18.0 * (t * (x * y))) + ((b * c) / z)))) - (27.0 * (j * k))
	else:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((z <= -1.25e+109) || !(z <= 3.1e+180))
		tmp = Float64(Float64(z * Float64(Float64(-4.0 * Float64(Float64(t * a) / z)) + Float64(Float64(18.0 * Float64(t * Float64(x * y))) + Float64(Float64(b * c) / z)))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((z <= -1.25e+109) || ~((z <= 3.1e+180)))
		tmp = (z * ((-4.0 * ((t * a) / z)) + ((18.0 * (t * (x * y))) + ((b * c) / z)))) - (27.0 * (j * k));
	else
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[z, -1.25e+109], N[Not[LessEqual[z, 3.1e+180]], $MachinePrecision]], N[(N[(z * N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(N[(18.0 * N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e109 or 3.09999999999999998e180 < z

   1. Initial program 71.2%

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

   3. Simplified 64.4%

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

   5. Taylor expanded in i around 0 67.6%

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

   6. Taylor expanded in z around inf 84.3%

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

   if -1.25e109 < z < 3.09999999999999998e180

   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 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
3. Recombined 2 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+109} \lor \neg \left(z \leq 3.1 \cdot 10^{+180}\right):\\ \;\;\;\;z \cdot \left(-4 \cdot \frac{t \cdot a}{z} + \left(18 \cdot \left(t \cdot \left(x \cdot y\right)\right) + \frac{b \cdot c}{z}\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+253}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot z\right) \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+71}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(z \cdot \left(18 \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(18 \cdot \left(t \cdot \left(x \cdot y\right)\right) + -27 \cdot \frac{j \cdot k}{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -7.8e+253)
   (- (+ (* b c) (* (* x z) (* y (* 18.0 t)))) (* 27.0 (* j k)))
   (if (<= y 7.8e+71)
     (-
      (+ (* b c) (* t (+ (* z (* 18.0 (* x y))) (* a -4.0))))
      (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
     (* z (+ (* 18.0 (* t (* x y))) (* -27.0 (/ (* j k) z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -7.8e+253) {
		tmp = ((b * c) + ((x * z) * (y * (18.0 * t)))) - (27.0 * (j * k));
	} else if (y <= 7.8e+71) {
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) + (a * -4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = z * ((18.0 * (t * (x * y))) + (-27.0 * ((j * k) / z)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (y <= (-7.8d+253)) then
        tmp = ((b * c) + ((x * z) * (y * (18.0d0 * t)))) - (27.0d0 * (j * k))
    else if (y <= 7.8d+71) then
        tmp = ((b * c) + (t * ((z * (18.0d0 * (x * y))) + (a * (-4.0d0))))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = z * ((18.0d0 * (t * (x * y))) + ((-27.0d0) * ((j * k) / z)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -7.8e+253) {
		tmp = ((b * c) + ((x * z) * (y * (18.0 * t)))) - (27.0 * (j * k));
	} else if (y <= 7.8e+71) {
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) + (a * -4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = z * ((18.0 * (t * (x * y))) + (-27.0 * ((j * k) / z)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if y <= -7.8e+253:
		tmp = ((b * c) + ((x * z) * (y * (18.0 * t)))) - (27.0 * (j * k))
	elif y <= 7.8e+71:
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) + (a * -4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = z * ((18.0 * (t * (x * y))) + (-27.0 * ((j * k) / z)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -7.8e+253)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(x * z) * Float64(y * Float64(18.0 * t)))) - Float64(27.0 * Float64(j * k)));
	elseif (y <= 7.8e+71)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(z * Float64(18.0 * Float64(x * y))) + Float64(a * -4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(z * Float64(Float64(18.0 * Float64(t * Float64(x * y))) + Float64(-27.0 * Float64(Float64(j * k) / z))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (y <= -7.8e+253)
		tmp = ((b * c) + ((x * z) * (y * (18.0 * t)))) - (27.0 * (j * k));
	elseif (y <= 7.8e+71)
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) + (a * -4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = z * ((18.0 * (t * (x * y))) + (-27.0 * ((j * k) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -7.8e+253], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] * N[(y * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e+71], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(z * N[(18.0 * N[(x * 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], N[(z * N[(N[(18.0 * N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.8000000000000003e253

   1. Initial program 39.2%

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

   3. Simplified 39.2%

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

   5. Taylor expanded in i around 0 39.2%

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

   6. Taylor expanded in x around inf 39.2%

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

      1. associate-*r* 39.2%

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

      2. *-commutative 39.2%

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

      3. associate-*r* 39.2%

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

      4. associate-*l* 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-*l* 99.6%

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

      7. *-commutative 99.6%

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

   8. Simplified 99.6%

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

   if -7.8000000000000003e253 < y < 7.8000000000000002e71

   1. Initial program 88.0%

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

   3. Simplified 89.7%

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

      1. associate-*r* 89.7%

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

      2. distribute-rgt-out-- 88.0%

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

      3. sub-neg 88.0%

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

      4. associate-*l* 84.9%

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

      5. *-commutative 84.9%

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

      6. *-commutative 84.9%

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

   6. Applied egg-rr 84.9%

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

      1. associate-*r* 88.0%

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

      2. distribute-rgt-neg-in 88.0%

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

      3. *-commutative 88.0%

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

      4. distribute-rgt-neg-in 88.0%

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

      5. metadata-eval 88.0%

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

      6. *-commutative 88.0%

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

      7. distribute-rgt-out 89.7%

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

      8. associate-*r* 89.7%

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

      9. *-commutative 89.7%

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

      10. *-commutative 89.7%

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

   8. Simplified 89.7%

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

   if 7.8000000000000002e71 < y

   1. Initial program 72.0%

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

   3. Simplified 72.5%

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

   5. Taylor expanded in t around inf 64.2%

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

   6. Taylor expanded in a around 0 56.7%

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

   7. Taylor expanded in z around inf 63.7%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+253}:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot z\right) \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+71}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(z \cdot \left(18 \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(18 \cdot \left(t \cdot \left(x \cdot y\right)\right) + -27 \cdot \frac{j \cdot k}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6 \cdot 10^{+77}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-315}:\\ \;\;\;\;y \cdot \left(x \cdot \left(t \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 7.4 \cdot 10^{-84}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+169}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -6e+77)
   (* b c)
   (if (<= (* b c) -1e-315)
     (* y (* x (* t (* 18.0 z))))
     (if (<= (* b c) 7.4e-84)
       (* j (* k -27.0))
       (if (<= (* b c) 1e+169) (* y (* 18.0 (* t (* x z)))) (* b c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -6e+77) {
		tmp = b * c;
	} else if ((b * c) <= -1e-315) {
		tmp = y * (x * (t * (18.0 * z)));
	} else if ((b * c) <= 7.4e-84) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 1e+169) {
		tmp = y * (18.0 * (t * (x * z)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-6d+77)) then
        tmp = b * c
    else if ((b * c) <= (-1d-315)) then
        tmp = y * (x * (t * (18.0d0 * z)))
    else if ((b * c) <= 7.4d-84) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 1d+169) then
        tmp = y * (18.0d0 * (t * (x * z)))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -6e+77) {
		tmp = b * c;
	} else if ((b * c) <= -1e-315) {
		tmp = y * (x * (t * (18.0 * z)));
	} else if ((b * c) <= 7.4e-84) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 1e+169) {
		tmp = y * (18.0 * (t * (x * z)));
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -6e+77:
		tmp = b * c
	elif (b * c) <= -1e-315:
		tmp = y * (x * (t * (18.0 * z)))
	elif (b * c) <= 7.4e-84:
		tmp = j * (k * -27.0)
	elif (b * c) <= 1e+169:
		tmp = y * (18.0 * (t * (x * z)))
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -6e+77)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1e-315)
		tmp = Float64(y * Float64(x * Float64(t * Float64(18.0 * z))));
	elseif (Float64(b * c) <= 7.4e-84)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 1e+169)
		tmp = Float64(y * Float64(18.0 * Float64(t * Float64(x * z))));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -6e+77)
		tmp = b * c;
	elseif ((b * c) <= -1e-315)
		tmp = y * (x * (t * (18.0 * z)));
	elseif ((b * c) <= 7.4e-84)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 1e+169)
		tmp = y * (18.0 * (t * (x * z)));
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -6e+77], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1e-315], N[(y * N[(x * N[(t * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7.4e-84], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+169], N[(y * N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -5.9999999999999996e77 or 9.99999999999999934e168 < (*.f64 b c)

   1. Initial program 82.3%

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

      1. pow1 82.3%

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

      2. associate-*l* 83.5%

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

      3. *-commutative 83.5%

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

   4. Applied egg-rr 83.5%

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

      1. unpow1 83.5%

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

      2. associate-*l* 87.3%

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

      3. *-commutative 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in b around inf 66.7%

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

   if -5.9999999999999996e77 < (*.f64 b c) < -9.999999985e-316

   1. Initial program 90.3%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in x around inf 50.7%

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

   6. Taylor expanded in y around inf 48.9%

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

   7. Taylor expanded in i around 0 40.1%

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

      1. *-commutative 40.1%

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

      2. *-commutative 40.1%

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

      3. associate-*l* 41.5%

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

      4. *-commutative 41.5%

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

      5. associate-*r* 41.5%

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

      6. *-commutative 41.5%

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

      7. associate-*r* 41.6%

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

      8. *-commutative 41.6%

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

      9. associate-*l* 41.5%

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

   9. Simplified 41.5%

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

   if -9.999999985e-316 < (*.f64 b c) < 7.3999999999999999e-84

   1. Initial program 79.6%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in j around inf 43.9%

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

      1. *-commutative 43.9%

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

      2. associate-*r* 45.5%

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

      3. *-commutative 45.5%

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

   7. Simplified 45.5%

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

   if 7.3999999999999999e-84 < (*.f64 b c) < 9.99999999999999934e168

   1. Initial program 77.5%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in x around inf 46.6%

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

   6. Taylor expanded in y around inf 52.4%

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

   7. Taylor expanded in i around 0 43.8%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6 \cdot 10^{+77}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-315}:\\ \;\;\;\;y \cdot \left(x \cdot \left(t \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 7.4 \cdot 10^{-84}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+169}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -1.34 \cdot 10^{+79}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-315}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.7 \cdot 10^{-85}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.55 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* y (* 18.0 (* t (* x z))))))
   (if (<= (* b c) -1.34e+79)
     (* b c)
     (if (<= (* b c) -1e-315)
       t_1
       (if (<= (* b c) 1.7e-85)
         (* j (* k -27.0))
         (if (<= (* b c) 1.55e+168) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = y * (18.0 * (t * (x * z)));
	double tmp;
	if ((b * c) <= -1.34e+79) {
		tmp = b * c;
	} else if ((b * c) <= -1e-315) {
		tmp = t_1;
	} else if ((b * c) <= 1.7e-85) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 1.55e+168) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (18.0d0 * (t * (x * z)))
    if ((b * c) <= (-1.34d+79)) then
        tmp = b * c
    else if ((b * c) <= (-1d-315)) then
        tmp = t_1
    else if ((b * c) <= 1.7d-85) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 1.55d+168) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = y * (18.0 * (t * (x * z)));
	double tmp;
	if ((b * c) <= -1.34e+79) {
		tmp = b * c;
	} else if ((b * c) <= -1e-315) {
		tmp = t_1;
	} else if ((b * c) <= 1.7e-85) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 1.55e+168) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = y * (18.0 * (t * (x * z)))
	tmp = 0
	if (b * c) <= -1.34e+79:
		tmp = b * c
	elif (b * c) <= -1e-315:
		tmp = t_1
	elif (b * c) <= 1.7e-85:
		tmp = j * (k * -27.0)
	elif (b * c) <= 1.55e+168:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(y * Float64(18.0 * Float64(t * Float64(x * z))))
	tmp = 0.0
	if (Float64(b * c) <= -1.34e+79)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1e-315)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.7e-85)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 1.55e+168)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = y * (18.0 * (t * (x * z)));
	tmp = 0.0;
	if ((b * c) <= -1.34e+79)
		tmp = b * c;
	elseif ((b * c) <= -1e-315)
		tmp = t_1;
	elseif ((b * c) <= 1.7e-85)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 1.55e+168)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(y * N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.34e+79], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1e-315], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.7e-85], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.55e+168], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.33999999999999993e79 or 1.54999999999999998e168 < (*.f64 b c)

   1. Initial program 82.3%

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

      1. pow1 82.3%

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

      2. associate-*l* 83.5%

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

      3. *-commutative 83.5%

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

   4. Applied egg-rr 83.5%

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

      1. unpow1 83.5%

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

      2. associate-*l* 87.3%

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

      3. *-commutative 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in b around inf 66.7%

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

   if -1.33999999999999993e79 < (*.f64 b c) < -9.999999985e-316 or 1.7e-85 < (*.f64 b c) < 1.54999999999999998e168

   1. Initial program 84.1%

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

   3. Simplified 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 48.7%

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

   6. Taylor expanded in y around inf 50.6%

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

   7. Taylor expanded in i around 0 41.9%

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

   if -9.999999985e-316 < (*.f64 b c) < 1.7e-85

   1. Initial program 79.6%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in j around inf 43.9%

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

      1. *-commutative 43.9%

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

      2. associate-*r* 45.5%

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

      3. *-commutative 45.5%

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

   7. Simplified 45.5%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.34 \cdot 10^{+79}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-315}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.7 \cdot 10^{-85}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.55 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 80.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_2 := b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.65:\\ \;\;\;\;t \cdot \left(t\_1 + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+76}:\\ \;\;\;\;\left(\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z)))) (t_2 (+ (* b c) (* t (- t_1 (* a 4.0))))))
   (if (<= t -4.6e+102)
     t_2
     (if (<= t -2.65)
       (+ (* t (+ t_1 (* a -4.0))) (* j (* k -27.0)))
       (if (<= t 1.1e+76)
         (- (- (+ (* b c) (* -4.0 (* t a))) (* (* x 4.0) i)) (* (* j 27.0) k))
         t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = (b * c) + (t * (t_1 - (a * 4.0)));
	double tmp;
	if (t <= -4.6e+102) {
		tmp = t_2;
	} else if (t <= -2.65) {
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	} else if (t <= 1.1e+76) {
		tmp = (((b * c) + (-4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    t_2 = (b * c) + (t * (t_1 - (a * 4.0d0)))
    if (t <= (-4.6d+102)) then
        tmp = t_2
    else if (t <= (-2.65d0)) then
        tmp = (t * (t_1 + (a * (-4.0d0)))) + (j * (k * (-27.0d0)))
    else if (t <= 1.1d+76) then
        tmp = (((b * c) + ((-4.0d0) * (t * a))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = (b * c) + (t * (t_1 - (a * 4.0)));
	double tmp;
	if (t <= -4.6e+102) {
		tmp = t_2;
	} else if (t <= -2.65) {
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	} else if (t <= 1.1e+76) {
		tmp = (((b * c) + (-4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	t_2 = (b * c) + (t * (t_1 - (a * 4.0)))
	tmp = 0
	if t <= -4.6e+102:
		tmp = t_2
	elif t <= -2.65:
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0))
	elif t <= 1.1e+76:
		tmp = (((b * c) + (-4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	t_2 = Float64(Float64(b * c) + Float64(t * Float64(t_1 - Float64(a * 4.0))))
	tmp = 0.0
	if (t <= -4.6e+102)
		tmp = t_2;
	elseif (t <= -2.65)
		tmp = Float64(Float64(t * Float64(t_1 + Float64(a * -4.0))) + Float64(j * Float64(k * -27.0)));
	elseif (t <= 1.1e+76)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	t_2 = (b * c) + (t * (t_1 - (a * 4.0)));
	tmp = 0.0;
	if (t <= -4.6e+102)
		tmp = t_2;
	elseif (t <= -2.65)
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	elseif (t <= 1.1e+76)
		tmp = (((b * c) + (-4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.6e+102], t$95$2, If[LessEqual[t, -2.65], N[(N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+76], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5999999999999998e102 or 1.1e76 < t

   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 84.7%

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

   5. Taylor expanded in i around 0 86.0%

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

   6. Taylor expanded in j around 0 86.3%

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

   if -4.5999999999999998e102 < t < -2.64999999999999991

   1. Initial program 85.9%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in t around inf 84.8%

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

   if -2.64999999999999991 < t < 1.1e76

   1. Initial program 83.3%

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

      1. pow1 83.3%

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

      2. associate-*l* 90.8%

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

      3. *-commutative 90.8%

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

   4. Applied egg-rr 90.8%

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

      1. unpow1 90.8%

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

      2. associate-*l* 94.9%

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

      3. *-commutative 94.9%

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

   6. Simplified 94.9%

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

   7. Taylor expanded in y around 0 85.7%

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

      1. *-commutative 85.7%

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

   9. Simplified 85.7%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+102}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -2.65:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+76}:\\ \;\;\;\;\left(\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 76.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_2 := b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -0.032:\\ \;\;\;\;t \cdot \left(t\_1 + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right)}{b}\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z)))) (t_2 (+ (* b c) (* t (- t_1 (* a 4.0))))))
   (if (<= t -1.75e+102)
     t_2
     (if (<= t -0.032)
       (+ (* t (+ t_1 (* a -4.0))) (* j (* k -27.0)))
       (if (<= t 4e+73)
         (- (* b (+ c (/ (* -4.0 (+ (* t a) (* x i))) b))) (* (* j 27.0) k))
         t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = (b * c) + (t * (t_1 - (a * 4.0)));
	double tmp;
	if (t <= -1.75e+102) {
		tmp = t_2;
	} else if (t <= -0.032) {
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	} else if (t <= 4e+73) {
		tmp = (b * (c + ((-4.0 * ((t * a) + (x * i))) / b))) - ((j * 27.0) * k);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    t_2 = (b * c) + (t * (t_1 - (a * 4.0d0)))
    if (t <= (-1.75d+102)) then
        tmp = t_2
    else if (t <= (-0.032d0)) then
        tmp = (t * (t_1 + (a * (-4.0d0)))) + (j * (k * (-27.0d0)))
    else if (t <= 4d+73) then
        tmp = (b * (c + (((-4.0d0) * ((t * a) + (x * i))) / b))) - ((j * 27.0d0) * k)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = (b * c) + (t * (t_1 - (a * 4.0)));
	double tmp;
	if (t <= -1.75e+102) {
		tmp = t_2;
	} else if (t <= -0.032) {
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	} else if (t <= 4e+73) {
		tmp = (b * (c + ((-4.0 * ((t * a) + (x * i))) / b))) - ((j * 27.0) * k);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	t_2 = (b * c) + (t * (t_1 - (a * 4.0)))
	tmp = 0
	if t <= -1.75e+102:
		tmp = t_2
	elif t <= -0.032:
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0))
	elif t <= 4e+73:
		tmp = (b * (c + ((-4.0 * ((t * a) + (x * i))) / b))) - ((j * 27.0) * k)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	t_2 = Float64(Float64(b * c) + Float64(t * Float64(t_1 - Float64(a * 4.0))))
	tmp = 0.0
	if (t <= -1.75e+102)
		tmp = t_2;
	elseif (t <= -0.032)
		tmp = Float64(Float64(t * Float64(t_1 + Float64(a * -4.0))) + Float64(j * Float64(k * -27.0)));
	elseif (t <= 4e+73)
		tmp = Float64(Float64(b * Float64(c + Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) / b))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	t_2 = (b * c) + (t * (t_1 - (a * 4.0)));
	tmp = 0.0;
	if (t <= -1.75e+102)
		tmp = t_2;
	elseif (t <= -0.032)
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	elseif (t <= 4e+73)
		tmp = (b * (c + ((-4.0 * ((t * a) + (x * i))) / b))) - ((j * 27.0) * k);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.75e+102], t$95$2, If[LessEqual[t, -0.032], N[(N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+73], N[(N[(b * N[(c + N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75000000000000005e102 or 3.99999999999999993e73 < t

   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 84.7%

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

   5. Taylor expanded in i around 0 86.0%

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

   6. Taylor expanded in j around 0 86.3%

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

   if -1.75000000000000005e102 < t < -0.032000000000000001

   1. Initial program 85.9%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in t around inf 84.8%

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

   if -0.032000000000000001 < t < 3.99999999999999993e73

   1. Initial program 83.3%

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

      1. pow1 83.3%

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

      2. associate-*l* 90.8%

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

      3. *-commutative 90.8%

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

   4. Applied egg-rr 90.8%

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

      1. unpow1 90.8%

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

      2. associate-*l* 94.9%

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

      3. *-commutative 94.9%

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

   6. Simplified 94.9%

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

   7. Taylor expanded in y around 0 85.7%

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

      1. *-commutative 85.7%

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

   9. Simplified 85.7%

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

   10. Taylor expanded in b around inf 78.3%

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

       1. associate--l+ 78.3%

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

       2. associate-*r/ 78.3%

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

       3. associate-*r/ 78.3%

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

       4. div-sub 78.3%

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

   12. Simplified 78.3%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+102}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -0.032:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(c + \frac{-4 \cdot \left(t \cdot a + x \cdot i\right)}{b}\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 72.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := t \cdot \left(18 \cdot t\_1 + a \cdot -4\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -800000000000:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27 + 18 \cdot \left(t \cdot t\_1\right)\\ \mathbf{elif}\;t \leq -2.5 \lor \neg \left(t \leq 6 \cdot 10^{+44}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* t (+ (* 18.0 t_1) (* a -4.0)))))
   (if (<= t -2.5e+37)
     t_2
     (if (<= t -800000000000.0)
       (+ (* (* j k) -27.0) (* 18.0 (* t t_1)))
       (if (or (<= t -2.5) (not (<= t 6e+44)))
         t_2
         (- (* b c) (+ (* 27.0 (* j k)) (* 4.0 (* x i)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double t_2 = t * ((18.0 * t_1) + (a * -4.0));
	double tmp;
	if (t <= -2.5e+37) {
		tmp = t_2;
	} else if (t <= -800000000000.0) {
		tmp = ((j * k) * -27.0) + (18.0 * (t * t_1));
	} else if ((t <= -2.5) || !(t <= 6e+44)) {
		tmp = t_2;
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = t * ((18.0d0 * t_1) + (a * (-4.0d0)))
    if (t <= (-2.5d+37)) then
        tmp = t_2
    else if (t <= (-800000000000.0d0)) then
        tmp = ((j * k) * (-27.0d0)) + (18.0d0 * (t * t_1))
    else if ((t <= (-2.5d0)) .or. (.not. (t <= 6d+44))) then
        tmp = t_2
    else
        tmp = (b * c) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double t_2 = t * ((18.0 * t_1) + (a * -4.0));
	double tmp;
	if (t <= -2.5e+37) {
		tmp = t_2;
	} else if (t <= -800000000000.0) {
		tmp = ((j * k) * -27.0) + (18.0 * (t * t_1));
	} else if ((t <= -2.5) || !(t <= 6e+44)) {
		tmp = t_2;
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (y * z)
	t_2 = t * ((18.0 * t_1) + (a * -4.0))
	tmp = 0
	if t <= -2.5e+37:
		tmp = t_2
	elif t <= -800000000000.0:
		tmp = ((j * k) * -27.0) + (18.0 * (t * t_1))
	elif (t <= -2.5) or not (t <= 6e+44):
		tmp = t_2
	else:
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(t * Float64(Float64(18.0 * t_1) + Float64(a * -4.0)))
	tmp = 0.0
	if (t <= -2.5e+37)
		tmp = t_2;
	elseif (t <= -800000000000.0)
		tmp = Float64(Float64(Float64(j * k) * -27.0) + Float64(18.0 * Float64(t * t_1)));
	elseif ((t <= -2.5) || !(t <= 6e+44))
		tmp = t_2;
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * i))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (y * z);
	t_2 = t * ((18.0 * t_1) + (a * -4.0));
	tmp = 0.0;
	if (t <= -2.5e+37)
		tmp = t_2;
	elseif (t <= -800000000000.0)
		tmp = ((j * k) * -27.0) + (18.0 * (t * t_1));
	elseif ((t <= -2.5) || ~((t <= 6e+44)))
		tmp = t_2;
	else
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * t$95$1), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+37], t$95$2, If[LessEqual[t, -800000000000.0], N[(N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision] + N[(18.0 * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.5], N[Not[LessEqual[t, 6e+44]], $MachinePrecision]], t$95$2, N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.49999999999999994e37 or -8e11 < t < -2.5 or 5.99999999999999974e44 < t

   1. Initial program 81.4%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in t around inf 76.8%

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

   6. Taylor expanded in t around inf 73.6%

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

   if -2.49999999999999994e37 < t < -8e11

   1. Initial program 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around inf 90.4%

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

   6. Taylor expanded in a around 0 90.4%

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

   if -2.5 < t < 5.99999999999999974e44

   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 80.8%

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

   5. Taylor expanded in t around 0 77.5%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -800000000000:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27 + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -2.5 \lor \neg \left(t \leq 6 \cdot 10^{+44}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 59.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -0.88:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10^{-137}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 9500000000000:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (+ (* 18.0 (* x (* y z))) (* a -4.0)))))
   (if (<= t -0.88)
     t_1
     (if (<= t 1e-137)
       (- (* b c) (* (* j 27.0) k))
       (if (<= t 1.15e-24)
         (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
         (if (<= t 9500000000000.0) (+ (* b c) (* j (* k -27.0))) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double tmp;
	if (t <= -0.88) {
		tmp = t_1;
	} else if (t <= 1e-137) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (t <= 1.15e-24) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (t <= 9500000000000.0) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))
    if (t <= (-0.88d0)) then
        tmp = t_1
    else if (t <= 1d-137) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else if (t <= 1.15d-24) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    else if (t <= 9500000000000.0d0) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double tmp;
	if (t <= -0.88) {
		tmp = t_1;
	} else if (t <= 1e-137) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (t <= 1.15e-24) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (t <= 9500000000000.0) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (x * (y * z))) + (a * -4.0))
	tmp = 0
	if t <= -0.88:
		tmp = t_1
	elif t <= 1e-137:
		tmp = (b * c) - ((j * 27.0) * k)
	elif t <= 1.15e-24:
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	elif t <= 9500000000000.0:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0)))
	tmp = 0.0
	if (t <= -0.88)
		tmp = t_1;
	elseif (t <= 1e-137)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 1.15e-24)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	elseif (t <= 9500000000000.0)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	tmp = 0.0;
	if (t <= -0.88)
		tmp = t_1;
	elseif (t <= 1e-137)
		tmp = (b * c) - ((j * 27.0) * k);
	elseif (t <= 1.15e-24)
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	elseif (t <= 9500000000000.0)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.88], t$95$1, If[LessEqual[t, 1e-137], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-24], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9500000000000.0], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -0.880000000000000004 or 9.5e12 < t

   1. Initial program 82.8%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in t around inf 77.1%

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

   6. Taylor expanded in t around inf 70.5%

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

   if -0.880000000000000004 < t < 9.99999999999999978e-138

   1. Initial program 80.1%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in t around 0 83.1%

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

   6. Taylor expanded in i around 0 66.0%

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

      1. associate-*r* 65.9%

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

   8. Simplified 65.9%

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

   if 9.99999999999999978e-138 < t < 1.1500000000000001e-24

   1. Initial program 91.5%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in x around inf 53.9%

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

      1. pow1 53.9%

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

   7. Applied egg-rr 53.9%

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

      1. unpow1 53.9%

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

      2. *-commutative 53.9%

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

      3. associate-*r* 57.9%

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

   9. Simplified 57.9%

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

   if 1.1500000000000001e-24 < t < 9.5e12

   1. Initial program 83.1%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in b around inf 99.7%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.88:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 10^{-137}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 9500000000000:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 59.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -0.0046:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-137}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \left(x \cdot \left(t \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+43}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (+ (* 18.0 (* x (* y z))) (* a -4.0)))))
   (if (<= t -0.0046)
     t_1
     (if (<= t 4.6e-137)
       (- (* b c) (* (* j 27.0) k))
       (if (<= t 1.72e-90)
         (* y (* x (* t (* 18.0 z))))
         (if (<= t 5.5e+43) (- (* b c) (* (* x 4.0) i)) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double tmp;
	if (t <= -0.0046) {
		tmp = t_1;
	} else if (t <= 4.6e-137) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (t <= 1.72e-90) {
		tmp = y * (x * (t * (18.0 * z)));
	} else if (t <= 5.5e+43) {
		tmp = (b * c) - ((x * 4.0) * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))
    if (t <= (-0.0046d0)) then
        tmp = t_1
    else if (t <= 4.6d-137) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else if (t <= 1.72d-90) then
        tmp = y * (x * (t * (18.0d0 * z)))
    else if (t <= 5.5d+43) then
        tmp = (b * c) - ((x * 4.0d0) * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double tmp;
	if (t <= -0.0046) {
		tmp = t_1;
	} else if (t <= 4.6e-137) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (t <= 1.72e-90) {
		tmp = y * (x * (t * (18.0 * z)));
	} else if (t <= 5.5e+43) {
		tmp = (b * c) - ((x * 4.0) * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (x * (y * z))) + (a * -4.0))
	tmp = 0
	if t <= -0.0046:
		tmp = t_1
	elif t <= 4.6e-137:
		tmp = (b * c) - ((j * 27.0) * k)
	elif t <= 1.72e-90:
		tmp = y * (x * (t * (18.0 * z)))
	elif t <= 5.5e+43:
		tmp = (b * c) - ((x * 4.0) * i)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0)))
	tmp = 0.0
	if (t <= -0.0046)
		tmp = t_1;
	elseif (t <= 4.6e-137)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 1.72e-90)
		tmp = Float64(y * Float64(x * Float64(t * Float64(18.0 * z))));
	elseif (t <= 5.5e+43)
		tmp = Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	tmp = 0.0;
	if (t <= -0.0046)
		tmp = t_1;
	elseif (t <= 4.6e-137)
		tmp = (b * c) - ((j * 27.0) * k);
	elseif (t <= 1.72e-90)
		tmp = y * (x * (t * (18.0 * z)));
	elseif (t <= 5.5e+43)
		tmp = (b * c) - ((x * 4.0) * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.0046], t$95$1, If[LessEqual[t, 4.6e-137], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.72e-90], N[(y * N[(x * N[(t * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+43], N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -0.0045999999999999999 or 5.49999999999999989e43 < t

   1. Initial program 82.2%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in t around inf 78.0%

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

   6. Taylor expanded in t around inf 71.2%

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

   if -0.0045999999999999999 < t < 4.60000000000000016e-137

   1. Initial program 79.3%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in t around 0 83.3%

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

   6. Taylor expanded in i around 0 66.3%

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

      1. associate-*r* 66.2%

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

   8. Simplified 66.2%

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

   if 4.60000000000000016e-137 < t < 1.72e-90

   1. Initial program 90.5%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in x around inf 61.0%

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

   6. Taylor expanded in y around inf 70.6%

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

   7. Taylor expanded in i around 0 70.6%

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

      1. *-commutative 70.6%

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

      2. *-commutative 70.6%

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

      3. associate-*l* 70.3%

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

      4. *-commutative 70.3%

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

      5. associate-*r* 70.3%

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

      6. *-commutative 70.3%

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

      7. associate-*r* 70.8%

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

      8. *-commutative 70.8%

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

      9. associate-*l* 70.8%

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

   9. Simplified 70.8%

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

   if 1.72e-90 < t < 5.49999999999999989e43

   1. Initial program 95.4%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in t around 0 74.1%

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

   6. Taylor expanded in i around inf 60.2%

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

      1. associate-*r* 56.1%

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

      2. *-commutative 56.1%

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

      3. associate-*r* 60.2%

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

   8. Simplified 60.2%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0046:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-137}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \left(x \cdot \left(t \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+43}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 74.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_2 := b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.85:\\ \;\;\;\;t \cdot \left(t\_1 + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-137}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z)))) (t_2 (+ (* b c) (* t (- t_1 (* a 4.0))))))
   (if (<= t -1.5e+102)
     t_2
     (if (<= t -1.85)
       (+ (* t (+ t_1 (* a -4.0))) (* j (* k -27.0)))
       (if (<= t 4.4e-137)
         (- (* b c) (+ (* 27.0 (* j k)) (* 4.0 (* x i))))
         t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = (b * c) + (t * (t_1 - (a * 4.0)));
	double tmp;
	if (t <= -1.5e+102) {
		tmp = t_2;
	} else if (t <= -1.85) {
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	} else if (t <= 4.4e-137) {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    t_2 = (b * c) + (t * (t_1 - (a * 4.0d0)))
    if (t <= (-1.5d+102)) then
        tmp = t_2
    else if (t <= (-1.85d0)) then
        tmp = (t * (t_1 + (a * (-4.0d0)))) + (j * (k * (-27.0d0)))
    else if (t <= 4.4d-137) then
        tmp = (b * c) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = (b * c) + (t * (t_1 - (a * 4.0)));
	double tmp;
	if (t <= -1.5e+102) {
		tmp = t_2;
	} else if (t <= -1.85) {
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	} else if (t <= 4.4e-137) {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	t_2 = (b * c) + (t * (t_1 - (a * 4.0)))
	tmp = 0
	if t <= -1.5e+102:
		tmp = t_2
	elif t <= -1.85:
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0))
	elif t <= 4.4e-137:
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	t_2 = Float64(Float64(b * c) + Float64(t * Float64(t_1 - Float64(a * 4.0))))
	tmp = 0.0
	if (t <= -1.5e+102)
		tmp = t_2;
	elseif (t <= -1.85)
		tmp = Float64(Float64(t * Float64(t_1 + Float64(a * -4.0))) + Float64(j * Float64(k * -27.0)));
	elseif (t <= 4.4e-137)
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * i))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	t_2 = (b * c) + (t * (t_1 - (a * 4.0)));
	tmp = 0.0;
	if (t <= -1.5e+102)
		tmp = t_2;
	elseif (t <= -1.85)
		tmp = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	elseif (t <= 4.4e-137)
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e+102], t$95$2, If[LessEqual[t, -1.85], N[(N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-137], N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4999999999999999e102 or 4.4000000000000002e-137 < t

   1. Initial program 84.4%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in i around 0 83.9%

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

   6. Taylor expanded in j around 0 81.8%

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

   if -1.4999999999999999e102 < t < -1.8500000000000001

   1. Initial program 85.9%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in t around inf 84.8%

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

   if -1.8500000000000001 < t < 4.4000000000000002e-137

   1. Initial program 79.3%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in t around 0 83.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+102}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.85:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-137}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 48.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+67}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+126} \lor \neg \left(x \leq 4 \cdot 10^{+169}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* y (* 18.0 (* t (* x z))))))
   (if (<= x -1.1e+155)
     t_1
     (if (<= x 3.8e+67)
       (- (* b c) (* (* j 27.0) k))
       (if (or (<= x 1.4e+126) (not (<= x 4e+169)))
         t_1
         (- (* b c) (* (* x 4.0) i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = y * (18.0 * (t * (x * z)));
	double tmp;
	if (x <= -1.1e+155) {
		tmp = t_1;
	} else if (x <= 3.8e+67) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if ((x <= 1.4e+126) || !(x <= 4e+169)) {
		tmp = t_1;
	} else {
		tmp = (b * c) - ((x * 4.0) * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (18.0d0 * (t * (x * z)))
    if (x <= (-1.1d+155)) then
        tmp = t_1
    else if (x <= 3.8d+67) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else if ((x <= 1.4d+126) .or. (.not. (x <= 4d+169))) then
        tmp = t_1
    else
        tmp = (b * c) - ((x * 4.0d0) * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = y * (18.0 * (t * (x * z)));
	double tmp;
	if (x <= -1.1e+155) {
		tmp = t_1;
	} else if (x <= 3.8e+67) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if ((x <= 1.4e+126) || !(x <= 4e+169)) {
		tmp = t_1;
	} else {
		tmp = (b * c) - ((x * 4.0) * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = y * (18.0 * (t * (x * z)))
	tmp = 0
	if x <= -1.1e+155:
		tmp = t_1
	elif x <= 3.8e+67:
		tmp = (b * c) - ((j * 27.0) * k)
	elif (x <= 1.4e+126) or not (x <= 4e+169):
		tmp = t_1
	else:
		tmp = (b * c) - ((x * 4.0) * i)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(y * Float64(18.0 * Float64(t * Float64(x * z))))
	tmp = 0.0
	if (x <= -1.1e+155)
		tmp = t_1;
	elseif (x <= 3.8e+67)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif ((x <= 1.4e+126) || !(x <= 4e+169))
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = y * (18.0 * (t * (x * z)));
	tmp = 0.0;
	if (x <= -1.1e+155)
		tmp = t_1;
	elseif (x <= 3.8e+67)
		tmp = (b * c) - ((j * 27.0) * k);
	elseif ((x <= 1.4e+126) || ~((x <= 4e+169)))
		tmp = t_1;
	else
		tmp = (b * c) - ((x * 4.0) * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(y * N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+155], t$95$1, If[LessEqual[x, 3.8e+67], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.4e+126], N[Not[LessEqual[x, 4e+169]], $MachinePrecision]], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1000000000000001e155 or 3.8000000000000002e67 < x < 1.40000000000000005e126 or 3.99999999999999974e169 < x

   1. Initial program 70.4%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in x around inf 79.1%

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

   6. Taylor expanded in y around inf 64.1%

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

   7. Taylor expanded in i around 0 63.1%

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

   if -1.1000000000000001e155 < x < 3.8000000000000002e67

   1. Initial program 88.2%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in t around 0 62.2%

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

   6. Taylor expanded in i around 0 56.3%

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

      1. associate-*r* 56.2%

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

   8. Simplified 56.2%

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

   if 1.40000000000000005e126 < x < 3.99999999999999974e169

   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 84.4%

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

   5. Taylor expanded in t around 0 77.7%

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

   6. Taylor expanded in i around inf 67.3%

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

      1. associate-*r* 67.3%

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

      2. *-commutative 67.3%

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

      3. associate-*r* 67.3%

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

   8. Simplified 67.3%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+67}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+126} \lor \neg \left(x \leq 4 \cdot 10^{+169}\right):\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 72.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+154} \lor \neg \left(x \leq 6.7 \cdot 10^{+65}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -8.5e+154) (not (<= x 6.7e+65)))
   (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
   (- (+ (* b c) (* -4.0 (* t a))) (* 27.0 (* j k)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -8.5e+154) || !(x <= 6.7e+65)) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-8.5d+154)) .or. (.not. (x <= 6.7d+65))) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -8.5e+154) || !(x <= 6.7e+65)) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -8.5e+154) or not (x <= 6.7e+65):
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -8.5e+154) || !(x <= 6.7e+65))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -8.5e+154) || ~((x <= 6.7e+65)))
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -8.5e+154], N[Not[LessEqual[x, 6.7e+65]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5000000000000002e154 or 6.6999999999999997e65 < x

   1. Initial program 72.0%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in x around inf 75.5%

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

      1. pow1 75.5%

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

   7. Applied egg-rr 75.5%

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

      1. unpow1 75.5%

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

      2. *-commutative 75.5%

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

      3. associate-*r* 77.7%

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

   9. Simplified 77.7%

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

   if -8.5000000000000002e154 < x < 6.6999999999999997e65

   1. Initial program 88.1%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in x around 0 77.8%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+154} \lor \neg \left(x \leq 6.7 \cdot 10^{+65}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 48.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+155} \lor \neg \left(x \leq 3 \cdot 10^{+67}\right):\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -1.9e+155) (not (<= x 3e+67)))
   (* y (* 18.0 (* t (* x z))))
   (- (* b c) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -1.9e+155) || !(x <= 3e+67)) {
		tmp = y * (18.0 * (t * (x * z)));
	} else {
		tmp = (b * c) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-1.9d+155)) .or. (.not. (x <= 3d+67))) then
        tmp = y * (18.0d0 * (t * (x * z)))
    else
        tmp = (b * c) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -1.9e+155) || !(x <= 3e+67)) {
		tmp = y * (18.0 * (t * (x * z)));
	} else {
		tmp = (b * c) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -1.9e+155) or not (x <= 3e+67):
		tmp = y * (18.0 * (t * (x * z)))
	else:
		tmp = (b * c) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -1.9e+155) || !(x <= 3e+67))
		tmp = Float64(y * Float64(18.0 * Float64(t * Float64(x * z))));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -1.9e+155) || ~((x <= 3e+67)))
		tmp = y * (18.0 * (t * (x * z)));
	else
		tmp = (b * c) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -1.9e+155], N[Not[LessEqual[x, 3e+67]], $MachinePrecision]], N[(y * N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9e155 or 3.0000000000000001e67 < x

   1. Initial program 71.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in x around inf 76.1%

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

   6. Taylor expanded in y around inf 60.5%

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

   7. Taylor expanded in i around 0 56.2%

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

   if -1.9e155 < x < 3.0000000000000001e67

   1. Initial program 88.2%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in t around 0 62.2%

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

   6. Taylor expanded in i around 0 56.3%

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

      1. associate-*r* 56.2%

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

   8. Simplified 56.2%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+155} \lor \neg \left(x \leq 3 \cdot 10^{+67}\right):\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 48.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+154} \lor \neg \left(x \leq 1.36 \cdot 10^{+66}\right):\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -8.6e+154) (not (<= x 1.36e+66)))
   (* y (* 18.0 (* t (* x z))))
   (+ (* b c) (* j (* k -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -8.6e+154) || !(x <= 1.36e+66)) {
		tmp = y * (18.0 * (t * (x * z)));
	} 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.
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 <= (-8.6d+154)) .or. (.not. (x <= 1.36d+66))) then
        tmp = y * (18.0d0 * (t * (x * z)))
    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;
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 <= -8.6e+154) || !(x <= 1.36e+66)) {
		tmp = y * (18.0 * (t * (x * z)));
	} 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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -8.6e+154) or not (x <= 1.36e+66):
		tmp = y * (18.0 * (t * (x * z)))
	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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -8.6e+154) || !(x <= 1.36e+66))
		tmp = Float64(y * Float64(18.0 * Float64(t * Float64(x * z))));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -8.6e+154) || ~((x <= 1.36e+66)))
		tmp = y * (18.0 * (t * (x * z)));
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -8.6e+154], N[Not[LessEqual[x, 1.36e+66]], $MachinePrecision]], N[(y * N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5999999999999995e154 or 1.36e66 < x

   1. Initial program 71.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in x around inf 76.1%

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

   6. Taylor expanded in y around inf 60.5%

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

   7. Taylor expanded in i around 0 56.2%

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

   if -8.5999999999999995e154 < x < 1.36e66

   1. Initial program 88.2%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in b around inf 56.3%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+154} \lor \neg \left(x \leq 1.36 \cdot 10^{+66}\right):\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 37.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7.5 \cdot 10^{+85} \lor \neg \left(b \cdot c \leq 7.8 \cdot 10^{+160}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -7.5e+85) (not (<= (* b c) 7.8e+160)))
   (* b c)
   (* (* j k) -27.0)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -7.5e+85) || !((b * c) <= 7.8e+160)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-7.5d+85)) .or. (.not. ((b * c) <= 7.8d+160))) then
        tmp = b * c
    else
        tmp = (j * k) * (-27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -7.5e+85) || !((b * c) <= 7.8e+160)) {
		tmp = b * c;
	} else {
		tmp = (j * k) * -27.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -7.5e+85) or not ((b * c) <= 7.8e+160):
		tmp = b * c
	else:
		tmp = (j * k) * -27.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -7.5e+85) || !(Float64(b * c) <= 7.8e+160))
		tmp = Float64(b * c);
	else
		tmp = Float64(Float64(j * k) * -27.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -7.5e+85) || ~(((b * c) <= 7.8e+160)))
		tmp = b * c;
	else
		tmp = (j * k) * -27.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -7.5e+85], N[Not[LessEqual[N[(b * c), $MachinePrecision], 7.8e+160]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -7.49999999999999942e85 or 7.80000000000000014e160 < (*.f64 b c)

   1. Initial program 82.3%

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

      1. pow1 82.3%

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

      2. associate-*l* 82.3%

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

      3. *-commutative 82.3%

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

   4. Applied egg-rr 82.3%

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

      1. unpow1 82.3%

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

      2. associate-*l* 87.3%

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

      3. *-commutative 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in b around inf 66.6%

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

   if -7.49999999999999942e85 < (*.f64 b c) < 7.80000000000000014e160

   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 85.6%

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

   5. Taylor expanded in j around inf 27.6%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7.5 \cdot 10^{+85} \lor \neg \left(b \cdot c \leq 7.8 \cdot 10^{+160}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 23.4% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.5%

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

   1. pow1 82.5%

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

   2. associate-*l* 83.2%

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

   3. *-commutative 83.2%

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

4. Applied egg-rr 83.2%

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

   1. unpow1 83.2%

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

   2. associate-*l* 85.7%

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

   3. *-commutative 85.7%

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

6. Simplified 85.7%

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

7. Taylor expanded in b around inf 24.3%

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

Developer target: 89.2% 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 2024087 
(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)))