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

Percentage Accurate: 84.9% → 89.9%

Time: 20.3s

Alternatives: 17

Speedup: 0.9×

• 50.5% 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: 84.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * 4.0) * i;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - t_1) - t_2) <= Double.POSITIVE_INFINITY) {
		tmp = (((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - t_1) - t_2;
	} else {
		tmp = t * (z * (((x * y) * -(-18.0)) - (4.0 * (a / 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])
[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
	tmp = 0
	if ((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - t_1) - t_2) <= math.inf:
		tmp = (((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - t_1) - t_2
	else:
		tmp = t * (z * (((x * y) * -(-18.0)) - (4.0 * (a / 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])
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)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - t_1) - t_2) <= Inf)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(x * Float64(z * Float64(18.0 * y))) - Float64(a * 4.0)))) - t_1) - t_2);
	else
		tmp = Float64(t * Float64(z * Float64(Float64(Float64(x * y) * Float64(-(-18.0))) - Float64(4.0 * Float64(a / 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])){:}
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;
	tmp = 0.0;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - t_1) - t_2) <= Inf)
		tmp = (((b * c) + (t * ((x * (z * (18.0 * y))) - (a * 4.0)))) - t_1) - t_2;
	else
		tmp = t * (z * (((x * y) * -(-18.0)) - (4.0 * (a / 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.
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]}, If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], Infinity], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(t * N[(z * N[(N[(N[(x * y), $MachinePrecision] * (--18.0)), $MachinePrecision] - N[(4.0 * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.1%

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

      1. distribute-rgt-out-- 93.1%

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

      2. associate-*r* 93.6%

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

      3. *-commutative 93.6%

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

      4. associate-*l* 93.6%

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

      5. associate-*r* 93.6%

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

   4. Applied egg-rr 93.6%

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

   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%

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

   3. Taylor expanded in t around -inf 67.4%

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

      1. associate-*r* 67.4%

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

      2. neg-mul-1 67.4%

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

      3. cancel-sign-sub-inv 67.4%

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

      4. metadata-eval 67.4%

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

      5. *-commutative 67.4%

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

      6. *-commutative 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in z around inf 70.1%

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

4. Final simplification 90.9%

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

Alternative 2: 38.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;b \cdot c \leq -8.8 \cdot 10^{+221}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.04 \cdot 10^{+21}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -4.1 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.2 \cdot 10^{-276}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2.2 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j k) -27.0)))
   (if (<= (* b c) -8.8e+221)
     (* b c)
     (if (<= (* b c) -1.04e+21)
       (* 18.0 (* y (* z (* x t))))
       (if (<= (* b c) -4.1e-303)
         t_1
         (if (<= (* b c) 1.2e-276)
           (* 18.0 (* t (* x (* y z))))
           (if (<= (* b c) 2.2e+127) t_1 (* b c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * k) * -27.0;
	double tmp;
	if ((b * c) <= -8.8e+221) {
		tmp = b * c;
	} else if ((b * c) <= -1.04e+21) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if ((b * c) <= -4.1e-303) {
		tmp = t_1;
	} else if ((b * c) <= 1.2e-276) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= 2.2e+127) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * k) * (-27.0d0)
    if ((b * c) <= (-8.8d+221)) then
        tmp = b * c
    else if ((b * c) <= (-1.04d+21)) then
        tmp = 18.0d0 * (y * (z * (x * t)))
    else if ((b * c) <= (-4.1d-303)) then
        tmp = t_1
    else if ((b * c) <= 1.2d-276) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if ((b * c) <= 2.2d+127) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * k) * -27.0;
	double tmp;
	if ((b * c) <= -8.8e+221) {
		tmp = b * c;
	} else if ((b * c) <= -1.04e+21) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if ((b * c) <= -4.1e-303) {
		tmp = t_1;
	} else if ((b * c) <= 1.2e-276) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= 2.2e+127) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * k) * -27.0
	tmp = 0
	if (b * c) <= -8.8e+221:
		tmp = b * c
	elif (b * c) <= -1.04e+21:
		tmp = 18.0 * (y * (z * (x * t)))
	elif (b * c) <= -4.1e-303:
		tmp = t_1
	elif (b * c) <= 1.2e-276:
		tmp = 18.0 * (t * (x * (y * z)))
	elif (b * c) <= 2.2e+127:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * k) * -27.0)
	tmp = 0.0
	if (Float64(b * c) <= -8.8e+221)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.04e+21)
		tmp = Float64(18.0 * Float64(y * Float64(z * Float64(x * t))));
	elseif (Float64(b * c) <= -4.1e-303)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.2e-276)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (Float64(b * c) <= 2.2e+127)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * k) * -27.0;
	tmp = 0.0;
	if ((b * c) <= -8.8e+221)
		tmp = b * c;
	elseif ((b * c) <= -1.04e+21)
		tmp = 18.0 * (y * (z * (x * t)));
	elseif ((b * c) <= -4.1e-303)
		tmp = t_1;
	elseif ((b * c) <= 1.2e-276)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif ((b * c) <= 2.2e+127)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -8.8e+221], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.04e+21], N[(18.0 * N[(y * N[(z * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -4.1e-303], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.2e-276], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.2e+127], t$95$1, N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -8.7999999999999998e221 or 2.2000000000000002e127 < (*.f64 b c)

   1. Initial program 82.7%

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

      1. distribute-rgt-out-- 84.2%

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

      2. associate-*r* 84.2%

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

      3. *-commutative 84.2%

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

      4. associate-*l* 84.2%

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

      5. associate-*r* 84.2%

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

   4. Applied egg-rr 84.2%

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

   5. Taylor expanded in b around inf 77.9%

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

   if -8.7999999999999998e221 < (*.f64 b c) < -1.04e21

   1. Initial program 68.8%

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

   3. Taylor expanded in c around inf 51.3%

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

      1. associate--l+ 51.3%

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

      2. fmm-def 51.3%

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

      3. associate-/l* 51.3%

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

      4. fma-define 51.3%

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

      5. associate-/l* 47.7%

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

      6. fma-define 47.7%

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

      7. associate-/l* 51.3%

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

      8. associate-*r/ 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in y around inf 30.8%

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

      1. associate-*r* 37.3%

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

      2. *-commutative 37.3%

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

      3. associate-*l* 34.5%

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

      4. *-commutative 34.5%

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

   8. Simplified 34.5%

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

   if -1.04e21 < (*.f64 b c) < -4.10000000000000018e-303 or 1.19999999999999991e-276 < (*.f64 b c) < 2.2000000000000002e127

   1. Initial program 83.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in j around inf 37.4%

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

   if -4.10000000000000018e-303 < (*.f64 b c) < 1.19999999999999991e-276

   1. Initial program 86.9%

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

   3. Taylor expanded in c around inf 38.2%

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

      1. associate--l+ 38.2%

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

      2. fmm-def 38.2%

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

      3. associate-/l* 35.5%

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

      4. fma-define 35.5%

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

      5. associate-/l* 30.4%

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

      6. fma-define 30.4%

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

      7. associate-/l* 25.2%

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

      8. associate-*r/ 25.2%

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

   5. Simplified 25.2%

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

   6. Taylor expanded in y around inf 46.0%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8.8 \cdot 10^{+221}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.04 \cdot 10^{+21}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -4.1 \cdot 10^{-303}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 1.2 \cdot 10^{-276}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2.2 \cdot 10^{+127}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;b \cdot c \leq -7.1 \cdot 10^{+205}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -4.3 \cdot 10^{+38}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -1.95 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{-277}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j k) -27.0)))
   (if (<= (* b c) -7.1e+205)
     (* b c)
     (if (<= (* b c) -4.3e+38)
       (* i (* x -4.0))
       (if (<= (* b c) -1.95e-303)
         t_1
         (if (<= (* b c) 1.6e-277)
           (* 18.0 (* t (* x (* y z))))
           (if (<= (* b c) 2e+127) t_1 (* b c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * k) * -27.0;
	double tmp;
	if ((b * c) <= -7.1e+205) {
		tmp = b * c;
	} else if ((b * c) <= -4.3e+38) {
		tmp = i * (x * -4.0);
	} else if ((b * c) <= -1.95e-303) {
		tmp = t_1;
	} else if ((b * c) <= 1.6e-277) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= 2e+127) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * k) * (-27.0d0)
    if ((b * c) <= (-7.1d+205)) then
        tmp = b * c
    else if ((b * c) <= (-4.3d+38)) then
        tmp = i * (x * (-4.0d0))
    else if ((b * c) <= (-1.95d-303)) then
        tmp = t_1
    else if ((b * c) <= 1.6d-277) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if ((b * c) <= 2d+127) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * k) * -27.0;
	double tmp;
	if ((b * c) <= -7.1e+205) {
		tmp = b * c;
	} else if ((b * c) <= -4.3e+38) {
		tmp = i * (x * -4.0);
	} else if ((b * c) <= -1.95e-303) {
		tmp = t_1;
	} else if ((b * c) <= 1.6e-277) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if ((b * c) <= 2e+127) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * k) * -27.0
	tmp = 0
	if (b * c) <= -7.1e+205:
		tmp = b * c
	elif (b * c) <= -4.3e+38:
		tmp = i * (x * -4.0)
	elif (b * c) <= -1.95e-303:
		tmp = t_1
	elif (b * c) <= 1.6e-277:
		tmp = 18.0 * (t * (x * (y * z)))
	elif (b * c) <= 2e+127:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * k) * -27.0)
	tmp = 0.0
	if (Float64(b * c) <= -7.1e+205)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -4.3e+38)
		tmp = Float64(i * Float64(x * -4.0));
	elseif (Float64(b * c) <= -1.95e-303)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.6e-277)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (Float64(b * c) <= 2e+127)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * k) * -27.0;
	tmp = 0.0;
	if ((b * c) <= -7.1e+205)
		tmp = b * c;
	elseif ((b * c) <= -4.3e+38)
		tmp = i * (x * -4.0);
	elseif ((b * c) <= -1.95e-303)
		tmp = t_1;
	elseif ((b * c) <= 1.6e-277)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif ((b * c) <= 2e+127)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -7.1e+205], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -4.3e+38], N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.95e-303], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.6e-277], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+127], t$95$1, N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -7.10000000000000024e205 or 1.99999999999999991e127 < (*.f64 b c)

   1. Initial program 82.7%

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

      1. distribute-rgt-out-- 84.2%

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

      2. associate-*r* 84.2%

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

      3. *-commutative 84.2%

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

      4. associate-*l* 84.2%

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

      5. associate-*r* 84.2%

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

   4. Applied egg-rr 84.2%

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

   5. Taylor expanded in b around inf 77.9%

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

   if -7.10000000000000024e205 < (*.f64 b c) < -4.2999999999999997e38

   1. Initial program 67.9%

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

      1. distribute-rgt-out-- 72.0%

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

      2. associate-*r* 72.3%

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

      3. *-commutative 72.3%

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

      4. associate-*l* 72.3%

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

      5. associate-*r* 72.3%

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

   4. Applied egg-rr 72.3%

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

   5. Taylor expanded in i around inf 39.6%

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

      1. associate-*r* 39.6%

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

      2. metadata-eval 39.6%

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

      3. distribute-lft-neg-in 39.6%

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

      4. distribute-lft-neg-in 39.6%

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

      5. *-commutative 39.6%

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

      6. associate-*r* 39.6%

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

      7. distribute-lft-neg-out 39.6%

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

      8. distribute-rgt-neg-in 39.6%

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

      9. metadata-eval 39.6%

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

      10. *-commutative 39.6%

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

      11. *-commutative 39.6%

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

      12. *-commutative 39.6%

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

   7. Simplified 39.6%

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

   if -4.2999999999999997e38 < (*.f64 b c) < -1.95e-303 or 1.5999999999999999e-277 < (*.f64 b c) < 1.99999999999999991e127

   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 88.1%

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

   5. Taylor expanded in j around inf 37.0%

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

   if -1.95e-303 < (*.f64 b c) < 1.5999999999999999e-277

   1. Initial program 86.9%

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

   3. Taylor expanded in c around inf 38.2%

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

      1. associate--l+ 38.2%

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

      2. fmm-def 38.2%

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

      3. associate-/l* 35.5%

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

      4. fma-define 35.5%

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

      5. associate-/l* 30.4%

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

      6. fma-define 30.4%

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

      7. associate-/l* 25.2%

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

      8. associate-*r/ 25.2%

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

   5. Simplified 25.2%

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

   6. Taylor expanded in y around inf 46.0%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7.1 \cdot 10^{+205}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -4.3 \cdot 10^{+38}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -1.95 \cdot 10^{-303}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{-277}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+127}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+187}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) -5e+187)
   (- (* b c) (+ (* 4.0 (* x i)) (* 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);
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) <= -5e+187) {
		tmp = (b * c) - ((4.0 * (x * i)) + (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.
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) <= (-5d+187)) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (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;
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) <= -5e+187) {
		tmp = (b * c) - ((4.0 * (x * i)) + (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])
[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) <= -5e+187:
		tmp = (b * c) - ((4.0 * (x * i)) + (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])
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) <= -5e+187)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + 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])){:}
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) <= -5e+187)
		tmp = (b * c) - ((4.0 * (x * i)) + (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.
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], -5e+187], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -5.0000000000000001e187

   1. Initial program 71.8%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in t around 0 87.6%

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

   if -5.0000000000000001e187 < (*.f64 b c)

   1. Initial program 83.7%

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

   3. Simplified 88.1%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+187}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-13} \lor \neg \left(t \leq 2.5 \cdot 10^{-121}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -7.5e-13) (not (<= t 2.5e-121)))
   (- (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0)))) (* x (* 4.0 i)))
   (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -7.5e-13) || !(t <= 2.5e-121)) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-7.5d-13)) .or. (.not. (t <= 2.5d-121))) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - (x * (4.0d0 * i))
    else
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -7.5e-13) || !(t <= 2.5e-121)) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -7.5e-13) or not (t <= 2.5e-121):
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i))
	else:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -7.5e-13) || !(t <= 2.5e-121))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(x * Float64(4.0 * i)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -7.5e-13) || ~((t <= 2.5e-121)))
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i));
	else
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -7.5e-13], N[Not[LessEqual[t, 2.5e-121]], $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[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5000000000000004e-13 or 2.49999999999999995e-121 < t

   1. Initial program 81.6%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in x around inf 79.0%

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

      1. associate-*r* 79.0%

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

      2. *-commutative 79.0%

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

   7. Simplified 79.0%

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

   if -7.5000000000000004e-13 < t < 2.49999999999999995e-121

   1. Initial program 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in t around 0 88.5%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-13} \lor \neg \left(t \leq 2.5 \cdot 10^{-121}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+123}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-77}:\\ \;\;\;\;t\_1 + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{+127}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4 + \left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + \frac{t \cdot \left(a \cdot -4\right)}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= (* b c) -1e+123)
     (+ (* b c) t_1)
     (if (<= (* b c) 2e-77)
       (+ t_1 (* a (* t -4.0)))
       (if (<= (* b c) 1.6e+127)
         (+ (* (* x i) -4.0) (* (* j k) -27.0))
         (* c (+ b (/ (* t (* a -4.0)) c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -1e+123) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= 2e-77) {
		tmp = t_1 + (a * (t * -4.0));
	} else if ((b * c) <= 1.6e+127) {
		tmp = ((x * i) * -4.0) + ((j * k) * -27.0);
	} else {
		tmp = c * (b + ((t * (a * -4.0)) / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if ((b * c) <= (-1d+123)) then
        tmp = (b * c) + t_1
    else if ((b * c) <= 2d-77) then
        tmp = t_1 + (a * (t * (-4.0d0)))
    else if ((b * c) <= 1.6d+127) then
        tmp = ((x * i) * (-4.0d0)) + ((j * k) * (-27.0d0))
    else
        tmp = c * (b + ((t * (a * (-4.0d0))) / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -1e+123) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= 2e-77) {
		tmp = t_1 + (a * (t * -4.0));
	} else if ((b * c) <= 1.6e+127) {
		tmp = ((x * i) * -4.0) + ((j * k) * -27.0);
	} else {
		tmp = c * (b + ((t * (a * -4.0)) / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if (b * c) <= -1e+123:
		tmp = (b * c) + t_1
	elif (b * c) <= 2e-77:
		tmp = t_1 + (a * (t * -4.0))
	elif (b * c) <= 1.6e+127:
		tmp = ((x * i) * -4.0) + ((j * k) * -27.0)
	else:
		tmp = c * (b + ((t * (a * -4.0)) / c))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -1e+123)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (Float64(b * c) <= 2e-77)
		tmp = Float64(t_1 + Float64(a * Float64(t * -4.0)));
	elseif (Float64(b * c) <= 1.6e+127)
		tmp = Float64(Float64(Float64(x * i) * -4.0) + Float64(Float64(j * k) * -27.0));
	else
		tmp = Float64(c * Float64(b + Float64(Float64(t * Float64(a * -4.0)) / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if ((b * c) <= -1e+123)
		tmp = (b * c) + t_1;
	elseif ((b * c) <= 2e-77)
		tmp = t_1 + (a * (t * -4.0));
	elseif ((b * c) <= 1.6e+127)
		tmp = ((x * i) * -4.0) + ((j * k) * -27.0);
	else
		tmp = c * (b + ((t * (a * -4.0)) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1e+123], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e-77], N[(t$95$1 + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.6e+127], N[(N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision] + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(c * N[(b + N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -9.99999999999999978e122

   1. Initial program 72.5%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in b around inf 77.3%

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

   if -9.99999999999999978e122 < (*.f64 b c) < 1.9999999999999999e-77

   1. Initial program 82.1%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in a around inf 58.1%

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

      1. metadata-eval 58.1%

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

      2. distribute-lft-neg-in 58.1%

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

      3. *-commutative 58.1%

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

      4. associate-*l* 58.1%

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

      5. distribute-lft-neg-in 58.1%

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

      6. distribute-lft-neg-in 58.1%

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

      7. metadata-eval 58.1%

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

   7. Simplified 58.1%

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

   if 1.9999999999999999e-77 < (*.f64 b c) < 1.59999999999999988e127

   1. Initial program 88.9%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in i around inf 56.5%

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

   6. Taylor expanded in j around 0 56.4%

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

   if 1.59999999999999988e127 < (*.f64 b c)

   1. Initial program 85.9%

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

   3. Taylor expanded in c around inf 88.5%

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

      1. associate--l+ 88.5%

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

      2. fmm-def 88.5%

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

      3. associate-/l* 88.5%

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

      4. fma-define 88.5%

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

      5. associate-/l* 88.5%

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

      6. fma-define 88.5%

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

      7. associate-/l* 93.1%

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

      8. associate-*r/ 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in a around inf 79.4%

      \[\leadsto c \cdot \left(b + \color{blue}{-4 \cdot \frac{a \cdot t}{c}}\right) \]
   7. Step-by-step derivation

      1. associate-*r/ 79.4%

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

      2. associate-*r* 79.4%

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

      3. *-commutative 79.4%

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

      4. *-commutative 79.4%

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

   8. Simplified 79.4%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+123}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-77}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{+127}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4 + \left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + \frac{t \cdot \left(a \cdot -4\right)}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-299}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+42}:\\ \;\;\;\;c \cdot \left(b + \frac{t \cdot \left(a \cdot -4\right)}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1.26e+85)
   (* x (+ (* (* y z) (* 18.0 t)) (* i -4.0)))
   (if (<= x 7.4e-299)
     (- (* b c) (* 27.0 (* j k)))
     (if (<= x 2.7e+42)
       (* c (+ b (/ (* t (* a -4.0)) c)))
       (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -1.26e+85) {
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	} else if (x <= 7.4e-299) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 2.7e+42) {
		tmp = c * (b + ((t * (a * -4.0)) / c));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-1.26d+85)) then
        tmp = x * (((y * z) * (18.0d0 * t)) + (i * (-4.0d0)))
    else if (x <= 7.4d-299) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (x <= 2.7d+42) then
        tmp = c * (b + ((t * (a * (-4.0d0))) / c))
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -1.26e+85) {
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	} else if (x <= 7.4e-299) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 2.7e+42) {
		tmp = c * (b + ((t * (a * -4.0)) / c));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -1.26e+85:
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0))
	elif x <= 7.4e-299:
		tmp = (b * c) - (27.0 * (j * k))
	elif x <= 2.7e+42:
		tmp = c * (b + ((t * (a * -4.0)) / c))
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -1.26e+85)
		tmp = Float64(x * Float64(Float64(Float64(y * z) * Float64(18.0 * t)) + Float64(i * -4.0)));
	elseif (x <= 7.4e-299)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (x <= 2.7e+42)
		tmp = Float64(c * Float64(b + Float64(Float64(t * Float64(a * -4.0)) / c)));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -1.26e+85)
		tmp = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	elseif (x <= 7.4e-299)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (x <= 2.7e+42)
		tmp = c * (b + ((t * (a * -4.0)) / c));
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -1.26e+85], N[(x * N[(N[(N[(y * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e-299], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+42], N[(c * N[(b + N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.26000000000000003e85

   1. Initial program 68.5%

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

      1. distribute-rgt-out-- 73.1%

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

      2. associate-*r* 75.3%

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

      3. *-commutative 75.3%

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

      4. associate-*l* 75.3%

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

      5. associate-*r* 75.3%

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

   4. Applied egg-rr 75.3%

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

   5. Taylor expanded in z around inf 66.0%

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

   6. Taylor expanded in x around inf 71.2%

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

      1. cancel-sign-sub-inv 71.2%

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

      2. associate-*r* 71.2%

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

      3. metadata-eval 71.2%

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

   8. Simplified 71.2%

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

   if -1.26000000000000003e85 < x < 7.40000000000000028e-299

   1. Initial program 93.4%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in x around 0 76.8%

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

   6. Taylor expanded in a around 0 63.5%

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

   if 7.40000000000000028e-299 < x < 2.7000000000000001e42

   1. Initial program 88.1%

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

   3. Taylor expanded in c around inf 76.4%

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

      1. associate--l+ 76.4%

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

      2. fmm-def 76.4%

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

      3. associate-/l* 76.4%

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

      4. fma-define 76.4%

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

      5. associate-/l* 73.8%

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

      6. fma-define 73.8%

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

      7. associate-/l* 72.5%

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

      8. associate-*r/ 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in a around inf 62.5%

      \[\leadsto c \cdot \left(b + \color{blue}{-4 \cdot \frac{a \cdot t}{c}}\right) \]
   7. Step-by-step derivation

      1. associate-*r/ 62.5%

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

      2. associate-*r* 62.5%

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

      3. *-commutative 62.5%

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

      4. *-commutative 62.5%

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

   8. Simplified 62.5%

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

   if 2.7000000000000001e42 < x

   1. Initial program 70.7%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in x around inf 73.9%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-299}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+42}:\\ \;\;\;\;c \cdot \left(b + \frac{t \cdot \left(a \cdot -4\right)}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-297}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+45}:\\ \;\;\;\;c \cdot \left(b + \frac{t \cdot \left(a \cdot -4\right)}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) (* 18.0 t)) (* i -4.0)))))
   (if (<= x -1.2e+82)
     t_1
     (if (<= x 4.6e-297)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= x 1.45e+45) (* c (+ b (/ (* t (* a -4.0)) c))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (((y * z) * (18.0 * t)) + (i * -4.0));
	double tmp;
	if (x <= -1.2e+82) {
		tmp = t_1;
	} else if (x <= 4.6e-297) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 1.45e+45) {
		tmp = c * (b + ((t * (a * -4.0)) / c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (((y * z) * (18.0d0 * t)) + (i * (-4.0d0)))
    if (x <= (-1.2d+82)) then
        tmp = t_1
    else if (x <= 4.6d-297) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (x <= 1.45d+45) then
        tmp = c * (b + ((t * (a * (-4.0d0))) / c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) * (18.0 * t)) + (i * -4.0));
	double tmp;
	if (x <= -1.2e+82) {
		tmp = t_1;
	} else if (x <= 4.6e-297) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 1.45e+45) {
		tmp = c * (b + ((t * (a * -4.0)) / c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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) * (18.0 * t)) + (i * -4.0))
	tmp = 0
	if x <= -1.2e+82:
		tmp = t_1
	elif x <= 4.6e-297:
		tmp = (b * c) - (27.0 * (j * k))
	elif x <= 1.45e+45:
		tmp = c * (b + ((t * (a * -4.0)) / c))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(Float64(Float64(y * z) * Float64(18.0 * t)) + Float64(i * -4.0)))
	tmp = 0.0
	if (x <= -1.2e+82)
		tmp = t_1;
	elseif (x <= 4.6e-297)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (x <= 1.45e+45)
		tmp = Float64(c * Float64(b + Float64(Float64(t * Float64(a * -4.0)) / c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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) * (18.0 * t)) + (i * -4.0));
	tmp = 0.0;
	if (x <= -1.2e+82)
		tmp = t_1;
	elseif (x <= 4.6e-297)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (x <= 1.45e+45)
		tmp = c * (b + ((t * (a * -4.0)) / c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(N[(N[(y * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+82], t$95$1, If[LessEqual[x, 4.6e-297], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45e+45], N[(c * N[(b + N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.19999999999999999e82 or 1.4499999999999999e45 < x

   1. Initial program 69.8%

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

      1. distribute-rgt-out-- 74.6%

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

      2. associate-*r* 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-*l* 78.3%

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

      5. associate-*r* 78.3%

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

   4. Applied egg-rr 78.3%

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

   5. Taylor expanded in z around inf 68.6%

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

   6. Taylor expanded in x around inf 72.7%

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

      1. cancel-sign-sub-inv 72.7%

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

      2. associate-*r* 72.7%

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

      3. metadata-eval 72.7%

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

   8. Simplified 72.7%

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

   if -1.19999999999999999e82 < x < 4.5999999999999998e-297

   1. Initial program 93.4%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in x around 0 76.8%

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

   6. Taylor expanded in a around 0 63.5%

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

   if 4.5999999999999998e-297 < x < 1.4499999999999999e45

   1. Initial program 88.1%

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

   3. Taylor expanded in c around inf 76.4%

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

      1. associate--l+ 76.4%

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

      2. fmm-def 76.4%

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

      3. associate-/l* 76.4%

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

      4. fma-define 76.4%

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

      5. associate-/l* 73.8%

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

      6. fma-define 73.8%

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

      7. associate-/l* 72.5%

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

      8. associate-*r/ 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in a around inf 62.5%

      \[\leadsto c \cdot \left(b + \color{blue}{-4 \cdot \frac{a \cdot t}{c}}\right) \]
   7. Step-by-step derivation

      1. associate-*r/ 62.5%

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

      2. associate-*r* 62.5%

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

      3. *-commutative 62.5%

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

      4. *-commutative 62.5%

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

   8. Simplified 62.5%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-297}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+45}:\\ \;\;\;\;c \cdot \left(b + \frac{t \cdot \left(a \cdot -4\right)}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right) + i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.5 \cdot 10^{+206}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.6 \cdot 10^{+39}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2.1 \cdot 10^{+127}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1.5e+206)
   (* b c)
   (if (<= (* b c) -2.6e+39)
     (* i (* x -4.0))
     (if (<= (* b c) 2.1e+127) (* (* j k) -27.0) (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.5e+206) {
		tmp = b * c;
	} else if ((b * c) <= -2.6e+39) {
		tmp = i * (x * -4.0);
	} else if ((b * c) <= 2.1e+127) {
		tmp = (j * k) * -27.0;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-1.5d+206)) then
        tmp = b * c
    else if ((b * c) <= (-2.6d+39)) then
        tmp = i * (x * (-4.0d0))
    else if ((b * c) <= 2.1d+127) then
        tmp = (j * k) * (-27.0d0)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.5e+206) {
		tmp = b * c;
	} else if ((b * c) <= -2.6e+39) {
		tmp = i * (x * -4.0);
	} else if ((b * c) <= 2.1e+127) {
		tmp = (j * k) * -27.0;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.5e+206:
		tmp = b * c
	elif (b * c) <= -2.6e+39:
		tmp = i * (x * -4.0)
	elif (b * c) <= 2.1e+127:
		tmp = (j * k) * -27.0
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1.5e+206)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.6e+39)
		tmp = Float64(i * Float64(x * -4.0));
	elseif (Float64(b * c) <= 2.1e+127)
		tmp = Float64(Float64(j * k) * -27.0);
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1.5e+206)
		tmp = b * c;
	elseif ((b * c) <= -2.6e+39)
		tmp = i * (x * -4.0);
	elseif ((b * c) <= 2.1e+127)
		tmp = (j * k) * -27.0;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1.5e+206], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.6e+39], N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.1e+127], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.5000000000000001e206 or 2.09999999999999992e127 < (*.f64 b c)

   1. Initial program 82.7%

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

      1. distribute-rgt-out-- 84.2%

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

      2. associate-*r* 84.2%

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

      3. *-commutative 84.2%

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

      4. associate-*l* 84.2%

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

      5. associate-*r* 84.2%

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

   4. Applied egg-rr 84.2%

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

   5. Taylor expanded in b around inf 77.9%

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

   if -1.5000000000000001e206 < (*.f64 b c) < -2.6e39

   1. Initial program 67.9%

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

      1. distribute-rgt-out-- 72.0%

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

      2. associate-*r* 72.3%

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

      3. *-commutative 72.3%

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

      4. associate-*l* 72.3%

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

      5. associate-*r* 72.3%

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

   4. Applied egg-rr 72.3%

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

   5. Taylor expanded in i around inf 39.6%

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

      1. associate-*r* 39.6%

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

      2. metadata-eval 39.6%

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

      3. distribute-lft-neg-in 39.6%

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

      4. distribute-lft-neg-in 39.6%

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

      5. *-commutative 39.6%

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

      6. associate-*r* 39.6%

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

      7. distribute-lft-neg-out 39.6%

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

      8. distribute-rgt-neg-in 39.6%

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

      9. metadata-eval 39.6%

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

      10. *-commutative 39.6%

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

      11. *-commutative 39.6%

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

      12. *-commutative 39.6%

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

   7. Simplified 39.6%

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

   if -2.6e39 < (*.f64 b c) < 2.09999999999999992e127

   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 89.1%

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

   5. Taylor expanded in j around inf 33.7%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.5 \cdot 10^{+206}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.6 \cdot 10^{+39}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2.1 \cdot 10^{+127}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+110}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - -18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+83}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(--18\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -1.7e+110)
   (* t (- (* a (- 4.0)) (* -18.0 (* x (* y z)))))
   (if (<= t 2.7e+83)
     (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
     (* t (- (* (* z (* x y)) (- -18.0)) (* a 4.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.7e+110) {
		tmp = t * ((a * -4.0) - (-18.0 * (x * (y * z))));
	} else if (t <= 2.7e+83) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = t * (((z * (x * y)) * -(-18.0)) - (a * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-1.7d+110)) then
        tmp = t * ((a * -4.0d0) - ((-18.0d0) * (x * (y * z))))
    else if (t <= 2.7d+83) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    else
        tmp = t * (((z * (x * y)) * -(-18.0d0)) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -1.7e+110) {
		tmp = t * ((a * -4.0) - (-18.0 * (x * (y * z))));
	} else if (t <= 2.7e+83) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = t * (((z * (x * y)) * -(-18.0)) - (a * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -1.7e+110:
		tmp = t * ((a * -4.0) - (-18.0 * (x * (y * z))))
	elif t <= 2.7e+83:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	else:
		tmp = t * (((z * (x * y)) * -(-18.0)) - (a * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -1.7e+110)
		tmp = Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(-18.0 * Float64(x * Float64(y * z)))));
	elseif (t <= 2.7e+83)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(x * y)) * Float64(-(-18.0))) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -1.7e+110)
		tmp = t * ((a * -4.0) - (-18.0 * (x * (y * z))));
	elseif (t <= 2.7e+83)
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	else
		tmp = t * (((z * (x * y)) * -(-18.0)) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -1.7e+110], N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(-18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+83], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * (--18.0)), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7000000000000001e110

   1. Initial program 71.1%

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

   3. Taylor expanded in t around -inf 84.9%

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

      1. associate-*r* 84.9%

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

      2. neg-mul-1 84.9%

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

      3. cancel-sign-sub-inv 84.9%

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

      4. metadata-eval 84.9%

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

      5. *-commutative 84.9%

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

      6. *-commutative 84.9%

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

   5. Simplified 84.9%

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

   if -1.7000000000000001e110 < t < 2.70000000000000007e83

   1. Initial program 85.8%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in t around 0 80.4%

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

   if 2.70000000000000007e83 < t

   1. Initial program 80.2%

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

   3. Taylor expanded in t around -inf 70.7%

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

      1. associate-*r* 70.7%

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

      2. neg-mul-1 70.7%

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

      3. cancel-sign-sub-inv 70.7%

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

      4. metadata-eval 70.7%

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

      5. *-commutative 70.7%

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

      6. *-commutative 70.7%

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

   5. Simplified 70.7%

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

      1. pow1 70.7%

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

      2. associate-*r* 72.5%

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

   7. Applied egg-rr 72.5%

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

      1. unpow1 72.5%

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

      2. *-commutative 72.5%

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

   9. Simplified 72.5%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+110}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - -18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+83}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(--18\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -210000 \lor \neg \left(t \leq 1.5 \cdot 10^{+34}\right):\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - -18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -210000.0) (not (<= t 1.5e+34)))
   (* t (- (* a (- 4.0)) (* -18.0 (* x (* y z)))))
   (- (* b c) (* 27.0 (* j k)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -210000.0) || !(t <= 1.5e+34)) {
		tmp = t * ((a * -4.0) - (-18.0 * (x * (y * z))));
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-210000.0d0)) .or. (.not. (t <= 1.5d+34))) then
        tmp = t * ((a * -4.0d0) - ((-18.0d0) * (x * (y * z))))
    else
        tmp = (b * c) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -210000.0) || !(t <= 1.5e+34)) {
		tmp = t * ((a * -4.0) - (-18.0 * (x * (y * z))));
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -210000.0) or not (t <= 1.5e+34):
		tmp = t * ((a * -4.0) - (-18.0 * (x * (y * z))))
	else:
		tmp = (b * c) - (27.0 * (j * k))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -210000.0) || !(t <= 1.5e+34))
		tmp = Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(-18.0 * Float64(x * Float64(y * z)))));
	else
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -210000.0) || ~((t <= 1.5e+34)))
		tmp = t * ((a * -4.0) - (-18.0 * (x * (y * z))));
	else
		tmp = (b * c) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -210000.0], N[Not[LessEqual[t, 1.5e+34]], $MachinePrecision]], N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(-18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1e5 or 1.50000000000000009e34 < t

   1. Initial program 80.9%

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

   3. Taylor expanded in t around -inf 71.2%

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

      1. associate-*r* 71.2%

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

      2. neg-mul-1 71.2%

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

      3. cancel-sign-sub-inv 71.2%

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

      4. metadata-eval 71.2%

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

      5. *-commutative 71.2%

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

      6. *-commutative 71.2%

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

   5. Simplified 71.2%

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

   if -2.1e5 < t < 1.50000000000000009e34

   1. Initial program 83.5%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in x around 0 67.9%

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

   6. Taylor expanded in a around 0 64.0%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -210000 \lor \neg \left(t \leq 1.5 \cdot 10^{+34}\right):\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - -18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -490000:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - -18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+36}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(--18\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -490000.0)
   (* t (- (* a (- 4.0)) (* -18.0 (* x (* y z)))))
   (if (<= t 3.9e+36)
     (- (* b c) (* 27.0 (* j k)))
     (* t (- (* (* z (* x y)) (- -18.0)) (* a 4.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -490000.0) {
		tmp = t * ((a * -4.0) - (-18.0 * (x * (y * z))));
	} else if (t <= 3.9e+36) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = t * (((z * (x * y)) * -(-18.0)) - (a * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-490000.0d0)) then
        tmp = t * ((a * -4.0d0) - ((-18.0d0) * (x * (y * z))))
    else if (t <= 3.9d+36) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else
        tmp = t * (((z * (x * y)) * -(-18.0d0)) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -490000.0) {
		tmp = t * ((a * -4.0) - (-18.0 * (x * (y * z))));
	} else if (t <= 3.9e+36) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = t * (((z * (x * y)) * -(-18.0)) - (a * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -490000.0:
		tmp = t * ((a * -4.0) - (-18.0 * (x * (y * z))))
	elif t <= 3.9e+36:
		tmp = (b * c) - (27.0 * (j * k))
	else:
		tmp = t * (((z * (x * y)) * -(-18.0)) - (a * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -490000.0)
		tmp = Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(-18.0 * Float64(x * Float64(y * z)))));
	elseif (t <= 3.9e+36)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(x * y)) * Float64(-(-18.0))) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -490000.0)
		tmp = t * ((a * -4.0) - (-18.0 * (x * (y * z))));
	elseif (t <= 3.9e+36)
		tmp = (b * c) - (27.0 * (j * k));
	else
		tmp = t * (((z * (x * y)) * -(-18.0)) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -490000.0], N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(-18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e+36], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * (--18.0)), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.9e5

   1. Initial program 77.7%

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

   3. Taylor expanded in t around -inf 75.4%

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

      1. associate-*r* 75.4%

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

      2. neg-mul-1 75.4%

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

      3. cancel-sign-sub-inv 75.4%

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

      4. metadata-eval 75.4%

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

      5. *-commutative 75.4%

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

      6. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -4.9e5 < t < 3.90000000000000021e36

   1. Initial program 83.5%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in x around 0 67.9%

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

   6. Taylor expanded in a around 0 64.0%

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

   if 3.90000000000000021e36 < t

   1. Initial program 84.2%

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

   3. Taylor expanded in t around -inf 66.6%

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

      1. associate-*r* 66.6%

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

      2. neg-mul-1 66.6%

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

      3. cancel-sign-sub-inv 66.6%

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

      4. metadata-eval 66.6%

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

      5. *-commutative 66.6%

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

      6. *-commutative 66.6%

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

   5. Simplified 66.6%

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

      1. pow1 66.6%

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

      2. associate-*r* 69.6%

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

   7. Applied egg-rr 69.6%

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

      1. unpow1 69.6%

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

      2. *-commutative 69.6%

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

   9. Simplified 69.6%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -490000:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - -18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+36}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(--18\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+107}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+29}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + \frac{t \cdot \left(a \cdot -4\right)}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -2.2e+107)
   (* 18.0 (* y (* z (* x t))))
   (if (<= t 9e+29)
     (- (* b c) (* 27.0 (* j k)))
     (* c (+ b (/ (* t (* a -4.0)) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -2.2e+107) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if (t <= 9e+29) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = c * (b + ((t * (a * -4.0)) / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-2.2d+107)) then
        tmp = 18.0d0 * (y * (z * (x * t)))
    else if (t <= 9d+29) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else
        tmp = c * (b + ((t * (a * (-4.0d0))) / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -2.2e+107) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if (t <= 9e+29) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = c * (b + ((t * (a * -4.0)) / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -2.2e+107:
		tmp = 18.0 * (y * (z * (x * t)))
	elif t <= 9e+29:
		tmp = (b * c) - (27.0 * (j * k))
	else:
		tmp = c * (b + ((t * (a * -4.0)) / c))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -2.2e+107)
		tmp = Float64(18.0 * Float64(y * Float64(z * Float64(x * t))));
	elseif (t <= 9e+29)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(c * Float64(b + Float64(Float64(t * Float64(a * -4.0)) / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -2.2e+107)
		tmp = 18.0 * (y * (z * (x * t)));
	elseif (t <= 9e+29)
		tmp = (b * c) - (27.0 * (j * k));
	else
		tmp = c * (b + ((t * (a * -4.0)) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -2.2e+107], N[(18.0 * N[(y * N[(z * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+29], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(b + N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2e107

   1. Initial program 72.3%

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

   3. Taylor expanded in c around inf 51.2%

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

      1. associate--l+ 51.2%

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

      2. fmm-def 51.2%

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

      3. associate-/l* 53.4%

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

      4. fma-define 53.4%

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

      5. associate-/l* 51.2%

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

      6. fma-define 51.2%

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

      7. associate-/l* 51.2%

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

      8. associate-*r/ 51.2%

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

   5. Simplified 51.2%

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

   6. Taylor expanded in y around inf 56.5%

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

      1. associate-*r* 58.4%

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

      2. *-commutative 58.4%

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

      3. associate-*l* 60.5%

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

      4. *-commutative 60.5%

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

   8. Simplified 60.5%

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

   if -2.2e107 < t < 9.0000000000000005e29

   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 86.4%

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

   5. Taylor expanded in x around 0 67.3%

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

   6. Taylor expanded in a around 0 62.4%

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

   if 9.0000000000000005e29 < t

   1. Initial program 84.5%

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

   3. Taylor expanded in c around inf 71.5%

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

      1. associate--l+ 71.5%

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

      2. fmm-def 71.6%

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

      3. associate-/l* 71.6%

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

      4. fma-define 71.6%

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

      5. associate-/l* 63.2%

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

      6. fma-define 63.2%

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

      7. associate-/l* 64.9%

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

      8. associate-*r/ 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in a around inf 53.7%

      \[\leadsto c \cdot \left(b + \color{blue}{-4 \cdot \frac{a \cdot t}{c}}\right) \]
   7. Step-by-step derivation

      1. associate-*r/ 53.7%

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

      2. associate-*r* 53.7%

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

      3. *-commutative 53.7%

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

      4. *-commutative 53.7%

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

   8. Simplified 53.7%

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

Alternative 14: 38.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.3 \cdot 10^{+42} \lor \neg \left(b \cdot c \leq 2.2 \cdot 10^{+127}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) -2.3e+42) (not (<= (* b c) 2.2e+127)))
   (* b c)
   (* (* j k) -27.0)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.3e+42) || !((b * c) <= 2.2e+127)) {
		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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-2.3d+42)) .or. (.not. ((b * c) <= 2.2d+127))) 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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.3e+42) || !((b * c) <= 2.2e+127)) {
		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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -2.3e+42) or not ((b * c) <= 2.2e+127):
		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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -2.3e+42) || !(Float64(b * c) <= 2.2e+127))
		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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -2.3e+42) || ~(((b * c) <= 2.2e+127)))
		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.
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], -2.3e+42], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2.2e+127]], $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) < -2.3e42 or 2.2000000000000002e127 < (*.f64 b c)

   1. Initial program 79.7%

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

      1. distribute-rgt-out-- 81.9%

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

      2. associate-*r* 82.0%

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

      3. *-commutative 82.0%

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

      4. associate-*l* 82.0%

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

      5. associate-*r* 82.0%

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

   4. Applied egg-rr 82.0%

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

   5. Taylor expanded in b around inf 63.3%

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

   if -2.3e42 < (*.f64 b c) < 2.2000000000000002e127

   1. Initial program 83.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in j around inf 33.5%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.3 \cdot 10^{+42} \lor \neg \left(b \cdot c \leq 2.2 \cdot 10^{+127}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+107}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -6.8e+107)
   (* 18.0 (* y (* z (* x t))))
   (if (<= t 1.45e+88) (- (* b c) (* 27.0 (* j k))) (* t (* a -4.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -6.8e+107) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if (t <= 1.45e+88) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= (-6.8d+107)) then
        tmp = 18.0d0 * (y * (z * (x * t)))
    else if (t <= 1.45d+88) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else
        tmp = t * (a * (-4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -6.8e+107) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if (t <= 1.45e+88) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -6.8e+107:
		tmp = 18.0 * (y * (z * (x * t)))
	elif t <= 1.45e+88:
		tmp = (b * c) - (27.0 * (j * k))
	else:
		tmp = t * (a * -4.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -6.8e+107)
		tmp = Float64(18.0 * Float64(y * Float64(z * Float64(x * t))));
	elseif (t <= 1.45e+88)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(t * Float64(a * -4.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -6.8e+107)
		tmp = 18.0 * (y * (z * (x * t)));
	elseif (t <= 1.45e+88)
		tmp = (b * c) - (27.0 * (j * k));
	else
		tmp = t * (a * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -6.8e+107], N[(18.0 * N[(y * N[(z * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+88], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.7999999999999994e107

   1. Initial program 72.3%

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

   3. Taylor expanded in c around inf 51.2%

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

      1. associate--l+ 51.2%

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

      2. fmm-def 51.2%

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

      3. associate-/l* 53.4%

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

      4. fma-define 53.4%

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

      5. associate-/l* 51.2%

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

      6. fma-define 51.2%

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

      7. associate-/l* 51.2%

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

      8. associate-*r/ 51.2%

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

   5. Simplified 51.2%

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

   6. Taylor expanded in y around inf 56.5%

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

      1. associate-*r* 58.4%

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

      2. *-commutative 58.4%

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

      3. associate-*l* 60.5%

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

      4. *-commutative 60.5%

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

   8. Simplified 60.5%

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

   if -6.7999999999999994e107 < t < 1.45e88

   1. Initial program 85.7%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in x around 0 67.6%

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

   6. Taylor expanded in a around 0 61.4%

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

   if 1.45e88 < t

   1. Initial program 79.7%

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

   3. Taylor expanded in t around -inf 70.0%

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

      1. associate-*r* 70.0%

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

      2. neg-mul-1 70.0%

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

      3. cancel-sign-sub-inv 70.0%

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

      4. metadata-eval 70.0%

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

      5. *-commutative 70.0%

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

      6. *-commutative 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in x around 0 46.1%

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

      1. *-commutative 46.1%

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

   8. Simplified 46.1%

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

   9. Taylor expanded in t around 0 46.1%

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

       1. *-commutative 46.1%

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

       2. associate-*r* 46.1%

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

       3. *-commutative 46.1%

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

       4. associate-*l* 46.1%

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

   11. Simplified 46.1%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+107}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 48.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+103}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -1.2e+103)
   (* 18.0 (* y (* z (* x t))))
   (if (<= t 9e+87) (+ (* b c) (* j (* k -27.0))) (* t (* a -4.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -1.2e+103) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if (t <= 9e+87) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 <= (-1.2d+103)) then
        tmp = 18.0d0 * (y * (z * (x * t)))
    else if (t <= 9d+87) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = t * (a * (-4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -1.2e+103) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if (t <= 9e+87) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 <= -1.2e+103:
		tmp = 18.0 * (y * (z * (x * t)))
	elif t <= 9e+87:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = t * (a * -4.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -1.2e+103)
		tmp = Float64(18.0 * Float64(y * Float64(z * Float64(x * t))));
	elseif (t <= 9e+87)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(t * Float64(a * -4.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 <= -1.2e+103)
		tmp = 18.0 * (y * (z * (x * t)));
	elseif (t <= 9e+87)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = t * (a * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -1.2e+103], N[(18.0 * N[(y * N[(z * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+87], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1999999999999999e103

   1. Initial program 72.3%

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

   3. Taylor expanded in c around inf 51.2%

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

      1. associate--l+ 51.2%

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

      2. fmm-def 51.2%

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

      3. associate-/l* 53.4%

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

      4. fma-define 53.4%

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

      5. associate-/l* 51.2%

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

      6. fma-define 51.2%

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

      7. associate-/l* 51.2%

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

      8. associate-*r/ 51.2%

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

   5. Simplified 51.2%

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

   6. Taylor expanded in y around inf 56.5%

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

      1. associate-*r* 58.4%

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

      2. *-commutative 58.4%

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

      3. associate-*l* 60.5%

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

      4. *-commutative 60.5%

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

   8. Simplified 60.5%

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

   if -1.1999999999999999e103 < t < 9.0000000000000005e87

   1. Initial program 85.7%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in b around inf 61.3%

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

   if 9.0000000000000005e87 < t

   1. Initial program 79.7%

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

   3. Taylor expanded in t around -inf 70.0%

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

      1. associate-*r* 70.0%

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

      2. neg-mul-1 70.0%

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

      3. cancel-sign-sub-inv 70.0%

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

      4. metadata-eval 70.0%

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

      5. *-commutative 70.0%

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

      6. *-commutative 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in x around 0 46.1%

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

      1. *-commutative 46.1%

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

   8. Simplified 46.1%

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

   9. Taylor expanded in t around 0 46.1%

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

       1. *-commutative 46.1%

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

       2. associate-*r* 46.1%

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

       3. *-commutative 46.1%

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

       4. associate-*l* 46.1%

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

   11. Simplified 46.1%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+103}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 24.5% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.2%

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

   1. distribute-rgt-out-- 85.0%

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

   2. associate-*r* 86.1%

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

   3. *-commutative 86.1%

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

   4. associate-*l* 86.1%

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

   5. associate-*r* 86.1%

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

4. Applied egg-rr 86.1%

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

5. Taylor expanded in b around inf 26.9%

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

Developer Target 1: 88.8% 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 2024152 
(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
  (! :herbie-platform default (if (< t -8105407698770699/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 8284013971902611/50000000000000) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))))))

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