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

Percentage Accurate: 85.5% → 91.2%

Time: 30.9s

Alternatives: 27

Speedup: 0.8×

• 50.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := 18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\\ t_3 := i \cdot \left(x \cdot 4\right)\\ t_4 := j \cdot \left(k \cdot 27\right) + x \cdot \left(4 \cdot i\right)\\ t_5 := t \cdot \left(a \cdot 4\right)\\ t_6 := \left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t\_5\right)\right) - t\_3\right) - t\_1\\ \mathbf{if}\;t\_6 \leq -\infty:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot x\right) - a \cdot 4\right)\right) - t\_4\\ \mathbf{elif}\;t\_6 \leq 5 \cdot 10^{+300}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(18 \cdot \left(y \cdot x\right)\right)\right) - t\_5\right)\right) - t\_3\right) - t\_1\\ \mathbf{elif}\;t\_6 \leq \infty:\\ \;\;\;\;\left(y \cdot \left(-4 \cdot \frac{a \cdot t}{y} + t\_2\right) + b \cdot c\right) - t\_4\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t\_2 + -27 \cdot \frac{j \cdot k}{y}\right)\\ \end{array} \end{array} \]

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 (* k (* j 27.0)))
        (t_2 (* 18.0 (* t (* x z))))
        (t_3 (* i (* x 4.0)))
        (t_4 (+ (* j (* k 27.0)) (* x (* 4.0 i))))
        (t_5 (* t (* a 4.0)))
        (t_6 (- (- (+ (* b c) (- (* t (* z (* y (* 18.0 x)))) t_5)) t_3) t_1)))
   (if (<= t_6 (- INFINITY))
     (- (+ (* b c) (* t (- (* (* y z) (* 18.0 x)) (* a 4.0)))) t_4)
     (if (<= t_6 5e+300)
       (- (- (+ (* b c) (- (* t (* z (* 18.0 (* y x)))) t_5)) t_3) t_1)
       (if (<= t_6 INFINITY)
         (- (+ (* y (+ (* -4.0 (/ (* a t) y)) t_2)) (* b c)) t_4)
         (* y (+ t_2 (* -27.0 (/ (* j k) y)))))))))

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 = k * (j * 27.0);
	double t_2 = 18.0 * (t * (x * z));
	double t_3 = i * (x * 4.0);
	double t_4 = (j * (k * 27.0)) + (x * (4.0 * i));
	double t_5 = t * (a * 4.0);
	double t_6 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - t_5)) - t_3) - t_1;
	double tmp;
	if (t_6 <= -((double) INFINITY)) {
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - t_4;
	} else if (t_6 <= 5e+300) {
		tmp = (((b * c) + ((t * (z * (18.0 * (y * x)))) - t_5)) - t_3) - t_1;
	} else if (t_6 <= ((double) INFINITY)) {
		tmp = ((y * ((-4.0 * ((a * t) / y)) + t_2)) + (b * c)) - t_4;
	} else {
		tmp = y * (t_2 + (-27.0 * ((j * k) / y)));
	}
	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 = k * (j * 27.0);
	double t_2 = 18.0 * (t * (x * z));
	double t_3 = i * (x * 4.0);
	double t_4 = (j * (k * 27.0)) + (x * (4.0 * i));
	double t_5 = t * (a * 4.0);
	double t_6 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - t_5)) - t_3) - t_1;
	double tmp;
	if (t_6 <= -Double.POSITIVE_INFINITY) {
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - t_4;
	} else if (t_6 <= 5e+300) {
		tmp = (((b * c) + ((t * (z * (18.0 * (y * x)))) - t_5)) - t_3) - t_1;
	} else if (t_6 <= Double.POSITIVE_INFINITY) {
		tmp = ((y * ((-4.0 * ((a * t) / y)) + t_2)) + (b * c)) - t_4;
	} else {
		tmp = y * (t_2 + (-27.0 * ((j * k) / y)));
	}
	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 = k * (j * 27.0)
	t_2 = 18.0 * (t * (x * z))
	t_3 = i * (x * 4.0)
	t_4 = (j * (k * 27.0)) + (x * (4.0 * i))
	t_5 = t * (a * 4.0)
	t_6 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - t_5)) - t_3) - t_1
	tmp = 0
	if t_6 <= -math.inf:
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - t_4
	elif t_6 <= 5e+300:
		tmp = (((b * c) + ((t * (z * (18.0 * (y * x)))) - t_5)) - t_3) - t_1
	elif t_6 <= math.inf:
		tmp = ((y * ((-4.0 * ((a * t) / y)) + t_2)) + (b * c)) - t_4
	else:
		tmp = y * (t_2 + (-27.0 * ((j * k) / y)))
	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(k * Float64(j * 27.0))
	t_2 = Float64(18.0 * Float64(t * Float64(x * z)))
	t_3 = Float64(i * Float64(x * 4.0))
	t_4 = Float64(Float64(j * Float64(k * 27.0)) + Float64(x * Float64(4.0 * i)))
	t_5 = Float64(t * Float64(a * 4.0))
	t_6 = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(18.0 * x)))) - t_5)) - t_3) - t_1)
	tmp = 0.0
	if (t_6 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(y * z) * Float64(18.0 * x)) - Float64(a * 4.0)))) - t_4);
	elseif (t_6 <= 5e+300)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(18.0 * Float64(y * x)))) - t_5)) - t_3) - t_1);
	elseif (t_6 <= Inf)
		tmp = Float64(Float64(Float64(y * Float64(Float64(-4.0 * Float64(Float64(a * t) / y)) + t_2)) + Float64(b * c)) - t_4);
	else
		tmp = Float64(y * Float64(t_2 + Float64(-27.0 * Float64(Float64(j * k) / y))));
	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 = k * (j * 27.0);
	t_2 = 18.0 * (t * (x * z));
	t_3 = i * (x * 4.0);
	t_4 = (j * (k * 27.0)) + (x * (4.0 * i));
	t_5 = t * (a * 4.0);
	t_6 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - t_5)) - t_3) - t_1;
	tmp = 0.0;
	if (t_6 <= -Inf)
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - t_4;
	elseif (t_6 <= 5e+300)
		tmp = (((b * c) + ((t * (z * (18.0 * (y * x)))) - t_5)) - t_3) - t_1;
	elseif (t_6 <= Inf)
		tmp = ((y * ((-4.0 * ((a * t) / y)) + t_2)) + (b * c)) - t_4;
	else
		tmp = y * (t_2 + (-27.0 * ((j * k) / y)));
	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[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$5), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$6, (-Infinity)], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision], If[LessEqual[t$95$6, 5e+300], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(18.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$5), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$6, Infinity], N[(N[(N[(y * N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision], N[(y * N[(t$95$2 + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 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 87.4%

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

   3. Simplified 98.2%

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

   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)) < 5.00000000000000026e300

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 99.1%

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

   if 5.00000000000000026e300 < (-.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 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in y around inf 96.6%

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

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

   1. Initial program 0.0%

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

   3. Simplified 20.0%

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

   5. Taylor expanded in y around inf 50.0%

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

      1. *-commutative 50.0%

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

   7. Simplified 50.0%

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

   8. Taylor expanded in y around inf 55.0%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right) \leq -\infty:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot x\right) - a \cdot 4\right)\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{elif}\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+300}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(18 \cdot \left(y \cdot x\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right) \leq \infty:\\ \;\;\;\;\left(y \cdot \left(-4 \cdot \frac{a \cdot t}{y} + 18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + b \cdot c\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + -27 \cdot \frac{j \cdot k}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+147}:\\ \;\;\;\;\left(y \cdot \left(-4 \cdot \frac{a \cdot t}{y} + 18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + b \cdot c\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -2e+147)
   (-
    (+ (* y (+ (* -4.0 (/ (* a t) y)) (* 18.0 (* t (* x z))))) (* b c))
    (+ (* j (* k 27.0)) (* x (* 4.0 i))))
   (+
    (fma t (fma x (* 18.0 (* y z)) (* -4.0 a)) (fma b c (* x (* -4.0 i))))
    (* 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 (y <= -2e+147) {
		tmp = ((y * ((-4.0 * ((a * t) / y)) + (18.0 * (t * (x * z))))) + (b * c)) - ((j * (k * 27.0)) + (x * (4.0 * i)));
	} else {
		tmp = fma(t, fma(x, (18.0 * (y * z)), (-4.0 * a)), fma(b, c, (x * (-4.0 * i)))) + (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 (y <= -2e+147)
		tmp = Float64(Float64(Float64(y * Float64(Float64(-4.0 * Float64(Float64(a * t) / y)) + Float64(18.0 * Float64(t * Float64(x * z))))) + Float64(b * c)) - Float64(Float64(j * Float64(k * 27.0)) + Float64(x * Float64(4.0 * i))));
	else
		tmp = Float64(fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(-4.0 * a)), fma(b, c, Float64(x * Float64(-4.0 * i)))) + Float64(j * Float64(k * -27.0)));
	end
	return 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[y, -2e+147], N[(N[(N[(y * N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2e147

   1. Initial program 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in y around inf 94.2%

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

   if -2e147 < y

   1. Initial program 88.2%

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

   3. Simplified 90.1%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+147}:\\ \;\;\;\;\left(y \cdot \left(-4 \cdot \frac{a \cdot t}{y} + 18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) + b \cdot c\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.2% accurate, 0.3× speedup

Math

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

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 (* i (* x 4.0)))
        (t_2 (* k (* j 27.0)))
        (t_3 (* t (* a 4.0)))
        (t_4 (- (- (+ (* b c) (- (* t (* z (* y (* 18.0 x)))) t_3)) t_1) t_2)))
   (if (<= t_4 (- INFINITY))
     (-
      (+ (* b c) (* t (- (* (* y z) (* 18.0 x)) (* a 4.0))))
      (+ (* j (* k 27.0)) (* x (* 4.0 i))))
     (if (<= t_4 INFINITY)
       (- (- (+ (* b c) (- (* t (* z (* 18.0 (* y x)))) t_3)) t_1) t_2)
       (* y (+ (* 18.0 (* t (* x z))) (* -27.0 (/ (* j k) y))))))))

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 = i * (x * 4.0);
	double t_2 = k * (j * 27.0);
	double t_3 = t * (a * 4.0);
	double t_4 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - t_3)) - t_1) - t_2;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (4.0 * i)));
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = (((b * c) + ((t * (z * (18.0 * (y * x)))) - t_3)) - t_1) - t_2;
	} else {
		tmp = y * ((18.0 * (t * (x * z))) + (-27.0 * ((j * k) / y)));
	}
	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 = i * (x * 4.0);
	double t_2 = k * (j * 27.0);
	double t_3 = t * (a * 4.0);
	double t_4 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - t_3)) - t_1) - t_2;
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (4.0 * i)));
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = (((b * c) + ((t * (z * (18.0 * (y * x)))) - t_3)) - t_1) - t_2;
	} else {
		tmp = y * ((18.0 * (t * (x * z))) + (-27.0 * ((j * k) / y)));
	}
	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 = i * (x * 4.0)
	t_2 = k * (j * 27.0)
	t_3 = t * (a * 4.0)
	t_4 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - t_3)) - t_1) - t_2
	tmp = 0
	if t_4 <= -math.inf:
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (4.0 * i)))
	elif t_4 <= math.inf:
		tmp = (((b * c) + ((t * (z * (18.0 * (y * x)))) - t_3)) - t_1) - t_2
	else:
		tmp = y * ((18.0 * (t * (x * z))) + (-27.0 * ((j * k) / y)))
	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(i * Float64(x * 4.0))
	t_2 = Float64(k * Float64(j * 27.0))
	t_3 = Float64(t * Float64(a * 4.0))
	t_4 = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(18.0 * x)))) - t_3)) - t_1) - t_2)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(y * z) * Float64(18.0 * x)) - Float64(a * 4.0)))) - Float64(Float64(j * Float64(k * 27.0)) + Float64(x * Float64(4.0 * i))));
	elseif (t_4 <= Inf)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(18.0 * Float64(y * x)))) - t_3)) - t_1) - t_2);
	else
		tmp = Float64(y * Float64(Float64(18.0 * Float64(t * Float64(x * z))) + Float64(-27.0 * Float64(Float64(j * k) / y))));
	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 = i * (x * 4.0);
	t_2 = k * (j * 27.0);
	t_3 = t * (a * 4.0);
	t_4 = (((b * c) + ((t * (z * (y * (18.0 * x)))) - t_3)) - t_1) - t_2;
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (4.0 * i)));
	elseif (t_4 <= Inf)
		tmp = (((b * c) + ((t * (z * (18.0 * (y * x)))) - t_3)) - t_1) - t_2;
	else
		tmp = y * ((18.0 * (t * (x * z))) + (-27.0 * ((j * k) / y)));
	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[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(18.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(y * N[(N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(N[(j * k), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 87.4%

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

   3. Simplified 98.2%

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

   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)) < +inf.0

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 96.7%

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

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

   1. Initial program 0.0%

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

   3. Simplified 20.0%

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

   5. Taylor expanded in y around inf 50.0%

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

      1. *-commutative 50.0%

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

   7. Simplified 50.0%

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

   8. Taylor expanded in y around inf 55.0%

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

4. Final simplification 93.8%

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

Alternative 4: 57.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+136}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{+31}:\\ \;\;\;\;c \cdot \left(b + -27 \cdot \left(j \cdot \frac{k}{c}\right)\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-32}:\\ \;\;\;\;b \cdot c - a \cdot \left(t \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-175}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-256}:\\ \;\;\;\;b \cdot c - i \cdot \left(x \cdot 4\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-302}:\\ \;\;\;\;j \cdot \left(k \cdot -27 + \frac{b \cdot c}{j}\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-145}:\\ \;\;\;\;t\_1 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;t \leq 8000000000000:\\ \;\;\;\;k \cdot \left(j \cdot -27 + \frac{b \cdot c}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -1.8e+136)
     t_2
     (if (<= t -3.05e+31)
       (* c (+ b (* -27.0 (* j (/ k c)))))
       (if (<= t -1.6e-32)
         (- (* b c) (* a (* t 4.0)))
         (if (<= t -1.7e-175)
           (+ (* b c) t_1)
           (if (<= t -2e-256)
             (- (* b c) (* i (* x 4.0)))
             (if (<= t 1.4e-302)
               (* j (+ (* k -27.0) (/ (* b c) j)))
               (if (<= t 1.55e-145)
                 (+ t_1 (* x (* -4.0 i)))
                 (if (<= t 8000000000000.0)
                   (* k (+ (* j -27.0) (/ (* b c) k)))
                   t_2))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.8e+136) {
		tmp = t_2;
	} else if (t <= -3.05e+31) {
		tmp = c * (b + (-27.0 * (j * (k / c))));
	} else if (t <= -1.6e-32) {
		tmp = (b * c) - (a * (t * 4.0));
	} else if (t <= -1.7e-175) {
		tmp = (b * c) + t_1;
	} else if (t <= -2e-256) {
		tmp = (b * c) - (i * (x * 4.0));
	} else if (t <= 1.4e-302) {
		tmp = j * ((k * -27.0) + ((b * c) / j));
	} else if (t <= 1.55e-145) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if (t <= 8000000000000.0) {
		tmp = k * ((j * -27.0) + ((b * c) / k));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-1.8d+136)) then
        tmp = t_2
    else if (t <= (-3.05d+31)) then
        tmp = c * (b + ((-27.0d0) * (j * (k / c))))
    else if (t <= (-1.6d-32)) then
        tmp = (b * c) - (a * (t * 4.0d0))
    else if (t <= (-1.7d-175)) then
        tmp = (b * c) + t_1
    else if (t <= (-2d-256)) then
        tmp = (b * c) - (i * (x * 4.0d0))
    else if (t <= 1.4d-302) then
        tmp = j * ((k * (-27.0d0)) + ((b * c) / j))
    else if (t <= 1.55d-145) then
        tmp = t_1 + (x * ((-4.0d0) * i))
    else if (t <= 8000000000000.0d0) then
        tmp = k * ((j * (-27.0d0)) + ((b * c) / k))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.8e+136) {
		tmp = t_2;
	} else if (t <= -3.05e+31) {
		tmp = c * (b + (-27.0 * (j * (k / c))));
	} else if (t <= -1.6e-32) {
		tmp = (b * c) - (a * (t * 4.0));
	} else if (t <= -1.7e-175) {
		tmp = (b * c) + t_1;
	} else if (t <= -2e-256) {
		tmp = (b * c) - (i * (x * 4.0));
	} else if (t <= 1.4e-302) {
		tmp = j * ((k * -27.0) + ((b * c) / j));
	} else if (t <= 1.55e-145) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if (t <= 8000000000000.0) {
		tmp = k * ((j * -27.0) + ((b * c) / k));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -1.8e+136:
		tmp = t_2
	elif t <= -3.05e+31:
		tmp = c * (b + (-27.0 * (j * (k / c))))
	elif t <= -1.6e-32:
		tmp = (b * c) - (a * (t * 4.0))
	elif t <= -1.7e-175:
		tmp = (b * c) + t_1
	elif t <= -2e-256:
		tmp = (b * c) - (i * (x * 4.0))
	elif t <= 1.4e-302:
		tmp = j * ((k * -27.0) + ((b * c) / j))
	elif t <= 1.55e-145:
		tmp = t_1 + (x * (-4.0 * i))
	elif t <= 8000000000000.0:
		tmp = k * ((j * -27.0) + ((b * c) / k))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -1.8e+136)
		tmp = t_2;
	elseif (t <= -3.05e+31)
		tmp = Float64(c * Float64(b + Float64(-27.0 * Float64(j * Float64(k / c)))));
	elseif (t <= -1.6e-32)
		tmp = Float64(Float64(b * c) - Float64(a * Float64(t * 4.0)));
	elseif (t <= -1.7e-175)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (t <= -2e-256)
		tmp = Float64(Float64(b * c) - Float64(i * Float64(x * 4.0)));
	elseif (t <= 1.4e-302)
		tmp = Float64(j * Float64(Float64(k * -27.0) + Float64(Float64(b * c) / j)));
	elseif (t <= 1.55e-145)
		tmp = Float64(t_1 + Float64(x * Float64(-4.0 * i)));
	elseif (t <= 8000000000000.0)
		tmp = Float64(k * Float64(Float64(j * -27.0) + Float64(Float64(b * c) / k)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -1.8e+136)
		tmp = t_2;
	elseif (t <= -3.05e+31)
		tmp = c * (b + (-27.0 * (j * (k / c))));
	elseif (t <= -1.6e-32)
		tmp = (b * c) - (a * (t * 4.0));
	elseif (t <= -1.7e-175)
		tmp = (b * c) + t_1;
	elseif (t <= -2e-256)
		tmp = (b * c) - (i * (x * 4.0));
	elseif (t <= 1.4e-302)
		tmp = j * ((k * -27.0) + ((b * c) / j));
	elseif (t <= 1.55e-145)
		tmp = t_1 + (x * (-4.0 * i));
	elseif (t <= 8000000000000.0)
		tmp = k * ((j * -27.0) + ((b * c) / k));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e+136], t$95$2, If[LessEqual[t, -3.05e+31], N[(c * N[(b + N[(-27.0 * N[(j * N[(k / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.6e-32], N[(N[(b * c), $MachinePrecision] - N[(a * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-175], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, -2e-256], N[(N[(b * c), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-302], N[(j * N[(N[(k * -27.0), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e-145], N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8000000000000.0], N[(k * N[(N[(j * -27.0), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -1.80000000000000003e136 or 8e12 < t

   1. Initial program 85.4%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in t around inf 71.5%

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

   if -1.80000000000000003e136 < t < -3.05000000000000005e31

   1. Initial program 94.4%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in b around inf 63.6%

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

   6. Taylor expanded in c around inf 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-/l* 73.9%

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

   8. Simplified 73.9%

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

   if -3.05000000000000005e31 < t < -1.6000000000000001e-32

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 92.7%

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

      1. distribute-lft-out 92.7%

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

      2. *-commutative 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in j around 0 77.4%

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

   7. Taylor expanded in a around inf 66.6%

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

      1. *-commutative 66.6%

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

      2. associate-*l* 66.6%

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

   9. Simplified 66.6%

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

   if -1.6000000000000001e-32 < t < -1.7e-175

   1. Initial program 88.3%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in b around inf 55.7%

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

   if -1.7e-175 < t < -1.99999999999999995e-256

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

      2. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in j around 0 98.5%

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

   7. Taylor expanded in a around 0 98.5%

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

      1. *-commutative 98.5%

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

      2. associate-*r* 98.5%

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

   9. Simplified 98.5%

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

   if -1.99999999999999995e-256 < t < 1.4e-302

   1. Initial program 86.4%

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

   3. Simplified 72.7%

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

   5. Taylor expanded in b around inf 85.8%

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

   6. Taylor expanded in j around inf 85.8%

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

   if 1.4e-302 < t < 1.55e-145

   1. Initial program 78.7%

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

   3. Simplified 75.9%

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

   5. Taylor expanded in i around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-*l* 77.8%

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

      4. *-commutative 77.8%

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

   7. Simplified 77.8%

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

   if 1.55e-145 < t < 8e12

   1. Initial program 85.2%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in b around inf 73.2%

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

   6. Taylor expanded in k around inf 73.4%

      \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j + \frac{b \cdot c}{k}\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{+31}:\\ \;\;\;\;c \cdot \left(b + -27 \cdot \left(j \cdot \frac{k}{c}\right)\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-32}:\\ \;\;\;\;b \cdot c - a \cdot \left(t \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-175}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-256}:\\ \;\;\;\;b \cdot c - i \cdot \left(x \cdot 4\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-302}:\\ \;\;\;\;j \cdot \left(k \cdot -27 + \frac{b \cdot c}{j}\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-145}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;t \leq 8000000000000:\\ \;\;\;\;k \cdot \left(j \cdot -27 + \frac{b \cdot c}{k}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := c \cdot \left(b + -27 \cdot \left(j \cdot \frac{k}{c}\right)\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t\_2 + x \cdot \left(-4 \cdot i\right)\\ t_4 := t\_2 + -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-183}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{-294}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-192}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+100}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* c (+ b (* -27.0 (* j (/ k c))))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* x (* -4.0 i))))
        (t_4 (+ t_2 (* -4.0 (* a t)))))
   (if (<= (* b c) -5e+192)
     t_1
     (if (<= (* b c) -2e-183)
       t_4
       (if (<= (* b c) -4e-294)
         t_3
         (if (<= (* b c) 5e-192) t_4 (if (<= (* b c) 2e+100) t_3 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 = c * (b + (-27.0 * (j * (k / c))));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (x * (-4.0 * i));
	double t_4 = t_2 + (-4.0 * (a * t));
	double tmp;
	if ((b * c) <= -5e+192) {
		tmp = t_1;
	} else if ((b * c) <= -2e-183) {
		tmp = t_4;
	} else if ((b * c) <= -4e-294) {
		tmp = t_3;
	} else if ((b * c) <= 5e-192) {
		tmp = t_4;
	} else if ((b * c) <= 2e+100) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = c * (b + ((-27.0d0) * (j * (k / c))))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + (x * ((-4.0d0) * i))
    t_4 = t_2 + ((-4.0d0) * (a * t))
    if ((b * c) <= (-5d+192)) then
        tmp = t_1
    else if ((b * c) <= (-2d-183)) then
        tmp = t_4
    else if ((b * c) <= (-4d-294)) then
        tmp = t_3
    else if ((b * c) <= 5d-192) then
        tmp = t_4
    else if ((b * c) <= 2d+100) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = c * (b + (-27.0 * (j * (k / c))));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (x * (-4.0 * i));
	double t_4 = t_2 + (-4.0 * (a * t));
	double tmp;
	if ((b * c) <= -5e+192) {
		tmp = t_1;
	} else if ((b * c) <= -2e-183) {
		tmp = t_4;
	} else if ((b * c) <= -4e-294) {
		tmp = t_3;
	} else if ((b * c) <= 5e-192) {
		tmp = t_4;
	} else if ((b * c) <= 2e+100) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 = c * (b + (-27.0 * (j * (k / c))))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (x * (-4.0 * i))
	t_4 = t_2 + (-4.0 * (a * t))
	tmp = 0
	if (b * c) <= -5e+192:
		tmp = t_1
	elif (b * c) <= -2e-183:
		tmp = t_4
	elif (b * c) <= -4e-294:
		tmp = t_3
	elif (b * c) <= 5e-192:
		tmp = t_4
	elif (b * c) <= 2e+100:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(c * Float64(b + Float64(-27.0 * Float64(j * Float64(k / c)))))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(x * Float64(-4.0 * i)))
	t_4 = Float64(t_2 + Float64(-4.0 * Float64(a * t)))
	tmp = 0.0
	if (Float64(b * c) <= -5e+192)
		tmp = t_1;
	elseif (Float64(b * c) <= -2e-183)
		tmp = t_4;
	elseif (Float64(b * c) <= -4e-294)
		tmp = t_3;
	elseif (Float64(b * c) <= 5e-192)
		tmp = t_4;
	elseif (Float64(b * c) <= 2e+100)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 = c * (b + (-27.0 * (j * (k / c))));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (x * (-4.0 * i));
	t_4 = t_2 + (-4.0 * (a * t));
	tmp = 0.0;
	if ((b * c) <= -5e+192)
		tmp = t_1;
	elseif ((b * c) <= -2e-183)
		tmp = t_4;
	elseif ((b * c) <= -4e-294)
		tmp = t_3;
	elseif ((b * c) <= 5e-192)
		tmp = t_4;
	elseif ((b * c) <= 2e+100)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(c * N[(b + N[(-27.0 * N[(j * N[(k / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+192], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -2e-183], t$95$4, If[LessEqual[N[(b * c), $MachinePrecision], -4e-294], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 5e-192], t$95$4, If[LessEqual[N[(b * c), $MachinePrecision], 2e+100], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5.00000000000000033e192 or 2.00000000000000003e100 < (*.f64 b c)

   1. Initial program 85.3%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in b around inf 77.7%

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

   6. Taylor expanded in c around inf 79.1%

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

      1. *-commutative 79.1%

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

      2. associate-/l* 80.5%

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

   8. Simplified 80.5%

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

   if -5.00000000000000033e192 < (*.f64 b c) < -2.00000000000000001e-183 or -4.00000000000000007e-294 < (*.f64 b c) < 5.0000000000000001e-192

   1. Initial program 87.8%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in a around inf 57.4%

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

   if -2.00000000000000001e-183 < (*.f64 b c) < -4.00000000000000007e-294 or 5.0000000000000001e-192 < (*.f64 b c) < 2.00000000000000003e100

   1. Initial program 88.3%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in i around inf 56.2%

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

      1. *-commutative 56.2%

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

      2. *-commutative 56.2%

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

      3. associate-*l* 56.2%

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

      4. *-commutative 56.2%

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

   7. Simplified 56.2%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+192}:\\ \;\;\;\;c \cdot \left(b + -27 \cdot \left(j \cdot \frac{k}{c}\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-183}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{-294}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-192}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+100}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b + -27 \cdot \left(j \cdot \frac{k}{c}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t\_2 + 18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{+277}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -4.4 \cdot 10^{+247}:\\ \;\;\;\;c \cdot \left(b + -27 \cdot \left(j \cdot \frac{k}{c}\right)\right)\\ \mathbf{elif}\;j \leq -2.05 \cdot 10^{+247}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \left(i \cdot \frac{x}{c}\right)\right)\\ \mathbf{elif}\;j \leq -3.1 \cdot 10^{+203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{+146}:\\ \;\;\;\;t\_2 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (+ (* a t) (* x i)))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* 18.0 (* x (* y (* t z)))))))
   (if (<= j -2.4e+277)
     t_3
     (if (<= j -4.4e+247)
       (* c (+ b (* -27.0 (* j (/ k c)))))
       (if (<= j -2.05e+247)
         (* c (+ b (* -4.0 (* i (/ x c)))))
         (if (<= j -3.1e+203)
           t_1
           (if (<= j -4.1e+146)
             (+ t_2 (* x (* -4.0 i)))
             (if (<= j 5.5e-67) t_1 t_3))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * ((a * t) + (x * i)));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (18.0 * (x * (y * (t * z))));
	double tmp;
	if (j <= -2.4e+277) {
		tmp = t_3;
	} else if (j <= -4.4e+247) {
		tmp = c * (b + (-27.0 * (j * (k / c))));
	} else if (j <= -2.05e+247) {
		tmp = c * (b + (-4.0 * (i * (x / c))));
	} else if (j <= -3.1e+203) {
		tmp = t_1;
	} else if (j <= -4.1e+146) {
		tmp = t_2 + (x * (-4.0 * i));
	} else if (j <= 5.5e-67) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * ((a * t) + (x * i)))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + (18.0d0 * (x * (y * (t * z))))
    if (j <= (-2.4d+277)) then
        tmp = t_3
    else if (j <= (-4.4d+247)) then
        tmp = c * (b + ((-27.0d0) * (j * (k / c))))
    else if (j <= (-2.05d+247)) then
        tmp = c * (b + ((-4.0d0) * (i * (x / c))))
    else if (j <= (-3.1d+203)) then
        tmp = t_1
    else if (j <= (-4.1d+146)) then
        tmp = t_2 + (x * ((-4.0d0) * i))
    else if (j <= 5.5d-67) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * ((a * t) + (x * i)));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (18.0 * (x * (y * (t * z))));
	double tmp;
	if (j <= -2.4e+277) {
		tmp = t_3;
	} else if (j <= -4.4e+247) {
		tmp = c * (b + (-27.0 * (j * (k / c))));
	} else if (j <= -2.05e+247) {
		tmp = c * (b + (-4.0 * (i * (x / c))));
	} else if (j <= -3.1e+203) {
		tmp = t_1;
	} else if (j <= -4.1e+146) {
		tmp = t_2 + (x * (-4.0 * i));
	} else if (j <= 5.5e-67) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * ((a * t) + (x * i)))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (18.0 * (x * (y * (t * z))))
	tmp = 0
	if j <= -2.4e+277:
		tmp = t_3
	elif j <= -4.4e+247:
		tmp = c * (b + (-27.0 * (j * (k / c))))
	elif j <= -2.05e+247:
		tmp = c * (b + (-4.0 * (i * (x / c))))
	elif j <= -3.1e+203:
		tmp = t_1
	elif j <= -4.1e+146:
		tmp = t_2 + (x * (-4.0 * i))
	elif j <= 5.5e-67:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(a * t) + Float64(x * i))))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(18.0 * Float64(x * Float64(y * Float64(t * z)))))
	tmp = 0.0
	if (j <= -2.4e+277)
		tmp = t_3;
	elseif (j <= -4.4e+247)
		tmp = Float64(c * Float64(b + Float64(-27.0 * Float64(j * Float64(k / c)))));
	elseif (j <= -2.05e+247)
		tmp = Float64(c * Float64(b + Float64(-4.0 * Float64(i * Float64(x / c)))));
	elseif (j <= -3.1e+203)
		tmp = t_1;
	elseif (j <= -4.1e+146)
		tmp = Float64(t_2 + Float64(x * Float64(-4.0 * i)));
	elseif (j <= 5.5e-67)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * ((a * t) + (x * i)));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (18.0 * (x * (y * (t * z))));
	tmp = 0.0;
	if (j <= -2.4e+277)
		tmp = t_3;
	elseif (j <= -4.4e+247)
		tmp = c * (b + (-27.0 * (j * (k / c))));
	elseif (j <= -2.05e+247)
		tmp = c * (b + (-4.0 * (i * (x / c))));
	elseif (j <= -3.1e+203)
		tmp = t_1;
	elseif (j <= -4.1e+146)
		tmp = t_2 + (x * (-4.0 * i));
	elseif (j <= 5.5e-67)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(18.0 * N[(x * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.4e+277], t$95$3, If[LessEqual[j, -4.4e+247], N[(c * N[(b + N[(-27.0 * N[(j * N[(k / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.05e+247], N[(c * N[(b + N[(-4.0 * N[(i * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.1e+203], t$95$1, If[LessEqual[j, -4.1e+146], N[(t$95$2 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.5e-67], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.39999999999999993e277 or 5.5000000000000003e-67 < j

   1. Initial program 82.0%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in y around inf 55.6%

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

      1. *-commutative 55.6%

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

   7. Simplified 55.6%

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

   8. Taylor expanded in x around 0 55.6%

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

      1. *-commutative 55.6%

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

      2. associate-*r* 55.9%

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

      3. associate-*l* 55.8%

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

   10. Simplified 55.8%

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

   if -2.39999999999999993e277 < j < -4.40000000000000022e247

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around inf 87.5%

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

   6. Taylor expanded in c around inf 87.7%

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

      1. *-commutative 87.7%

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

      2. associate-/l* 87.7%

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

   8. Simplified 87.7%

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

   if -4.40000000000000022e247 < j < -2.0500000000000001e247

   1. Initial program 87.2%

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

   3. Taylor expanded in y around 0 78.3%

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

      1. distribute-lft-out 78.3%

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

      2. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in j around 0 57.9%

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

   7. Taylor expanded in a around 0 40.5%

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

      1. *-commutative 40.5%

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

      2. associate-*r* 40.5%

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

   9. Simplified 40.5%

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

   10. Taylor expanded in c around inf 38.4%

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

       1. associate-/l* 38.6%

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

   12. Simplified 38.6%

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

   if -2.0500000000000001e247 < j < -3.1e203 or -4.1000000000000004e146 < j < 5.5000000000000003e-67

   1. Initial program 90.9%

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

   3. Taylor expanded in y around 0 79.8%

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

      1. distribute-lft-out 79.8%

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

      2. *-commutative 79.8%

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

   5. Simplified 79.8%

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

   6. Taylor expanded in j around 0 69.7%

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

   if -3.1e203 < j < -4.1000000000000004e146

   1. Initial program 69.0%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in i around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*l* 76.9%

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

      4. *-commutative 76.9%

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

   7. Simplified 76.9%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{+277}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -4.4 \cdot 10^{+247}:\\ \;\;\;\;c \cdot \left(b + -27 \cdot \left(j \cdot \frac{k}{c}\right)\right)\\ \mathbf{elif}\;j \leq -2.05 \cdot 10^{+247}:\\ \;\;\;\;c \cdot \left(b + -4 \cdot \left(i \cdot \frac{x}{c}\right)\right)\\ \mathbf{elif}\;j \leq -3.1 \cdot 10^{+203}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{+146}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-67}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+276}:\\ \;\;\;\;j \cdot \left(b \cdot \frac{c}{j} - k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot x\right) - a \cdot 4\right)\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(4 \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* k (* j 27.0)) -1e+276)
   (* j (- (* b (/ c j)) (* k 27.0)))
   (-
    (+ (* b c) (* t (- (* (* y z) (* 18.0 x)) (* a 4.0))))
    (+ (* j (* k 27.0)) (* x (* 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 ((k * (j * 27.0)) <= -1e+276) {
		tmp = j * ((b * (c / j)) - (k * 27.0));
	} else {
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (4.0 * i)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((k * (j * 27.0d0)) <= (-1d+276)) then
        tmp = j * ((b * (c / j)) - (k * 27.0d0))
    else
        tmp = ((b * c) + (t * (((y * z) * (18.0d0 * x)) - (a * 4.0d0)))) - ((j * (k * 27.0d0)) + (x * (4.0d0 * i)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k * (j * 27.0)) <= -1e+276) {
		tmp = j * ((b * (c / j)) - (k * 27.0));
	} else {
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (4.0 * i)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (k * (j * 27.0)) <= -1e+276:
		tmp = j * ((b * (c / j)) - (k * 27.0))
	else:
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (4.0 * i)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * Float64(j * 27.0)) <= -1e+276)
		tmp = Float64(j * Float64(Float64(b * Float64(c / j)) - Float64(k * 27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(y * z) * Float64(18.0 * x)) - Float64(a * 4.0)))) - Float64(Float64(j * Float64(k * 27.0)) + Float64(x * 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 ((k * (j * 27.0)) <= -1e+276)
		tmp = j * ((b * (c / j)) - (k * 27.0));
	else
		tmp = ((b * c) + (t * (((y * z) * (18.0 * x)) - (a * 4.0)))) - ((j * (k * 27.0)) + (x * (4.0 * i)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision], -1e+276], N[(j * N[(N[(b * N[(c / j), $MachinePrecision]), $MachinePrecision] - N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.0000000000000001e276

   1. Initial program 69.4%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in b around inf 82.5%

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

   6. Taylor expanded in j around -inf 86.9%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(-1 \cdot \frac{b \cdot c}{j} + 27 \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 86.9%

         \[\leadsto \color{blue}{-j \cdot \left(-1 \cdot \frac{b \cdot c}{j} + 27 \cdot k\right)} \]

      2. *-commutative 86.9%

         \[\leadsto -\color{blue}{\left(-1 \cdot \frac{b \cdot c}{j} + 27 \cdot k\right) \cdot j} \]

      3. distribute-rgt-neg-in 86.9%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{b \cdot c}{j} + 27 \cdot k\right) \cdot \left(-j\right)} \]

      4. +-commutative 86.9%

         \[\leadsto \color{blue}{\left(27 \cdot k + -1 \cdot \frac{b \cdot c}{j}\right)} \cdot \left(-j\right) \]

      5. mul-1-neg 86.9%

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

      6. unsub-neg 86.9%

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

      7. associate-/l* 95.6%

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

   8. Simplified 95.6%

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

   if -1.0000000000000001e276 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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 90.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+276}:\\ \;\;\;\;j \cdot \left(b \cdot \frac{c}{j} - k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot x\right) - a \cdot 4\right)\right) - \left(j \cdot \left(k \cdot 27\right) + x \cdot \left(4 \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.8 \cdot 10^{+184}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -6 \cdot 10^{+14} \lor \neg \left(b \cdot c \leq -1.2 \cdot 10^{-103}\right) \land b \cdot c \leq 1.85 \cdot 10^{-187}:\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1.8e+184)
   (* b c)
   (if (or (<= (* b c) -6e+14)
           (and (not (<= (* b c) -1.2e-103)) (<= (* b c) 1.85e-187)))
     (* -4.0 (+ (* a t) (* x i)))
     (+ (* b c) (* j (* k -27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.8e+184) {
		tmp = b * c;
	} else if (((b * c) <= -6e+14) || (!((b * c) <= -1.2e-103) && ((b * c) <= 1.85e-187))) {
		tmp = -4.0 * ((a * t) + (x * i));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-1.8d+184)) then
        tmp = b * c
    else if (((b * c) <= (-6d+14)) .or. (.not. ((b * c) <= (-1.2d-103))) .and. ((b * c) <= 1.85d-187)) then
        tmp = (-4.0d0) * ((a * t) + (x * i))
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.8e+184) {
		tmp = b * c;
	} else if (((b * c) <= -6e+14) || (!((b * c) <= -1.2e-103) && ((b * c) <= 1.85e-187))) {
		tmp = -4.0 * ((a * t) + (x * i));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.8e+184:
		tmp = b * c
	elif ((b * c) <= -6e+14) or (not ((b * c) <= -1.2e-103) and ((b * c) <= 1.85e-187)):
		tmp = -4.0 * ((a * t) + (x * i))
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1.8e+184)
		tmp = Float64(b * c);
	elseif ((Float64(b * c) <= -6e+14) || (!(Float64(b * c) <= -1.2e-103) && (Float64(b * c) <= 1.85e-187)))
		tmp = Float64(-4.0 * Float64(Float64(a * t) + Float64(x * i)));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1.8e+184)
		tmp = b * c;
	elseif (((b * c) <= -6e+14) || (~(((b * c) <= -1.2e-103)) && ((b * c) <= 1.85e-187)))
		tmp = -4.0 * ((a * t) + (x * i));
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1.8e+184], N[(b * c), $MachinePrecision], If[Or[LessEqual[N[(b * c), $MachinePrecision], -6e+14], And[N[Not[LessEqual[N[(b * c), $MachinePrecision], -1.2e-103]], $MachinePrecision], LessEqual[N[(b * c), $MachinePrecision], 1.85e-187]]], N[(-4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.80000000000000007e184

   1. Initial program 81.3%

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

   3. Taylor expanded in x around 0 81.3%

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

   4. Taylor expanded in b around inf 75.2%

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

   if -1.80000000000000007e184 < (*.f64 b c) < -6e14 or -1.2000000000000001e-103 < (*.f64 b c) < 1.85000000000000005e-187

   1. Initial program 86.5%

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

   3. Taylor expanded in y around 0 73.7%

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

      1. distribute-lft-out 73.7%

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

      2. *-commutative 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in j around 0 51.9%

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

   7. Taylor expanded in b around 0 50.3%

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

   if -6e14 < (*.f64 b c) < -1.2000000000000001e-103 or 1.85000000000000005e-187 < (*.f64 b c)

   1. Initial program 89.5%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in b around inf 61.1%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.8 \cdot 10^{+184}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -6 \cdot 10^{+14} \lor \neg \left(b \cdot c \leq -1.2 \cdot 10^{-103}\right) \land b \cdot c \leq 1.85 \cdot 10^{-187}:\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a + t\_1\right)\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+122}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-25}:\\ \;\;\;\;\left(b \cdot c - \left(a \cdot t\right) \cdot 4\right) - t\_2\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-155}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 22500000:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 18.0 (* x (* y z))))
        (t_2 (* k (* j 27.0)))
        (t_3 (+ (* j (* k -27.0)) (* t (+ (* -4.0 a) t_1)))))
   (if (<= t -3.9e+122)
     t_3
     (if (<= t -6.2e-25)
       (- (- (* b c) (* (* a t) 4.0)) t_2)
       (if (<= t -9.8e-155)
         t_3
         (if (<= t 22500000.0)
           (- (- (* b c) (* 4.0 (* x i))) t_2)
           (+ (* b c) (* t (- t_1 (* 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 t_1 = 18.0 * (x * (y * z));
	double t_2 = k * (j * 27.0);
	double t_3 = (j * (k * -27.0)) + (t * ((-4.0 * a) + t_1));
	double tmp;
	if (t <= -3.9e+122) {
		tmp = t_3;
	} else if (t <= -6.2e-25) {
		tmp = ((b * c) - ((a * t) * 4.0)) - t_2;
	} else if (t <= -9.8e-155) {
		tmp = t_3;
	} else if (t <= 22500000.0) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_2;
	} else {
		tmp = (b * c) + (t * (t_1 - (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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    t_2 = k * (j * 27.0d0)
    t_3 = (j * (k * (-27.0d0))) + (t * (((-4.0d0) * a) + t_1))
    if (t <= (-3.9d+122)) then
        tmp = t_3
    else if (t <= (-6.2d-25)) then
        tmp = ((b * c) - ((a * t) * 4.0d0)) - t_2
    else if (t <= (-9.8d-155)) then
        tmp = t_3
    else if (t <= 22500000.0d0) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_2
    else
        tmp = (b * c) + (t * (t_1 - (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 t_1 = 18.0 * (x * (y * z));
	double t_2 = k * (j * 27.0);
	double t_3 = (j * (k * -27.0)) + (t * ((-4.0 * a) + t_1));
	double tmp;
	if (t <= -3.9e+122) {
		tmp = t_3;
	} else if (t <= -6.2e-25) {
		tmp = ((b * c) - ((a * t) * 4.0)) - t_2;
	} else if (t <= -9.8e-155) {
		tmp = t_3;
	} else if (t <= 22500000.0) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_2;
	} else {
		tmp = (b * c) + (t * (t_1 - (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):
	t_1 = 18.0 * (x * (y * z))
	t_2 = k * (j * 27.0)
	t_3 = (j * (k * -27.0)) + (t * ((-4.0 * a) + t_1))
	tmp = 0
	if t <= -3.9e+122:
		tmp = t_3
	elif t <= -6.2e-25:
		tmp = ((b * c) - ((a * t) * 4.0)) - t_2
	elif t <= -9.8e-155:
		tmp = t_3
	elif t <= 22500000.0:
		tmp = ((b * c) - (4.0 * (x * i))) - t_2
	else:
		tmp = (b * c) + (t * (t_1 - (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)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	t_2 = Float64(k * Float64(j * 27.0))
	t_3 = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(-4.0 * a) + t_1)))
	tmp = 0.0
	if (t <= -3.9e+122)
		tmp = t_3;
	elseif (t <= -6.2e-25)
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(a * t) * 4.0)) - t_2);
	elseif (t <= -9.8e-155)
		tmp = t_3;
	elseif (t <= 22500000.0)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_2);
	else
		tmp = Float64(Float64(b * c) + Float64(t * Float64(t_1 - 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)
	t_1 = 18.0 * (x * (y * z));
	t_2 = k * (j * 27.0);
	t_3 = (j * (k * -27.0)) + (t * ((-4.0 * a) + t_1));
	tmp = 0.0;
	if (t <= -3.9e+122)
		tmp = t_3;
	elseif (t <= -6.2e-25)
		tmp = ((b * c) - ((a * t) * 4.0)) - t_2;
	elseif (t <= -9.8e-155)
		tmp = t_3;
	elseif (t <= 22500000.0)
		tmp = ((b * c) - (4.0 * (x * i))) - t_2;
	else
		tmp = (b * c) + (t * (t_1 - (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_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(-4.0 * a), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+122], t$95$3, If[LessEqual[t, -6.2e-25], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t, -9.8e-155], t$95$3, If[LessEqual[t, 22500000.0], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.8999999999999999e122 or -6.19999999999999989e-25 < t < -9.80000000000000026e-155

   1. Initial program 85.2%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in t around inf 79.6%

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

   if -3.8999999999999999e122 < t < -6.19999999999999989e-25

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0 75.9%

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

   if -9.80000000000000026e-155 < t < 2.25e7

   1. Initial program 84.8%

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

   3. Taylor expanded in t around 0 91.8%

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

   if 2.25e7 < t

   1. Initial program 89.7%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in j around 0 87.9%

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

   6. Taylor expanded in i around 0 81.6%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+122}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-25}:\\ \;\;\;\;\left(b \cdot c - \left(a \cdot t\right) \cdot 4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-155}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 22500000:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+136}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-42}:\\ \;\;\;\;\left(b \cdot c - \left(a \cdot t\right) \cdot 4\right) - t\_1\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-92}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 31000000:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* k (* j 27.0)))
        (t_2 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))))
   (if (<= t -1.8e+136)
     t_2
     (if (<= t -4.5e-42)
       (- (- (* b c) (* (* a t) 4.0)) t_1)
       (if (<= t -7.2e-92)
         (+ (* j (* k -27.0)) (* 18.0 (* x (* y (* t z)))))
         (if (<= t 31000000.0) (- (- (* b c) (* 4.0 (* x i))) t_1) t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -1.8e+136) {
		tmp = t_2;
	} else if (t <= -4.5e-42) {
		tmp = ((b * c) - ((a * t) * 4.0)) - t_1;
	} else if (t <= -7.2e-92) {
		tmp = (j * (k * -27.0)) + (18.0 * (x * (y * (t * z))));
	} else if (t <= 31000000.0) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    t_2 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    if (t <= (-1.8d+136)) then
        tmp = t_2
    else if (t <= (-4.5d-42)) then
        tmp = ((b * c) - ((a * t) * 4.0d0)) - t_1
    else if (t <= (-7.2d-92)) then
        tmp = (j * (k * (-27.0d0))) + (18.0d0 * (x * (y * (t * z))))
    else if (t <= 31000000.0d0) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -1.8e+136) {
		tmp = t_2;
	} else if (t <= -4.5e-42) {
		tmp = ((b * c) - ((a * t) * 4.0)) - t_1;
	} else if (t <= -7.2e-92) {
		tmp = (j * (k * -27.0)) + (18.0 * (x * (y * (t * z))));
	} else if (t <= 31000000.0) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	tmp = 0
	if t <= -1.8e+136:
		tmp = t_2
	elif t <= -4.5e-42:
		tmp = ((b * c) - ((a * t) * 4.0)) - t_1
	elif t <= -7.2e-92:
		tmp = (j * (k * -27.0)) + (18.0 * (x * (y * (t * z))))
	elif t <= 31000000.0:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	t_2 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))))
	tmp = 0.0
	if (t <= -1.8e+136)
		tmp = t_2;
	elseif (t <= -4.5e-42)
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(a * t) * 4.0)) - t_1);
	elseif (t <= -7.2e-92)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(18.0 * Float64(x * Float64(y * Float64(t * z)))));
	elseif (t <= 31000000.0)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	t_2 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	tmp = 0.0;
	if (t <= -1.8e+136)
		tmp = t_2;
	elseif (t <= -4.5e-42)
		tmp = ((b * c) - ((a * t) * 4.0)) - t_1;
	elseif (t <= -7.2e-92)
		tmp = (j * (k * -27.0)) + (18.0 * (x * (y * (t * z))));
	elseif (t <= 31000000.0)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e+136], t$95$2, If[LessEqual[t, -4.5e-42], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, -7.2e-92], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(x * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 31000000.0], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.80000000000000003e136 or 3.1e7 < t

   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 89.5%

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

   5. Taylor expanded in j around 0 84.8%

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

   6. Taylor expanded in i around 0 82.2%

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

   if -1.80000000000000003e136 < t < -4.5e-42

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0 78.9%

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

   if -4.5e-42 < t < -7.20000000000000032e-92

   1. Initial program 92.0%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in y around inf 51.8%

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

      1. *-commutative 51.8%

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

   7. Simplified 51.8%

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

   8. Taylor expanded in x around 0 51.8%

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

      1. *-commutative 51.8%

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

      2. associate-*r* 59.4%

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

      3. associate-*l* 59.4%

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

   10. Simplified 59.4%

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

   if -7.20000000000000032e-92 < t < 3.1e7

   1. Initial program 84.9%

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

   3. Taylor expanded in t around 0 87.3%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+136}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-42}:\\ \;\;\;\;\left(b \cdot c - \left(a \cdot t\right) \cdot 4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-92}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 31000000:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -1.05 \cdot 10^{+189}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -10500000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -4.3 \cdot 10^{-107}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 4.7 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (+ (* a t) (* x i)))))
   (if (<= (* b c) -1.05e+189)
     (* b c)
     (if (<= (* b c) -10500000000.0)
       t_1
       (if (<= (* b c) -4.3e-107)
         (* -27.0 (* j k))
         (if (<= (* b c) 4.7e+100) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * ((a * t) + (x * i));
	double tmp;
	if ((b * c) <= -1.05e+189) {
		tmp = b * c;
	} else if ((b * c) <= -10500000000.0) {
		tmp = t_1;
	} else if ((b * c) <= -4.3e-107) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 4.7e+100) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * ((a * t) + (x * i))
    if ((b * c) <= (-1.05d+189)) then
        tmp = b * c
    else if ((b * c) <= (-10500000000.0d0)) then
        tmp = t_1
    else if ((b * c) <= (-4.3d-107)) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 4.7d+100) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * ((a * t) + (x * i));
	double tmp;
	if ((b * c) <= -1.05e+189) {
		tmp = b * c;
	} else if ((b * c) <= -10500000000.0) {
		tmp = t_1;
	} else if ((b * c) <= -4.3e-107) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 4.7e+100) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * ((a * t) + (x * i))
	tmp = 0
	if (b * c) <= -1.05e+189:
		tmp = b * c
	elif (b * c) <= -10500000000.0:
		tmp = t_1
	elif (b * c) <= -4.3e-107:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 4.7e+100:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(Float64(a * t) + Float64(x * i)))
	tmp = 0.0
	if (Float64(b * c) <= -1.05e+189)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -10500000000.0)
		tmp = t_1;
	elseif (Float64(b * c) <= -4.3e-107)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 4.7e+100)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * ((a * t) + (x * i));
	tmp = 0.0;
	if ((b * c) <= -1.05e+189)
		tmp = b * c;
	elseif ((b * c) <= -10500000000.0)
		tmp = t_1;
	elseif ((b * c) <= -4.3e-107)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 4.7e+100)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.05e+189], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -10500000000.0], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -4.3e-107], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.7e+100], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.04999999999999996e189 or 4.7e100 < (*.f64 b c)

   1. Initial program 85.3%

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

   3. Taylor expanded in x around 0 85.3%

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

   4. Taylor expanded in b around inf 69.9%

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

   if -1.04999999999999996e189 < (*.f64 b c) < -1.05e10 or -4.2999999999999997e-107 < (*.f64 b c) < 4.7e100

   1. Initial program 87.7%

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

   3. Taylor expanded in y around 0 74.7%

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

      1. distribute-lft-out 74.7%

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

      2. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in j around 0 51.2%

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

   7. Taylor expanded in b around 0 46.3%

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

   if -1.05e10 < (*.f64 b c) < -4.2999999999999997e-107

   1. Initial program 89.9%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in j around inf 56.5%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.05 \cdot 10^{+189}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -10500000000:\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -4.3 \cdot 10^{-107}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 4.7 \cdot 10^{+100}:\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ t_2 := b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{if}\;k \leq -2.8 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 1.26 \cdot 10^{-164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 1.2 \cdot 10^{-136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 4 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(a \cdot t\right) \cdot 4\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k -27.0)) (* 18.0 (* t (* x (* y z))))))
        (t_2 (- (* b c) (* 4.0 (+ (* a t) (* x i))))))
   (if (<= k -2.8e-47)
     t_1
     (if (<= k 1.26e-164)
       t_2
       (if (<= k 1.2e-136)
         t_1
         (if (<= k 4e+27)
           t_2
           (- (- (* b c) (* (* a t) 4.0)) (* k (* j 27.0)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (18.0 * (t * (x * (y * z))));
	double t_2 = (b * c) - (4.0 * ((a * t) + (x * i)));
	double tmp;
	if (k <= -2.8e-47) {
		tmp = t_1;
	} else if (k <= 1.26e-164) {
		tmp = t_2;
	} else if (k <= 1.2e-136) {
		tmp = t_1;
	} else if (k <= 4e+27) {
		tmp = t_2;
	} else {
		tmp = ((b * c) - ((a * t) * 4.0)) - (k * (j * 27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + (18.0d0 * (t * (x * (y * z))))
    t_2 = (b * c) - (4.0d0 * ((a * t) + (x * i)))
    if (k <= (-2.8d-47)) then
        tmp = t_1
    else if (k <= 1.26d-164) then
        tmp = t_2
    else if (k <= 1.2d-136) then
        tmp = t_1
    else if (k <= 4d+27) then
        tmp = t_2
    else
        tmp = ((b * c) - ((a * t) * 4.0d0)) - (k * (j * 27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (18.0 * (t * (x * (y * z))));
	double t_2 = (b * c) - (4.0 * ((a * t) + (x * i)));
	double tmp;
	if (k <= -2.8e-47) {
		tmp = t_1;
	} else if (k <= 1.26e-164) {
		tmp = t_2;
	} else if (k <= 1.2e-136) {
		tmp = t_1;
	} else if (k <= 4e+27) {
		tmp = t_2;
	} else {
		tmp = ((b * c) - ((a * t) * 4.0)) - (k * (j * 27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + (18.0 * (t * (x * (y * z))))
	t_2 = (b * c) - (4.0 * ((a * t) + (x * i)))
	tmp = 0
	if k <= -2.8e-47:
		tmp = t_1
	elif k <= 1.26e-164:
		tmp = t_2
	elif k <= 1.2e-136:
		tmp = t_1
	elif k <= 4e+27:
		tmp = t_2
	else:
		tmp = ((b * c) - ((a * t) * 4.0)) - (k * (j * 27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))))
	t_2 = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(a * t) + Float64(x * i))))
	tmp = 0.0
	if (k <= -2.8e-47)
		tmp = t_1;
	elseif (k <= 1.26e-164)
		tmp = t_2;
	elseif (k <= 1.2e-136)
		tmp = t_1;
	elseif (k <= 4e+27)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(a * t) * 4.0)) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (18.0 * (t * (x * (y * z))));
	t_2 = (b * c) - (4.0 * ((a * t) + (x * i)));
	tmp = 0.0;
	if (k <= -2.8e-47)
		tmp = t_1;
	elseif (k <= 1.26e-164)
		tmp = t_2;
	elseif (k <= 1.2e-136)
		tmp = t_1;
	elseif (k <= 4e+27)
		tmp = t_2;
	else
		tmp = ((b * c) - ((a * t) * 4.0)) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.8e-47], t$95$1, If[LessEqual[k, 1.26e-164], t$95$2, If[LessEqual[k, 1.2e-136], t$95$1, If[LessEqual[k, 4e+27], t$95$2, N[(N[(N[(b * c), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if k < -2.79999999999999993e-47 or 1.26e-164 < k < 1.1999999999999999e-136

   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 85.2%

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

   5. Taylor expanded in y around inf 55.8%

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

      1. *-commutative 55.8%

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

   7. Simplified 55.8%

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

   if -2.79999999999999993e-47 < k < 1.26e-164 or 1.1999999999999999e-136 < k < 4.0000000000000001e27

   1. Initial program 91.1%

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

   3. Taylor expanded in y around 0 81.6%

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

      1. distribute-lft-out 81.6%

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

      2. *-commutative 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in j around 0 77.0%

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

   if 4.0000000000000001e27 < k

   1. Initial program 84.7%

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

   3. Taylor expanded in x around 0 72.4%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.8 \cdot 10^{-47}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.26 \cdot 10^{-164}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{elif}\;k \leq 1.2 \cdot 10^{-136}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{+27}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(a \cdot t\right) \cdot 4\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -6.5 \cdot 10^{+249}:\\ \;\;\;\;t\_1 + 18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{+202}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot \left(x + \frac{a \cdot t}{i}\right)\right)\\ \mathbf{elif}\;j \leq -1.46 \cdot 10^{+144}:\\ \;\;\;\;t\_1 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-68}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + 18 \cdot \left(t \cdot \left(z \cdot \left(y \cdot x\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= j -6.5e+249)
     (+ t_1 (* 18.0 (* x (* y (* t z)))))
     (if (<= j -5.2e+202)
       (- (* b c) (* 4.0 (* i (+ x (/ (* a t) i)))))
       (if (<= j -1.46e+144)
         (+ t_1 (* x (* -4.0 i)))
         (if (<= j 5e-68)
           (- (* b c) (* 4.0 (+ (* a t) (* x i))))
           (+ t_1 (* 18.0 (* t (* z (* y x)))))))))))

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 (j <= -6.5e+249) {
		tmp = t_1 + (18.0 * (x * (y * (t * z))));
	} else if (j <= -5.2e+202) {
		tmp = (b * c) - (4.0 * (i * (x + ((a * t) / i))));
	} else if (j <= -1.46e+144) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if (j <= 5e-68) {
		tmp = (b * c) - (4.0 * ((a * t) + (x * i)));
	} else {
		tmp = t_1 + (18.0 * (t * (z * (y * x))));
	}
	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 (j <= (-6.5d+249)) then
        tmp = t_1 + (18.0d0 * (x * (y * (t * z))))
    else if (j <= (-5.2d+202)) then
        tmp = (b * c) - (4.0d0 * (i * (x + ((a * t) / i))))
    else if (j <= (-1.46d+144)) then
        tmp = t_1 + (x * ((-4.0d0) * i))
    else if (j <= 5d-68) then
        tmp = (b * c) - (4.0d0 * ((a * t) + (x * i)))
    else
        tmp = t_1 + (18.0d0 * (t * (z * (y * x))))
    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 (j <= -6.5e+249) {
		tmp = t_1 + (18.0 * (x * (y * (t * z))));
	} else if (j <= -5.2e+202) {
		tmp = (b * c) - (4.0 * (i * (x + ((a * t) / i))));
	} else if (j <= -1.46e+144) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if (j <= 5e-68) {
		tmp = (b * c) - (4.0 * ((a * t) + (x * i)));
	} else {
		tmp = t_1 + (18.0 * (t * (z * (y * x))));
	}
	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 j <= -6.5e+249:
		tmp = t_1 + (18.0 * (x * (y * (t * z))))
	elif j <= -5.2e+202:
		tmp = (b * c) - (4.0 * (i * (x + ((a * t) / i))))
	elif j <= -1.46e+144:
		tmp = t_1 + (x * (-4.0 * i))
	elif j <= 5e-68:
		tmp = (b * c) - (4.0 * ((a * t) + (x * i)))
	else:
		tmp = t_1 + (18.0 * (t * (z * (y * x))))
	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 (j <= -6.5e+249)
		tmp = Float64(t_1 + Float64(18.0 * Float64(x * Float64(y * Float64(t * z)))));
	elseif (j <= -5.2e+202)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(i * Float64(x + Float64(Float64(a * t) / i)))));
	elseif (j <= -1.46e+144)
		tmp = Float64(t_1 + Float64(x * Float64(-4.0 * i)));
	elseif (j <= 5e-68)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(a * t) + Float64(x * i))));
	else
		tmp = Float64(t_1 + Float64(18.0 * Float64(t * Float64(z * Float64(y * x)))));
	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 (j <= -6.5e+249)
		tmp = t_1 + (18.0 * (x * (y * (t * z))));
	elseif (j <= -5.2e+202)
		tmp = (b * c) - (4.0 * (i * (x + ((a * t) / i))));
	elseif (j <= -1.46e+144)
		tmp = t_1 + (x * (-4.0 * i));
	elseif (j <= 5e-68)
		tmp = (b * c) - (4.0 * ((a * t) + (x * i)));
	else
		tmp = t_1 + (18.0 * (t * (z * (y * x))));
	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[j, -6.5e+249], N[(t$95$1 + N[(18.0 * N[(x * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.2e+202], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * N[(x + N[(N[(a * t), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.46e+144], N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e-68], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(18.0 * N[(t * N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -6.50000000000000028e249

   1. Initial program 77.4%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in y around inf 78.5%

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

      1. *-commutative 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in x around 0 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*r* 85.3%

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

      3. associate-*l* 85.3%

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

   10. Simplified 85.3%

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

   if -6.50000000000000028e249 < j < -5.2000000000000004e202

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 92.0%

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

      1. distribute-lft-out 92.0%

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

      2. *-commutative 92.0%

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

   5. Simplified 92.0%

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

   6. Taylor expanded in i around inf 92.1%

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

   7. Taylor expanded in j around 0 75.6%

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

   if -5.2000000000000004e202 < j < -1.46e144

   1. Initial program 69.0%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in i around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*l* 76.9%

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

      4. *-commutative 76.9%

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

   7. Simplified 76.9%

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

   if -1.46e144 < j < 4.99999999999999971e-68

   1. Initial program 90.2%

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

   3. Taylor expanded in y around 0 78.9%

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

      1. distribute-lft-out 78.9%

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

      2. *-commutative 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in j around 0 69.5%

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

   if 4.99999999999999971e-68 < j

   1. Initial program 84.2%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in y around inf 53.9%

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

      1. *-commutative 53.9%

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

   7. Simplified 53.9%

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

      1. pow1 53.9%

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

   9. Applied egg-rr 53.9%

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

       1. unpow1 53.9%

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

       2. associate-*r* 57.7%

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

   11. Simplified 57.7%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.5 \cdot 10^{+249}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{+202}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot \left(x + \frac{a \cdot t}{i}\right)\right)\\ \mathbf{elif}\;j \leq -1.46 \cdot 10^{+144}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-68}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(y \cdot x\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 64.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ t_3 := b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{if}\;k \leq -8.6 \cdot 10^{-48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 1.26 \cdot 10^{-164}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;k \leq 1.95 \cdot 10^{-136}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{+131}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1 + 18 \cdot \left(t \cdot \left(z \cdot \left(y \cdot x\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ t_1 (* 18.0 (* t (* x (* y z))))))
        (t_3 (- (* b c) (* 4.0 (+ (* a t) (* x i))))))
   (if (<= k -8.6e-48)
     t_2
     (if (<= k 1.26e-164)
       t_3
       (if (<= k 1.95e-136)
         t_2
         (if (<= k 1.6e+131) t_3 (+ t_1 (* 18.0 (* t (* z (* y x)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (18.0 * (t * (x * (y * z))));
	double t_3 = (b * c) - (4.0 * ((a * t) + (x * i)));
	double tmp;
	if (k <= -8.6e-48) {
		tmp = t_2;
	} else if (k <= 1.26e-164) {
		tmp = t_3;
	} else if (k <= 1.95e-136) {
		tmp = t_2;
	} else if (k <= 1.6e+131) {
		tmp = t_3;
	} else {
		tmp = t_1 + (18.0 * (t * (z * (y * x))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + (18.0d0 * (t * (x * (y * z))))
    t_3 = (b * c) - (4.0d0 * ((a * t) + (x * i)))
    if (k <= (-8.6d-48)) then
        tmp = t_2
    else if (k <= 1.26d-164) then
        tmp = t_3
    else if (k <= 1.95d-136) then
        tmp = t_2
    else if (k <= 1.6d+131) then
        tmp = t_3
    else
        tmp = t_1 + (18.0d0 * (t * (z * (y * x))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (18.0 * (t * (x * (y * z))));
	double t_3 = (b * c) - (4.0 * ((a * t) + (x * i)));
	double tmp;
	if (k <= -8.6e-48) {
		tmp = t_2;
	} else if (k <= 1.26e-164) {
		tmp = t_3;
	} else if (k <= 1.95e-136) {
		tmp = t_2;
	} else if (k <= 1.6e+131) {
		tmp = t_3;
	} else {
		tmp = t_1 + (18.0 * (t * (z * (y * x))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (18.0 * (t * (x * (y * z))))
	t_3 = (b * c) - (4.0 * ((a * t) + (x * i)))
	tmp = 0
	if k <= -8.6e-48:
		tmp = t_2
	elif k <= 1.26e-164:
		tmp = t_3
	elif k <= 1.95e-136:
		tmp = t_2
	elif k <= 1.6e+131:
		tmp = t_3
	else:
		tmp = t_1 + (18.0 * (t * (z * (y * x))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))))
	t_3 = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(a * t) + Float64(x * i))))
	tmp = 0.0
	if (k <= -8.6e-48)
		tmp = t_2;
	elseif (k <= 1.26e-164)
		tmp = t_3;
	elseif (k <= 1.95e-136)
		tmp = t_2;
	elseif (k <= 1.6e+131)
		tmp = t_3;
	else
		tmp = Float64(t_1 + Float64(18.0 * Float64(t * Float64(z * Float64(y * x)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (18.0 * (t * (x * (y * z))));
	t_3 = (b * c) - (4.0 * ((a * t) + (x * i)));
	tmp = 0.0;
	if (k <= -8.6e-48)
		tmp = t_2;
	elseif (k <= 1.26e-164)
		tmp = t_3;
	elseif (k <= 1.95e-136)
		tmp = t_2;
	elseif (k <= 1.6e+131)
		tmp = t_3;
	else
		tmp = t_1 + (18.0 * (t * (z * (y * x))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -8.6e-48], t$95$2, If[LessEqual[k, 1.26e-164], t$95$3, If[LessEqual[k, 1.95e-136], t$95$2, If[LessEqual[k, 1.6e+131], t$95$3, N[(t$95$1 + N[(18.0 * N[(t * N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if k < -8.6e-48 or 1.26e-164 < k < 1.94999999999999988e-136

   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 85.2%

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

   5. Taylor expanded in y around inf 55.8%

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

      1. *-commutative 55.8%

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

   7. Simplified 55.8%

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

   if -8.6e-48 < k < 1.26e-164 or 1.94999999999999988e-136 < k < 1.6000000000000001e131

   1. Initial program 90.2%

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

   3. Taylor expanded in y around 0 80.9%

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

      1. distribute-lft-out 80.9%

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

      2. *-commutative 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in j around 0 70.2%

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

   if 1.6000000000000001e131 < k

   1. Initial program 82.8%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in y around inf 61.1%

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

      1. *-commutative 61.1%

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

   7. Simplified 61.1%

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

      1. pow1 61.1%

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

   9. Applied egg-rr 61.1%

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

       1. unpow1 61.1%

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

       2. associate-*r* 63.8%

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

   11. Simplified 63.8%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -8.6 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.26 \cdot 10^{-164}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{elif}\;k \leq 1.95 \cdot 10^{-136}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{+131}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(y \cdot x\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{if}\;k \leq -2.6:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{-197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq 1.95 \cdot 10^{-136}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;k \leq 4.3 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27 + \frac{b \cdot c}{k}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (+ (* a t) (* x i))))))
   (if (<= k -2.6)
     (+ (* j (* k -27.0)) (* -4.0 (* a t)))
     (if (<= k 1.55e-197)
       t_1
       (if (<= k 1.95e-136)
         (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
         (if (<= k 4.3e+128) t_1 (* k (+ (* j -27.0) (/ (* b c) k)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * ((a * t) + (x * i)));
	double tmp;
	if (k <= -2.6) {
		tmp = (j * (k * -27.0)) + (-4.0 * (a * t));
	} else if (k <= 1.55e-197) {
		tmp = t_1;
	} else if (k <= 1.95e-136) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (k <= 4.3e+128) {
		tmp = t_1;
	} else {
		tmp = k * ((j * -27.0) + ((b * c) / k));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * ((a * t) + (x * i)))
    if (k <= (-2.6d0)) then
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * (a * t))
    else if (k <= 1.55d-197) then
        tmp = t_1
    else if (k <= 1.95d-136) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (k <= 4.3d+128) then
        tmp = t_1
    else
        tmp = k * ((j * (-27.0d0)) + ((b * c) / k))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * ((a * t) + (x * i)));
	double tmp;
	if (k <= -2.6) {
		tmp = (j * (k * -27.0)) + (-4.0 * (a * t));
	} else if (k <= 1.55e-197) {
		tmp = t_1;
	} else if (k <= 1.95e-136) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (k <= 4.3e+128) {
		tmp = t_1;
	} else {
		tmp = k * ((j * -27.0) + ((b * c) / k));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * ((a * t) + (x * i)))
	tmp = 0
	if k <= -2.6:
		tmp = (j * (k * -27.0)) + (-4.0 * (a * t))
	elif k <= 1.55e-197:
		tmp = t_1
	elif k <= 1.95e-136:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif k <= 4.3e+128:
		tmp = t_1
	else:
		tmp = k * ((j * -27.0) + ((b * c) / k))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(a * t) + Float64(x * i))))
	tmp = 0.0
	if (k <= -2.6)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(a * t)));
	elseif (k <= 1.55e-197)
		tmp = t_1;
	elseif (k <= 1.95e-136)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (k <= 4.3e+128)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(Float64(j * -27.0) + Float64(Float64(b * c) / k)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * ((a * t) + (x * i)));
	tmp = 0.0;
	if (k <= -2.6)
		tmp = (j * (k * -27.0)) + (-4.0 * (a * t));
	elseif (k <= 1.55e-197)
		tmp = t_1;
	elseif (k <= 1.95e-136)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (k <= 4.3e+128)
		tmp = t_1;
	else
		tmp = k * ((j * -27.0) + ((b * c) / k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.6], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.55e-197], t$95$1, If[LessEqual[k, 1.95e-136], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.3e+128], t$95$1, N[(k * N[(N[(j * -27.0), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -2.60000000000000009

   1. Initial program 84.3%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in a around inf 58.3%

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

   if -2.60000000000000009 < k < 1.55000000000000014e-197 or 1.94999999999999988e-136 < k < 4.29999999999999975e128

   1. Initial program 89.9%

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

   3. Taylor expanded in y around 0 80.3%

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

      1. distribute-lft-out 80.3%

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

      2. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in j around 0 69.3%

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

   if 1.55000000000000014e-197 < k < 1.94999999999999988e-136

   1. Initial program 77.8%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in x around inf 65.4%

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

   if 4.29999999999999975e128 < k

   1. Initial program 83.3%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in b around inf 62.3%

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

   6. Taylor expanded in k around inf 65.1%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.6:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{-197}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{elif}\;k \leq 1.95 \cdot 10^{-136}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;k \leq 4.3 \cdot 10^{+128}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27 + \frac{b \cdot c}{k}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 82.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+123}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a + t\_1\right)\\ \mathbf{elif}\;t \leq 0.0145:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z)))))
   (if (<= t -9.5e+123)
     (+ (* j (* k -27.0)) (* t (+ (* -4.0 a) t_1)))
     (if (<= t 0.0145)
       (- (- (* b c) (* 4.0 (+ (* a t) (* x i)))) (* k (* j 27.0)))
       (- (+ (* b c) (* t (- t_1 (* a 4.0)))) (* 4.0 (* x i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -9.5e+123) {
		tmp = (j * (k * -27.0)) + (t * ((-4.0 * a) + t_1));
	} else if (t <= 0.0145) {
		tmp = ((b * c) - (4.0 * ((a * t) + (x * i)))) - (k * (j * 27.0));
	} else {
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    if (t <= (-9.5d+123)) then
        tmp = (j * (k * (-27.0d0))) + (t * (((-4.0d0) * a) + t_1))
    else if (t <= 0.0145d0) then
        tmp = ((b * c) - (4.0d0 * ((a * t) + (x * i)))) - (k * (j * 27.0d0))
    else
        tmp = ((b * c) + (t * (t_1 - (a * 4.0d0)))) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -9.5e+123) {
		tmp = (j * (k * -27.0)) + (t * ((-4.0 * a) + t_1));
	} else if (t <= 0.0145) {
		tmp = ((b * c) - (4.0 * ((a * t) + (x * i)))) - (k * (j * 27.0));
	} else {
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	tmp = 0
	if t <= -9.5e+123:
		tmp = (j * (k * -27.0)) + (t * ((-4.0 * a) + t_1))
	elif t <= 0.0145:
		tmp = ((b * c) - (4.0 * ((a * t) + (x * i)))) - (k * (j * 27.0))
	else:
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	tmp = 0.0
	if (t <= -9.5e+123)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(-4.0 * a) + t_1)));
	elseif (t <= 0.0145)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(a * t) + Float64(x * i)))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(t_1 - Float64(a * 4.0)))) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	tmp = 0.0;
	if (t <= -9.5e+123)
		tmp = (j * (k * -27.0)) + (t * ((-4.0 * a) + t_1));
	elseif (t <= 0.0145)
		tmp = ((b * c) - (4.0 * ((a * t) + (x * i)))) - (k * (j * 27.0));
	else
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+123], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(-4.0 * a), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.0145], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.4999999999999996e123

   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 87.9%

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

   5. Taylor expanded in t around inf 86.5%

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

   if -9.4999999999999996e123 < t < 0.0145000000000000007

   1. Initial program 88.4%

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

   3. Taylor expanded in y around 0 86.5%

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

      1. distribute-lft-out 86.5%

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

      2. *-commutative 86.5%

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

   5. Simplified 86.5%

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

   if 0.0145000000000000007 < t

   1. Initial program 88.5%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in j around 0 88.3%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+123}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 0.0145:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 70.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t \leq -5.1 \cdot 10^{+139}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(y \cdot z\right) \cdot \left(x \cdot -18\right)\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-32}:\\ \;\;\;\;\left(b \cdot c - \left(a \cdot t\right) \cdot 4\right) - t\_1\\ \mathbf{elif}\;t \leq 0.0195:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j 27.0))))
   (if (<= t -5.1e+139)
     (* t (- (* a (- 4.0)) (* (* y z) (* x -18.0))))
     (if (<= t -1.65e-32)
       (- (- (* b c) (* (* a t) 4.0)) t_1)
       (if (<= t 0.0195)
         (- (- (* b c) (* 4.0 (* x i))) t_1)
         (- (* b c) (* 4.0 (+ (* a t) (* x i)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t <= -5.1e+139) {
		tmp = t * ((a * -4.0) - ((y * z) * (x * -18.0)));
	} else if (t <= -1.65e-32) {
		tmp = ((b * c) - ((a * t) * 4.0)) - t_1;
	} else if (t <= 0.0195) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = (b * c) - (4.0 * ((a * t) + (x * i)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (j * 27.0d0)
    if (t <= (-5.1d+139)) then
        tmp = t * ((a * -4.0d0) - ((y * z) * (x * (-18.0d0))))
    else if (t <= (-1.65d-32)) then
        tmp = ((b * c) - ((a * t) * 4.0d0)) - t_1
    else if (t <= 0.0195d0) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else
        tmp = (b * c) - (4.0d0 * ((a * t) + (x * i)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * 27.0);
	double tmp;
	if (t <= -5.1e+139) {
		tmp = t * ((a * -4.0) - ((y * z) * (x * -18.0)));
	} else if (t <= -1.65e-32) {
		tmp = ((b * c) - ((a * t) * 4.0)) - t_1;
	} else if (t <= 0.0195) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else {
		tmp = (b * c) - (4.0 * ((a * t) + (x * i)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if t <= -5.1e+139:
		tmp = t * ((a * -4.0) - ((y * z) * (x * -18.0)))
	elif t <= -1.65e-32:
		tmp = ((b * c) - ((a * t) * 4.0)) - t_1
	elif t <= 0.0195:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	else:
		tmp = (b * c) - (4.0 * ((a * t) + (x * i)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t <= -5.1e+139)
		tmp = Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(Float64(y * z) * Float64(x * -18.0))));
	elseif (t <= -1.65e-32)
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(a * t) * 4.0)) - t_1);
	elseif (t <= 0.0195)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(a * t) + Float64(x * i))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (t <= -5.1e+139)
		tmp = t * ((a * -4.0) - ((y * z) * (x * -18.0)));
	elseif (t <= -1.65e-32)
		tmp = ((b * c) - ((a * t) * 4.0)) - t_1;
	elseif (t <= 0.0195)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	else
		tmp = (b * c) - (4.0 * ((a * t) + (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.1e+139], N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] * N[(x * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.65e-32], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 0.0195], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.10000000000000037e139

   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 79.6%

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

      1. associate-*r* 79.6%

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

      2. neg-mul-1 79.6%

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

      3. cancel-sign-sub-inv 79.6%

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

      4. associate-*r* 79.6%

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

      5. metadata-eval 79.6%

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

      6. *-commutative 79.6%

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

   5. Simplified 79.6%

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

   if -5.10000000000000037e139 < t < -1.65000000000000013e-32

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 77.5%

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

   if -1.65000000000000013e-32 < t < 0.0195

   1. Initial program 86.4%

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

   3. Taylor expanded in t around 0 83.6%

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

   if 0.0195 < t

   1. Initial program 88.5%

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

   3. Taylor expanded in y around 0 74.7%

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

      1. distribute-lft-out 74.7%

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

      2. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in j around 0 69.5%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+139}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(y \cdot z\right) \cdot \left(x \cdot -18\right)\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-32}:\\ \;\;\;\;\left(b \cdot c - \left(a \cdot t\right) \cdot 4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 0.0195:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -1.55 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.62 \cdot 10^{+103}:\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{+77} \lor \neg \left(j \leq 7.6 \cdot 10^{-105}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - a \cdot \left(t \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* k -27.0)))))
   (if (<= j -1.55e+126)
     t_1
     (if (<= j -1.62e+103)
       (* -4.0 (+ (* a t) (* x i)))
       (if (or (<= j -4.5e+77) (not (<= j 7.6e-105)))
         t_1
         (- (* b c) (* a (* t 4.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (j <= -1.55e+126) {
		tmp = t_1;
	} else if (j <= -1.62e+103) {
		tmp = -4.0 * ((a * t) + (x * i));
	} else if ((j <= -4.5e+77) || !(j <= 7.6e-105)) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (a * (t * 4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    if (j <= (-1.55d+126)) then
        tmp = t_1
    else if (j <= (-1.62d+103)) then
        tmp = (-4.0d0) * ((a * t) + (x * i))
    else if ((j <= (-4.5d+77)) .or. (.not. (j <= 7.6d-105))) then
        tmp = t_1
    else
        tmp = (b * c) - (a * (t * 4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (j <= -1.55e+126) {
		tmp = t_1;
	} else if (j <= -1.62e+103) {
		tmp = -4.0 * ((a * t) + (x * i));
	} else if ((j <= -4.5e+77) || !(j <= 7.6e-105)) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (a * (t * 4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if j <= -1.55e+126:
		tmp = t_1
	elif j <= -1.62e+103:
		tmp = -4.0 * ((a * t) + (x * i))
	elif (j <= -4.5e+77) or not (j <= 7.6e-105):
		tmp = t_1
	else:
		tmp = (b * c) - (a * (t * 4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (j <= -1.55e+126)
		tmp = t_1;
	elseif (j <= -1.62e+103)
		tmp = Float64(-4.0 * Float64(Float64(a * t) + Float64(x * i)));
	elseif ((j <= -4.5e+77) || !(j <= 7.6e-105))
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) - Float64(a * Float64(t * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (j <= -1.55e+126)
		tmp = t_1;
	elseif (j <= -1.62e+103)
		tmp = -4.0 * ((a * t) + (x * i));
	elseif ((j <= -4.5e+77) || ~((j <= 7.6e-105)))
		tmp = t_1;
	else
		tmp = (b * c) - (a * (t * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.55e+126], t$95$1, If[LessEqual[j, -1.62e+103], N[(-4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, -4.5e+77], N[Not[LessEqual[j, 7.6e-105]], $MachinePrecision]], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(a * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.55e126 or -1.62000000000000007e103 < j < -4.50000000000000024e77 or 7.5999999999999995e-105 < j

   1. Initial program 84.2%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in b around inf 56.9%

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

   if -1.55e126 < j < -1.62000000000000007e103

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 73.6%

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

      1. distribute-lft-out 73.6%

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

      2. *-commutative 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in j around 0 72.9%

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

   7. Taylor expanded in b around 0 72.5%

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

   if -4.50000000000000024e77 < j < 7.5999999999999995e-105

   1. Initial program 89.4%

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

   3. Taylor expanded in y around 0 77.6%

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

      1. distribute-lft-out 77.6%

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

      2. *-commutative 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in j around 0 69.2%

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

   7. Taylor expanded in a around inf 54.0%

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

      1. *-commutative 54.0%

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

      2. associate-*l* 54.0%

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

   9. Simplified 54.0%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.55 \cdot 10^{+126}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -1.62 \cdot 10^{+103}:\\ \;\;\;\;-4 \cdot \left(a \cdot t + x \cdot i\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{+77} \lor \neg \left(j \leq 7.6 \cdot 10^{-105}\right):\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - a \cdot \left(t \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 81.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+127}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a + t\_1\right)\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+25}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 18.0 (* x (* y z)))))
   (if (<= t -2e+127)
     (+ (* j (* k -27.0)) (* t (+ (* -4.0 a) t_1)))
     (if (<= t 6.7e+25)
       (- (- (* b c) (* 4.0 (+ (* a t) (* x i)))) (* k (* j 27.0)))
       (+ (* b c) (* t (- t_1 (* 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 t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -2e+127) {
		tmp = (j * (k * -27.0)) + (t * ((-4.0 * a) + t_1));
	} else if (t <= 6.7e+25) {
		tmp = ((b * c) - (4.0 * ((a * t) + (x * i)))) - (k * (j * 27.0));
	} else {
		tmp = (b * c) + (t * (t_1 - (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) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    if (t <= (-2d+127)) then
        tmp = (j * (k * (-27.0d0))) + (t * (((-4.0d0) * a) + t_1))
    else if (t <= 6.7d+25) then
        tmp = ((b * c) - (4.0d0 * ((a * t) + (x * i)))) - (k * (j * 27.0d0))
    else
        tmp = (b * c) + (t * (t_1 - (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 t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -2e+127) {
		tmp = (j * (k * -27.0)) + (t * ((-4.0 * a) + t_1));
	} else if (t <= 6.7e+25) {
		tmp = ((b * c) - (4.0 * ((a * t) + (x * i)))) - (k * (j * 27.0));
	} else {
		tmp = (b * c) + (t * (t_1 - (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):
	t_1 = 18.0 * (x * (y * z))
	tmp = 0
	if t <= -2e+127:
		tmp = (j * (k * -27.0)) + (t * ((-4.0 * a) + t_1))
	elif t <= 6.7e+25:
		tmp = ((b * c) - (4.0 * ((a * t) + (x * i)))) - (k * (j * 27.0))
	else:
		tmp = (b * c) + (t * (t_1 - (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)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	tmp = 0.0
	if (t <= -2e+127)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(-4.0 * a) + t_1)));
	elseif (t <= 6.7e+25)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(a * t) + Float64(x * i)))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(Float64(b * c) + Float64(t * Float64(t_1 - 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)
	t_1 = 18.0 * (x * (y * z));
	tmp = 0.0;
	if (t <= -2e+127)
		tmp = (j * (k * -27.0)) + (t * ((-4.0 * a) + t_1));
	elseif (t <= 6.7e+25)
		tmp = ((b * c) - (4.0 * ((a * t) + (x * i)))) - (k * (j * 27.0));
	else
		tmp = (b * c) + (t * (t_1 - (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_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+127], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(-4.0 * a), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.7e+25], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.99999999999999991e127

   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 87.9%

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

   5. Taylor expanded in t around inf 86.5%

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

   if -1.99999999999999991e127 < t < 6.70000000000000037e25

   1. Initial program 88.5%

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

   3. Taylor expanded in y around 0 86.8%

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

      1. distribute-lft-out 86.8%

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

      2. *-commutative 86.8%

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

   5. Simplified 86.8%

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

   if 6.70000000000000037e25 < t

   1. Initial program 88.1%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in j around 0 86.0%

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

   6. Taylor expanded in i around 0 84.2%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+127}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+25}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(a \cdot t + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 52.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -9.2 \cdot 10^{-48}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -4.4 \cdot 10^{-263}:\\ \;\;\;\;i \cdot \left(b \cdot \frac{c}{i} + -4 \cdot x\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{+25}:\\ \;\;\;\;b \cdot c - a \cdot \left(t \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27 + \frac{b \cdot c}{k}\right)\\ \end{array} \end{array} \]

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 (<= k -9.2e-48)
   (+ (* b c) (* j (* k -27.0)))
   (if (<= k -4.4e-263)
     (* i (+ (* b (/ c i)) (* -4.0 x)))
     (if (<= k 1.4e+25)
       (- (* b c) (* a (* t 4.0)))
       (* k (+ (* j -27.0) (/ (* b c) 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 (k <= -9.2e-48) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (k <= -4.4e-263) {
		tmp = i * ((b * (c / i)) + (-4.0 * x));
	} else if (k <= 1.4e+25) {
		tmp = (b * c) - (a * (t * 4.0));
	} else {
		tmp = k * ((j * -27.0) + ((b * c) / 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 (k <= (-9.2d-48)) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (k <= (-4.4d-263)) then
        tmp = i * ((b * (c / i)) + ((-4.0d0) * x))
    else if (k <= 1.4d+25) then
        tmp = (b * c) - (a * (t * 4.0d0))
    else
        tmp = k * ((j * (-27.0d0)) + ((b * c) / 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 (k <= -9.2e-48) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (k <= -4.4e-263) {
		tmp = i * ((b * (c / i)) + (-4.0 * x));
	} else if (k <= 1.4e+25) {
		tmp = (b * c) - (a * (t * 4.0));
	} else {
		tmp = k * ((j * -27.0) + ((b * c) / 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 k <= -9.2e-48:
		tmp = (b * c) + (j * (k * -27.0))
	elif k <= -4.4e-263:
		tmp = i * ((b * (c / i)) + (-4.0 * x))
	elif k <= 1.4e+25:
		tmp = (b * c) - (a * (t * 4.0))
	else:
		tmp = k * ((j * -27.0) + ((b * c) / 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 (k <= -9.2e-48)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (k <= -4.4e-263)
		tmp = Float64(i * Float64(Float64(b * Float64(c / i)) + Float64(-4.0 * x)));
	elseif (k <= 1.4e+25)
		tmp = Float64(Float64(b * c) - Float64(a * Float64(t * 4.0)));
	else
		tmp = Float64(k * Float64(Float64(j * -27.0) + Float64(Float64(b * c) / 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 (k <= -9.2e-48)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (k <= -4.4e-263)
		tmp = i * ((b * (c / i)) + (-4.0 * x));
	elseif (k <= 1.4e+25)
		tmp = (b * c) - (a * (t * 4.0));
	else
		tmp = k * ((j * -27.0) + ((b * c) / 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[k, -9.2e-48], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4.4e-263], N[(i * N[(N[(b * N[(c / i), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.4e+25], N[(N[(b * c), $MachinePrecision] - N[(a * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(N[(j * -27.0), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -9.2000000000000003e-48

   1. Initial program 85.5%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in b around inf 50.4%

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

   if -9.2000000000000003e-48 < k < -4.4000000000000001e-263

   1. Initial program 86.6%

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

   3. Taylor expanded in y around 0 77.4%

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

      1. distribute-lft-out 77.4%

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

      2. *-commutative 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in j around 0 77.3%

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

   7. Taylor expanded in a around 0 55.0%

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

      1. *-commutative 55.0%

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

      2. associate-*r* 55.0%

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

   9. Simplified 55.0%

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

   10. Taylor expanded in i around inf 51.4%

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

       1. cancel-sign-sub-inv 51.4%

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

       2. associate-/l* 49.4%

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

       3. metadata-eval 49.4%

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

   12. Simplified 49.4%

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

   if -4.4000000000000001e-263 < k < 1.4000000000000001e25

   1. Initial program 92.1%

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

   3. Taylor expanded in y around 0 80.2%

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

      1. distribute-lft-out 80.2%

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

      2. *-commutative 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in j around 0 72.3%

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

   7. Taylor expanded in a around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. associate-*l* 52.2%

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

   9. Simplified 52.2%

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

   if 1.4000000000000001e25 < k

   1. Initial program 84.7%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in b around inf 62.1%

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

   6. Taylor expanded in k around inf 63.6%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -9.2 \cdot 10^{-48}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -4.4 \cdot 10^{-263}:\\ \;\;\;\;i \cdot \left(b \cdot \frac{c}{i} + -4 \cdot x\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{+25}:\\ \;\;\;\;b \cdot c - a \cdot \left(t \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27 + \frac{b \cdot c}{k}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 37.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.65 \cdot 10^{+184}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.32 \cdot 10^{+48}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1.65e+184)
   (* b c)
   (if (<= (* b c) -1.32e+48)
     (* -4.0 (* a t))
     (if (<= (* b c) 3.6e+47) (* 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) <= -1.65e+184) {
		tmp = b * c;
	} else if ((b * c) <= -1.32e+48) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 3.6e+47) {
		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) <= (-1.65d+184)) then
        tmp = b * c
    else if ((b * c) <= (-1.32d+48)) then
        tmp = (-4.0d0) * (a * t)
    else if ((b * c) <= 3.6d+47) 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) <= -1.65e+184) {
		tmp = b * c;
	} else if ((b * c) <= -1.32e+48) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 3.6e+47) {
		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) <= -1.65e+184:
		tmp = b * c
	elif (b * c) <= -1.32e+48:
		tmp = -4.0 * (a * t)
	elif (b * c) <= 3.6e+47:
		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) <= -1.65e+184)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.32e+48)
		tmp = Float64(-4.0 * Float64(a * t));
	elseif (Float64(b * c) <= 3.6e+47)
		tmp = Float64(j * Float64(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) <= -1.65e+184)
		tmp = b * c;
	elseif ((b * c) <= -1.32e+48)
		tmp = -4.0 * (a * t);
	elseif ((b * c) <= 3.6e+47)
		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], -1.65e+184], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.32e+48], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.6e+47], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.6499999999999999e184 or 3.60000000000000008e47 < (*.f64 b c)

   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 x around 0 84.5%

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

   4. Taylor expanded in b around inf 65.1%

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

   if -1.6499999999999999e184 < (*.f64 b c) < -1.32e48

   1. Initial program 95.1%

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

   3. Taylor expanded in x around 0 95.3%

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

   4. Taylor expanded in a around inf 41.8%

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

      1. *-commutative 41.8%

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

   6. Simplified 41.8%

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

   if -1.32e48 < (*.f64 b c) < 3.60000000000000008e47

   1. Initial program 87.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in j around inf 33.8%

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

      1. *-commutative 33.8%

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

      2. associate-*r* 33.1%

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

      3. *-commutative 33.1%

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

   7. Simplified 33.1%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.65 \cdot 10^{+184}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.32 \cdot 10^{+48}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 37.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.5 \cdot 10^{+184}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.2 \cdot 10^{+49}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 7.3 \cdot 10^{+47}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) -6.5e+184)
   (* b c)
   (if (<= (* b c) -1.2e+49)
     (* -4.0 (* a t))
     (if (<= (* b c) 7.3e+47) (* -27.0 (* j k)) (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -6.5e+184) {
		tmp = b * c;
	} else if ((b * c) <= -1.2e+49) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 7.3e+47) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-6.5d+184)) then
        tmp = b * c
    else if ((b * c) <= (-1.2d+49)) then
        tmp = (-4.0d0) * (a * t)
    else if ((b * c) <= 7.3d+47) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -6.5e+184) {
		tmp = b * c;
	} else if ((b * c) <= -1.2e+49) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 7.3e+47) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -6.5e+184:
		tmp = b * c
	elif (b * c) <= -1.2e+49:
		tmp = -4.0 * (a * t)
	elif (b * c) <= 7.3e+47:
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -6.5e+184)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.2e+49)
		tmp = Float64(-4.0 * Float64(a * t));
	elseif (Float64(b * c) <= 7.3e+47)
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -6.5e+184)
		tmp = b * c;
	elseif ((b * c) <= -1.2e+49)
		tmp = -4.0 * (a * t);
	elseif ((b * c) <= 7.3e+47)
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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], -6.5e+184], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.2e+49], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7.3e+47], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -6.50000000000000002e184 or 7.3000000000000001e47 < (*.f64 b c)

   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 x around 0 84.5%

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

   4. Taylor expanded in b around inf 65.1%

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

   if -6.50000000000000002e184 < (*.f64 b c) < -1.2e49

   1. Initial program 95.1%

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

   3. Taylor expanded in x around 0 95.3%

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

   4. Taylor expanded in a around inf 41.8%

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

      1. *-commutative 41.8%

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

   6. Simplified 41.8%

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

   if -1.2e49 < (*.f64 b c) < 7.3000000000000001e47

   1. Initial program 87.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in j around inf 33.8%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.5 \cdot 10^{+184}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.2 \cdot 10^{+49}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 7.3 \cdot 10^{+47}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 56.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+192} \lor \neg \left(b \cdot c \leq 10^{+96}\right):\\ \;\;\;\;c \cdot \left(b + -27 \cdot \left(j \cdot \frac{k}{c}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -5e+192) (not (<= (* b c) 1e+96)))
   (* c (+ b (* -27.0 (* j (/ k c)))))
   (+ (* j (* k -27.0)) (* -4.0 (* a t)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -5e+192) || !((b * c) <= 1e+96)) {
		tmp = c * (b + (-27.0 * (j * (k / c))));
	} else {
		tmp = (j * (k * -27.0)) + (-4.0 * (a * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-5d+192)) .or. (.not. ((b * c) <= 1d+96))) then
        tmp = c * (b + ((-27.0d0) * (j * (k / c))))
    else
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * (a * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -5e+192) || !((b * c) <= 1e+96)) {
		tmp = c * (b + (-27.0 * (j * (k / c))));
	} else {
		tmp = (j * (k * -27.0)) + (-4.0 * (a * t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -5e+192) or not ((b * c) <= 1e+96):
		tmp = c * (b + (-27.0 * (j * (k / c))))
	else:
		tmp = (j * (k * -27.0)) + (-4.0 * (a * t))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -5e+192) || !(Float64(b * c) <= 1e+96))
		tmp = Float64(c * Float64(b + Float64(-27.0 * Float64(j * Float64(k / c)))));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(a * t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -5e+192) || ~(((b * c) <= 1e+96)))
		tmp = c * (b + (-27.0 * (j * (k / c))));
	else
		tmp = (j * (k * -27.0)) + (-4.0 * (a * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -5e+192], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1e+96]], $MachinePrecision]], N[(c * N[(b + N[(-27.0 * N[(j * N[(k / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -5.00000000000000033e192 or 1.00000000000000005e96 < (*.f64 b c)

   1. Initial program 85.5%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in b around inf 76.8%

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

   6. Taylor expanded in c around inf 78.2%

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

      1. *-commutative 78.2%

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

      2. associate-/l* 79.5%

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

   8. Simplified 79.5%

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

   if -5.00000000000000033e192 < (*.f64 b c) < 1.00000000000000005e96

   1. Initial program 87.9%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in a around inf 52.8%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+192} \lor \neg \left(b \cdot c \leq 10^{+96}\right):\\ \;\;\;\;c \cdot \left(b + -27 \cdot \left(j \cdot \frac{k}{c}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 52.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;k \leq -1.95 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -5.5 \cdot 10^{-264}:\\ \;\;\;\;i \cdot \left(b \cdot \frac{c}{i} + -4 \cdot x\right)\\ \mathbf{elif}\;k \leq 1.15 \cdot 10^{+29}:\\ \;\;\;\;b \cdot c - a \cdot \left(t \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (+ (* b c) (* j (* k -27.0)))))
   (if (<= k -1.95e-47)
     t_1
     (if (<= k -5.5e-264)
       (* i (+ (* b (/ c i)) (* -4.0 x)))
       (if (<= k 1.15e+29) (- (* b c) (* a (* t 4.0))) 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 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (k <= -1.95e-47) {
		tmp = t_1;
	} else if (k <= -5.5e-264) {
		tmp = i * ((b * (c / i)) + (-4.0 * x));
	} else if (k <= 1.15e+29) {
		tmp = (b * c) - (a * (t * 4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    if (k <= (-1.95d-47)) then
        tmp = t_1
    else if (k <= (-5.5d-264)) then
        tmp = i * ((b * (c / i)) + ((-4.0d0) * x))
    else if (k <= 1.15d+29) then
        tmp = (b * c) - (a * (t * 4.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (k <= -1.95e-47) {
		tmp = t_1;
	} else if (k <= -5.5e-264) {
		tmp = i * ((b * (c / i)) + (-4.0 * x));
	} else if (k <= 1.15e+29) {
		tmp = (b * c) - (a * (t * 4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if k <= -1.95e-47:
		tmp = t_1
	elif k <= -5.5e-264:
		tmp = i * ((b * (c / i)) + (-4.0 * x))
	elif k <= 1.15e+29:
		tmp = (b * c) - (a * (t * 4.0))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (k <= -1.95e-47)
		tmp = t_1;
	elseif (k <= -5.5e-264)
		tmp = Float64(i * Float64(Float64(b * Float64(c / i)) + Float64(-4.0 * x)));
	elseif (k <= 1.15e+29)
		tmp = Float64(Float64(b * c) - Float64(a * Float64(t * 4.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (k <= -1.95e-47)
		tmp = t_1;
	elseif (k <= -5.5e-264)
		tmp = i * ((b * (c / i)) + (-4.0 * x));
	elseif (k <= 1.15e+29)
		tmp = (b * c) - (a * (t * 4.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.95e-47], t$95$1, If[LessEqual[k, -5.5e-264], N[(i * N[(N[(b * N[(c / i), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.15e+29], N[(N[(b * c), $MachinePrecision] - N[(a * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if k < -1.94999999999999989e-47 or 1.1500000000000001e29 < k

   1. Initial program 85.0%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in b around inf 55.6%

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

   if -1.94999999999999989e-47 < k < -5.5000000000000001e-264

   1. Initial program 86.6%

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

   3. Taylor expanded in y around 0 77.4%

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

      1. distribute-lft-out 77.4%

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

      2. *-commutative 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in j around 0 77.3%

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

   7. Taylor expanded in a around 0 55.0%

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

      1. *-commutative 55.0%

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

      2. associate-*r* 55.0%

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

   9. Simplified 55.0%

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

   10. Taylor expanded in i around inf 51.4%

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

       1. cancel-sign-sub-inv 51.4%

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

       2. associate-/l* 49.4%

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

       3. metadata-eval 49.4%

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

   12. Simplified 49.4%

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

   if -5.5000000000000001e-264 < k < 1.1500000000000001e29

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0 80.5%

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

      1. distribute-lft-out 80.5%

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

      2. *-commutative 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in j around 0 71.2%

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

   7. Taylor expanded in a around inf 51.4%

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

      1. *-commutative 51.4%

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

      2. associate-*l* 51.4%

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

   9. Simplified 51.4%

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

Alternative 25: 53.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;k \leq -8.5 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -3.2 \cdot 10^{-206}:\\ \;\;\;\;b \cdot c - i \cdot \left(x \cdot 4\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+26}:\\ \;\;\;\;b \cdot c - a \cdot \left(t \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (+ (* b c) (* j (* k -27.0)))))
   (if (<= k -8.5e-48)
     t_1
     (if (<= k -3.2e-206)
       (- (* b c) (* i (* x 4.0)))
       (if (<= k 2.1e+26) (- (* b c) (* a (* t 4.0))) 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 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (k <= -8.5e-48) {
		tmp = t_1;
	} else if (k <= -3.2e-206) {
		tmp = (b * c) - (i * (x * 4.0));
	} else if (k <= 2.1e+26) {
		tmp = (b * c) - (a * (t * 4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    if (k <= (-8.5d-48)) then
        tmp = t_1
    else if (k <= (-3.2d-206)) then
        tmp = (b * c) - (i * (x * 4.0d0))
    else if (k <= 2.1d+26) then
        tmp = (b * c) - (a * (t * 4.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (k <= -8.5e-48) {
		tmp = t_1;
	} else if (k <= -3.2e-206) {
		tmp = (b * c) - (i * (x * 4.0));
	} else if (k <= 2.1e+26) {
		tmp = (b * c) - (a * (t * 4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if k <= -8.5e-48:
		tmp = t_1
	elif k <= -3.2e-206:
		tmp = (b * c) - (i * (x * 4.0))
	elif k <= 2.1e+26:
		tmp = (b * c) - (a * (t * 4.0))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (k <= -8.5e-48)
		tmp = t_1;
	elseif (k <= -3.2e-206)
		tmp = Float64(Float64(b * c) - Float64(i * Float64(x * 4.0)));
	elseif (k <= 2.1e+26)
		tmp = Float64(Float64(b * c) - Float64(a * Float64(t * 4.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (k <= -8.5e-48)
		tmp = t_1;
	elseif (k <= -3.2e-206)
		tmp = (b * c) - (i * (x * 4.0));
	elseif (k <= 2.1e+26)
		tmp = (b * c) - (a * (t * 4.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -8.5e-48], t$95$1, If[LessEqual[k, -3.2e-206], N[(N[(b * c), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.1e+26], N[(N[(b * c), $MachinePrecision] - N[(a * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if k < -8.5000000000000004e-48 or 2.1000000000000001e26 < k

   1. Initial program 85.1%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in b around inf 55.9%

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

   if -8.5000000000000004e-48 < k < -3.19999999999999976e-206

   1. Initial program 86.1%

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

   3. Taylor expanded in y around 0 80.6%

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

      1. distribute-lft-out 80.6%

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

      2. *-commutative 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in j around 0 80.6%

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

   7. Taylor expanded in a around 0 58.9%

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

      1. *-commutative 58.9%

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

      2. associate-*r* 58.9%

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

   9. Simplified 58.9%

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

   if -3.19999999999999976e-206 < k < 2.1000000000000001e26

   1. Initial program 91.3%

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

   3. Taylor expanded in y around 0 78.2%

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

      1. distribute-lft-out 78.2%

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

      2. *-commutative 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in j around 0 71.9%

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

   7. Taylor expanded in a around inf 51.1%

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

      1. *-commutative 51.1%

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

      2. associate-*l* 51.1%

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

   9. Simplified 51.1%

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

Alternative 26: 37.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.2 \cdot 10^{+152} \lor \neg \left(b \cdot c \leq 2.35 \cdot 10^{+47}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -3.2e+152) (not (<= (* b c) 2.35e+47)))
   (* b c)
   (* -27.0 (* j k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -3.2e+152) || !((b * c) <= 2.35e+47)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-3.2d+152)) .or. (.not. ((b * c) <= 2.35d+47))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -3.2e+152) || !((b * c) <= 2.35e+47)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -3.2e+152) or not ((b * c) <= 2.35e+47):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -3.2e+152) || !(Float64(b * c) <= 2.35e+47))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -3.2e+152) || ~(((b * c) <= 2.35e+47)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -3.2e+152], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2.35e+47]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -3.20000000000000005e152 or 2.34999999999999982e47 < (*.f64 b c)

   1. Initial program 84.9%

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

   3. Taylor expanded in x around 0 84.9%

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

   4. Taylor expanded in b around inf 60.8%

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

   if -3.20000000000000005e152 < (*.f64 b c) < 2.34999999999999982e47

   1. Initial program 88.5%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in j around inf 32.4%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.2 \cdot 10^{+152} \lor \neg \left(b \cdot c \leq 2.35 \cdot 10^{+47}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 23.9% 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 87.2%

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

3. Taylor expanded in x around 0 87.2%

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

4. Taylor expanded in b around inf 25.4%

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

Developer target: 89.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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