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

Percentage Accurate: 86.1% → 92.7%

Time: 22.1s

Alternatives: 22

Speedup: 0.9×

• 49.8% 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: 86.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right) + \left(b \cdot c - a \cdot \left(t \cdot 4\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ t_2 := \left(b \cdot c - \left(t \cdot \left(a \cdot 4\right) - \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+234}:\\ \;\;\;\;t\_2 - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+ (* x (* (* 18.0 y) (* z t))) (- (* b c) (* a (* t 4.0))))
          (+ (* x (* 4.0 i)) (* j (* 27.0 k)))))
        (t_2
         (-
          (- (* b c) (- (* t (* a 4.0)) (* (* (* (* x 18.0) y) z) t)))
          (* (* x 4.0) i))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 2e+234)
       (- t_2 (* k (* j 27.0)))
       (if (<= t_2 INFINITY)
         t_1
         (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((x * ((18.0 * y) * (z * t))) + ((b * c) - (a * (t * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	double t_2 = ((b * c) - ((t * (a * 4.0)) - ((((x * 18.0) * y) * z) * t))) - ((x * 4.0) * i);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 2e+234) {
		tmp = t_2 - (k * (j * 27.0));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((x * ((18.0 * y) * (z * t))) + ((b * c) - (a * (t * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	double t_2 = ((b * c) - ((t * (a * 4.0)) - ((((x * 18.0) * y) * z) * t))) - ((x * 4.0) * i);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 2e+234) {
		tmp = t_2 - (k * (j * 27.0));
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((x * ((18.0 * y) * (z * t))) + ((b * c) - (a * (t * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	t_2 = ((b * c) - ((t * (a * 4.0)) - ((((x * 18.0) * y) * z) * t))) - ((x * 4.0) * i)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 2e+234:
		tmp = t_2 - (k * (j * 27.0))
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(18.0 * y) * Float64(z * t))) + Float64(Float64(b * c) - Float64(a * Float64(t * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))))
	t_2 = Float64(Float64(Float64(b * c) - Float64(Float64(t * Float64(a * 4.0)) - Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t))) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 2e+234)
		tmp = Float64(t_2 - Float64(k * Float64(j * 27.0)));
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((x * ((18.0 * y) * (z * t))) + ((b * c) - (a * (t * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	t_2 = ((b * c) - ((t * (a * 4.0)) - ((((x * 18.0) * y) * z) * t))) - ((x * 4.0) * i);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 2e+234)
		tmp = t_2 - (k * (j * 27.0));
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(18.0 * y), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] - N[(a * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] - N[(N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 2e+234], N[(t$95$2 - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$1, N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.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)) < -inf.0 or 2.00000000000000004e234 < (-.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)) < +inf.0

   1. Initial program 81.3%

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

   3. Simplified 85.9%

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

      1. associate-*r* 81.3%

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

      2. distribute-rgt-out-- 81.3%

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

      3. associate-+l- 81.3%

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

      4. associate-*l* 84.1%

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

      5. fmm-def 84.1%

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

      6. associate-*l* 84.1%

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

      7. *-commutative 84.1%

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

   6. Applied egg-rr 84.1%

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

      1. fmm-undef 84.1%

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

      2. *-commutative 84.1%

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

   8. Simplified 84.1%

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

      1. sub-neg 84.1%

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

      2. associate-*l* 92.8%

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

      3. *-commutative 92.8%

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

   10. Applied egg-rr 92.8%

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

       1. unsub-neg 92.8%

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

       2. associate-*r* 92.8%

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

   12. Simplified 92.8%

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

   if -inf.0 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 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)) < 2.00000000000000004e234

   1. Initial program 98.8%

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

   if +inf.0 < (-.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))

   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 27.3%

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

   5. Taylor expanded in x around inf 77.3%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b \cdot c - \left(t \cdot \left(a \cdot 4\right) - \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i \leq -\infty:\\ \;\;\;\;\left(x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right) + \left(b \cdot c - a \cdot \left(t \cdot 4\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;\left(b \cdot c - \left(t \cdot \left(a \cdot 4\right) - \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i \leq 2 \cdot 10^{+234}:\\ \;\;\;\;\left(\left(b \cdot c - \left(t \cdot \left(a \cdot 4\right) - \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;\left(b \cdot c - \left(t \cdot \left(a \cdot 4\right) - \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i \leq \infty:\\ \;\;\;\;\left(x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right) + \left(b \cdot c - a \cdot \left(t \cdot 4\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 36.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -2.12 \cdot 10^{+117}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -1.05 \cdot 10^{-291}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.8 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 7 \cdot 10^{+30}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 8 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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 (* x i))))
   (if (<= (* b c) -2.12e+117)
     (* b c)
     (if (<= (* b c) -2e-74)
       (* t (* a -4.0))
       (if (<= (* b c) -1.05e-291)
         (* j (* k -27.0))
         (if (<= (* b c) 1.8e-306)
           t_1
           (if (<= (* b c) 7e+30)
             (* -27.0 (* j k))
             (if (<= (* b c) 8e+144) 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 * (x * i);
	double tmp;
	if ((b * c) <= -2.12e+117) {
		tmp = b * c;
	} else if ((b * c) <= -2e-74) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= -1.05e-291) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 1.8e-306) {
		tmp = t_1;
	} else if ((b * c) <= 7e+30) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 8e+144) {
		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) * (x * i)
    if ((b * c) <= (-2.12d+117)) then
        tmp = b * c
    else if ((b * c) <= (-2d-74)) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= (-1.05d-291)) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 1.8d-306) then
        tmp = t_1
    else if ((b * c) <= 7d+30) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 8d+144) 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 * (x * i);
	double tmp;
	if ((b * c) <= -2.12e+117) {
		tmp = b * c;
	} else if ((b * c) <= -2e-74) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= -1.05e-291) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 1.8e-306) {
		tmp = t_1;
	} else if ((b * c) <= 7e+30) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 8e+144) {
		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 * (x * i)
	tmp = 0
	if (b * c) <= -2.12e+117:
		tmp = b * c
	elif (b * c) <= -2e-74:
		tmp = t * (a * -4.0)
	elif (b * c) <= -1.05e-291:
		tmp = j * (k * -27.0)
	elif (b * c) <= 1.8e-306:
		tmp = t_1
	elif (b * c) <= 7e+30:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 8e+144:
		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(x * i))
	tmp = 0.0
	if (Float64(b * c) <= -2.12e+117)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2e-74)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= -1.05e-291)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 1.8e-306)
		tmp = t_1;
	elseif (Float64(b * c) <= 7e+30)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 8e+144)
		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 * (x * i);
	tmp = 0.0;
	if ((b * c) <= -2.12e+117)
		tmp = b * c;
	elseif ((b * c) <= -2e-74)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= -1.05e-291)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 1.8e-306)
		tmp = t_1;
	elseif ((b * c) <= 7e+30)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 8e+144)
		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[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.12e+117], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e-74], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.05e-291], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.8e-306], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 7e+30], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 8e+144], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -2.1200000000000001e117 or 8.00000000000000019e144 < (*.f64 b c)

   1. Initial program 82.3%

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

   3. Simplified 87.0%

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

      1. associate-*r* 83.5%

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

      2. distribute-rgt-out-- 82.3%

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

      3. associate-+l- 82.3%

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

      4. associate-*l* 79.7%

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

      5. fmm-def 82.1%

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

      6. associate-*l* 82.1%

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

      7. *-commutative 82.1%

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

   6. Applied egg-rr 82.1%

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

      1. fmm-undef 79.7%

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

      2. *-commutative 79.7%

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

   8. Simplified 79.7%

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

   9. Taylor expanded in b around inf 57.2%

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

   if -2.1200000000000001e117 < (*.f64 b c) < -1.99999999999999992e-74

   1. Initial program 77.3%

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

   3. Simplified 80.3%

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

      1. associate-*r* 83.0%

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

      2. distribute-rgt-out-- 80.2%

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

      3. associate-+l- 80.2%

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

      4. associate-*l* 80.5%

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

      5. fmm-def 83.3%

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

      6. associate-*l* 83.4%

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

      7. *-commutative 83.4%

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

   6. Applied egg-rr 83.4%

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

      1. fmm-undef 80.5%

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

      2. *-commutative 80.5%

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

   8. Simplified 80.5%

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

   9. Taylor expanded in a around inf 37.3%

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

       1. metadata-eval 37.3%

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

       2. distribute-lft-neg-in 37.3%

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

       3. associate-*r* 37.3%

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

       4. *-commutative 37.3%

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

       5. distribute-rgt-neg-in 37.3%

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

       6. distribute-lft-neg-in 37.3%

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

       7. metadata-eval 37.3%

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

   11. Simplified 37.3%

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

   if -1.99999999999999992e-74 < (*.f64 b c) < -1.05e-291

   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 89.7%

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

      1. associate-*r* 89.7%

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

      2. distribute-rgt-out-- 89.7%

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

      3. associate-+l- 89.7%

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

      4. associate-*l* 92.8%

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

      5. fmm-def 92.8%

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

      6. associate-*l* 92.7%

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

      7. *-commutative 92.7%

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

   6. Applied egg-rr 92.7%

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

      1. fmm-undef 92.7%

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

      2. *-commutative 92.7%

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

   8. Simplified 92.7%

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

      1. sub-neg 92.7%

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

      2. associate-*l* 92.6%

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

      3. *-commutative 92.6%

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

   10. Applied egg-rr 92.6%

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

       1. unsub-neg 92.6%

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

       2. associate-*r* 92.6%

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

   12. Simplified 92.6%

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

   13. Taylor expanded in j around inf 40.7%

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

       1. *-commutative 40.7%

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

       2. associate-*l* 40.8%

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

   15. Simplified 40.8%

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

   if -1.05e-291 < (*.f64 b c) < 1.79999999999999996e-306 or 7.00000000000000042e30 < (*.f64 b c) < 8.00000000000000019e144

   1. Initial program 75.9%

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

   3. Simplified 77.4%

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

      1. associate-*r* 77.5%

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

      2. distribute-rgt-out-- 75.9%

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

      3. associate-+l- 75.9%

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

      4. associate-*l* 75.7%

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

      5. fmm-def 75.7%

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

      6. associate-*l* 75.7%

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

      7. *-commutative 75.7%

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

   6. Applied egg-rr 75.7%

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

      1. fmm-undef 75.7%

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

      2. *-commutative 75.7%

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

   8. Simplified 75.7%

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

      1. sub-neg 75.7%

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

      2. associate-*l* 82.3%

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

      3. *-commutative 82.3%

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

   10. Applied egg-rr 82.3%

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

       1. unsub-neg 82.3%

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

       2. associate-*r* 82.3%

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

   12. Simplified 82.3%

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

   13. Taylor expanded in i around inf 39.0%

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

       1. *-commutative 39.0%

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

   15. Simplified 39.0%

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

   if 1.79999999999999996e-306 < (*.f64 b c) < 7.00000000000000042e30

   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 87.5%

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

   5. Taylor expanded in j around inf 44.8%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.12 \cdot 10^{+117}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -1.05 \cdot 10^{-291}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.8 \cdot 10^{-306}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 7 \cdot 10^{+30}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 8 \cdot 10^{+144}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := \left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - t\_1\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{-49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-302}:\\ \;\;\;\;\left(b \cdot c - t\_1\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+15}:\\ \;\;\;\;\left(b \cdot c + a \cdot \left(18 \cdot \left(\left(y \cdot \left(x \cdot t\right)\right) \cdot \frac{z}{a}\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (- (- (* b c) (* t (- (* a 4.0) (* 18.0 (* x (* y z)))))) t_1)))
   (if (<= t -7.2e-49)
     t_2
     (if (<= t 2.05e-302)
       (- (- (* b c) t_1) (* k (* j 27.0)))
       (if (<= t 4e+15)
         (-
          (+ (* b c) (* a (* 18.0 (* (* y (* x t)) (/ z a)))))
          (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
         t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - t_1;
	double tmp;
	if (t <= -7.2e-49) {
		tmp = t_2;
	} else if (t <= 2.05e-302) {
		tmp = ((b * c) - t_1) - (k * (j * 27.0));
	} else if (t <= 4e+15) {
		tmp = ((b * c) + (a * (18.0 * ((y * (x * t)) * (z / a))))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = 4.0d0 * (x * i)
    t_2 = ((b * c) - (t * ((a * 4.0d0) - (18.0d0 * (x * (y * z)))))) - t_1
    if (t <= (-7.2d-49)) then
        tmp = t_2
    else if (t <= 2.05d-302) then
        tmp = ((b * c) - t_1) - (k * (j * 27.0d0))
    else if (t <= 4d+15) then
        tmp = ((b * c) + (a * (18.0d0 * ((y * (x * t)) * (z / a))))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - t_1;
	double tmp;
	if (t <= -7.2e-49) {
		tmp = t_2;
	} else if (t <= 2.05e-302) {
		tmp = ((b * c) - t_1) - (k * (j * 27.0));
	} else if (t <= 4e+15) {
		tmp = ((b * c) + (a * (18.0 * ((y * (x * t)) * (z / a))))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - t_1
	tmp = 0
	if t <= -7.2e-49:
		tmp = t_2
	elif t <= 2.05e-302:
		tmp = ((b * c) - t_1) - (k * (j * 27.0))
	elif t <= 4e+15:
		tmp = ((b * c) + (a * (18.0 * ((y * (x * t)) * (z / a))))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(18.0 * Float64(x * Float64(y * z)))))) - t_1)
	tmp = 0.0
	if (t <= -7.2e-49)
		tmp = t_2;
	elseif (t <= 2.05e-302)
		tmp = Float64(Float64(Float64(b * c) - t_1) - Float64(k * Float64(j * 27.0)));
	elseif (t <= 4e+15)
		tmp = Float64(Float64(Float64(b * c) + Float64(a * Float64(18.0 * Float64(Float64(y * Float64(x * t)) * Float64(z / a))))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - t_1;
	tmp = 0.0;
	if (t <= -7.2e-49)
		tmp = t_2;
	elseif (t <= 2.05e-302)
		tmp = ((b * c) - t_1) - (k * (j * 27.0));
	elseif (t <= 4e+15)
		tmp = ((b * c) + (a * (18.0 * ((y * (x * t)) * (z / a))))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t, -7.2e-49], t$95$2, If[LessEqual[t, 2.05e-302], N[(N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+15], N[(N[(N[(b * c), $MachinePrecision] + N[(a * N[(18.0 * N[(N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.19999999999999939e-49 or 4e15 < t

   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 90.4%

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

   5. Taylor expanded in j around 0 86.6%

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

   if -7.19999999999999939e-49 < t < 2.0499999999999999e-302

   1. Initial program 77.3%

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

   3. Taylor expanded in t around 0 86.7%

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

   if 2.0499999999999999e-302 < t < 4e15

   1. Initial program 77.6%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in a around inf 74.0%

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

      1. fma-define 74.0%

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

      2. associate-/l* 72.8%

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

      3. associate-/l* 75.3%

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

   7. Simplified 75.3%

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

   8. Taylor expanded in x around inf 68.2%

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

      1. associate-*r* 74.1%

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

      2. associate-*r/ 71.7%

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

      3. associate-*r/ 75.4%

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

      4. associate-*l* 78.9%

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

      5. *-commutative 78.9%

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

   10. Simplified 78.9%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-49}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-302}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+15}:\\ \;\;\;\;\left(b \cdot c + a \cdot \left(18 \cdot \left(\left(y \cdot \left(x \cdot t\right)\right) \cdot \frac{z}{a}\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{-192}:\\ \;\;\;\;\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - t \cdot \left(a \cdot 4 - x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-109}:\\ \;\;\;\;\left(x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right) + \left(b \cdot c - a \cdot \left(t \cdot 4\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* x (* 4.0 i)) (* j (* 27.0 k)))))
   (if (<= t -9.2e-192)
     (-
      (-
       (- (* b c) (* (* x 4.0) i))
       (* t (- (* a 4.0) (* x (* z (* 18.0 y))))))
      (* k (* j 27.0)))
     (if (<= t 5e-109)
       (- (+ (* x (* (* 18.0 y) (* z t))) (- (* b c) (* a (* t 4.0)))) t_1)
       (- (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 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 = (x * (4.0 * i)) + (j * (27.0 * k));
	double tmp;
	if (t <= -9.2e-192) {
		tmp = (((b * c) - ((x * 4.0) * i)) - (t * ((a * 4.0) - (x * (z * (18.0 * y)))))) - (k * (j * 27.0));
	} else if (t <= 5e-109) {
		tmp = ((x * ((18.0 * y) * (z * t))) + ((b * c) - (a * (t * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (4.0d0 * i)) + (j * (27.0d0 * k))
    if (t <= (-9.2d-192)) then
        tmp = (((b * c) - ((x * 4.0d0) * i)) - (t * ((a * 4.0d0) - (x * (z * (18.0d0 * y)))))) - (k * (j * 27.0d0))
    else if (t <= 5d-109) then
        tmp = ((x * ((18.0d0 * y) * (z * t))) + ((b * c) - (a * (t * 4.0d0)))) - t_1
    else
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	double tmp;
	if (t <= -9.2e-192) {
		tmp = (((b * c) - ((x * 4.0) * i)) - (t * ((a * 4.0) - (x * (z * (18.0 * y)))))) - (k * (j * 27.0));
	} else if (t <= 5e-109) {
		tmp = ((x * ((18.0 * y) * (z * t))) + ((b * c) - (a * (t * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * (4.0 * i)) + (j * (27.0 * k))
	tmp = 0
	if t <= -9.2e-192:
		tmp = (((b * c) - ((x * 4.0) * i)) - (t * ((a * 4.0) - (x * (z * (18.0 * y)))))) - (k * (j * 27.0))
	elif t <= 5e-109:
		tmp = ((x * ((18.0 * y) * (z * t))) + ((b * c) - (a * (t * 4.0)))) - t_1
	else:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - 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(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k)))
	tmp = 0.0
	if (t <= -9.2e-192)
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i)) - Float64(t * Float64(Float64(a * 4.0) - Float64(x * Float64(z * Float64(18.0 * y)))))) - Float64(k * Float64(j * 27.0)));
	elseif (t <= 5e-109)
		tmp = Float64(Float64(Float64(x * Float64(Float64(18.0 * y) * Float64(z * t))) + Float64(Float64(b * c) - Float64(a * Float64(t * 4.0)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	tmp = 0.0;
	if (t <= -9.2e-192)
		tmp = (((b * c) - ((x * 4.0) * i)) - (t * ((a * 4.0) - (x * (z * (18.0 * y)))))) - (k * (j * 27.0));
	elseif (t <= 5e-109)
		tmp = ((x * ((18.0 * y) * (z * t))) + ((b * c) - (a * (t * 4.0)))) - t_1;
	else
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - 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[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2e-192], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-109], N[(N[(N[(x * N[(N[(18.0 * y), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] - N[(a * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.20000000000000073e-192

   1. Initial program 88.6%

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

      1. associate--l+ 88.6%

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

      2. distribute-rgt-out-- 92.8%

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

      3. associate-*r* 93.7%

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

      4. associate-*l* 93.8%

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

      5. associate-*r* 93.7%

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

      6. *-commutative 93.7%

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

   4. Applied egg-rr 93.7%

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

   if -9.20000000000000073e-192 < t < 5.0000000000000002e-109

   1. Initial program 70.0%

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

   3. Simplified 71.2%

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

      1. associate-*r* 71.1%

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

      2. distribute-rgt-out-- 71.1%

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

      3. associate-+l- 71.1%

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

      4. associate-*l* 80.0%

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

      5. fmm-def 80.0%

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

      6. associate-*l* 80.0%

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

      7. *-commutative 80.0%

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

   6. Applied egg-rr 80.0%

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

      1. fmm-undef 80.0%

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

      2. *-commutative 80.0%

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

   8. Simplified 80.0%

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

      1. sub-neg 80.0%

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

      2. associate-*l* 90.4%

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

      3. *-commutative 90.4%

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

   10. Applied egg-rr 90.4%

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

       1. unsub-neg 90.4%

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

       2. associate-*r* 90.4%

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

   12. Simplified 90.4%

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

   if 5.0000000000000002e-109 < t

   1. Initial program 86.6%

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

   3. Simplified 88.0%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-192}:\\ \;\;\;\;\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - t \cdot \left(a \cdot 4 - x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-109}:\\ \;\;\;\;\left(x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right) + \left(b \cdot c - a \cdot \left(t \cdot 4\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 36.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -1.4 \cdot 10^{+194}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -4.6 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 6.8 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 2.4 \cdot 10^{+31}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 6.3 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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 (* x i))))
   (if (<= (* b c) -1.4e+194)
     (* b c)
     (if (<= (* b c) -4.6e-271)
       (* t (* 18.0 (* x (* y z))))
       (if (<= (* b c) 6.8e-306)
         t_1
         (if (<= (* b c) 2.4e+31)
           (* -27.0 (* j k))
           (if (<= (* b c) 6.3e+144) 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 * (x * i);
	double tmp;
	if ((b * c) <= -1.4e+194) {
		tmp = b * c;
	} else if ((b * c) <= -4.6e-271) {
		tmp = t * (18.0 * (x * (y * z)));
	} else if ((b * c) <= 6.8e-306) {
		tmp = t_1;
	} else if ((b * c) <= 2.4e+31) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 6.3e+144) {
		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) * (x * i)
    if ((b * c) <= (-1.4d+194)) then
        tmp = b * c
    else if ((b * c) <= (-4.6d-271)) then
        tmp = t * (18.0d0 * (x * (y * z)))
    else if ((b * c) <= 6.8d-306) then
        tmp = t_1
    else if ((b * c) <= 2.4d+31) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 6.3d+144) 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 * (x * i);
	double tmp;
	if ((b * c) <= -1.4e+194) {
		tmp = b * c;
	} else if ((b * c) <= -4.6e-271) {
		tmp = t * (18.0 * (x * (y * z)));
	} else if ((b * c) <= 6.8e-306) {
		tmp = t_1;
	} else if ((b * c) <= 2.4e+31) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 6.3e+144) {
		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 * (x * i)
	tmp = 0
	if (b * c) <= -1.4e+194:
		tmp = b * c
	elif (b * c) <= -4.6e-271:
		tmp = t * (18.0 * (x * (y * z)))
	elif (b * c) <= 6.8e-306:
		tmp = t_1
	elif (b * c) <= 2.4e+31:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 6.3e+144:
		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(x * i))
	tmp = 0.0
	if (Float64(b * c) <= -1.4e+194)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -4.6e-271)
		tmp = Float64(t * Float64(18.0 * Float64(x * Float64(y * z))));
	elseif (Float64(b * c) <= 6.8e-306)
		tmp = t_1;
	elseif (Float64(b * c) <= 2.4e+31)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 6.3e+144)
		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 * (x * i);
	tmp = 0.0;
	if ((b * c) <= -1.4e+194)
		tmp = b * c;
	elseif ((b * c) <= -4.6e-271)
		tmp = t * (18.0 * (x * (y * z)));
	elseif ((b * c) <= 6.8e-306)
		tmp = t_1;
	elseif ((b * c) <= 2.4e+31)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 6.3e+144)
		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[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.4e+194], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -4.6e-271], N[(t * N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6.8e-306], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 2.4e+31], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6.3e+144], t$95$1, N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.40000000000000005e194 or 6.30000000000000024e144 < (*.f64 b c)

   1. Initial program 79.5%

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

   3. Simplified 84.0%

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

      1. associate-*r* 81.0%

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

      2. distribute-rgt-out-- 79.5%

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

      3. associate-+l- 79.5%

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

      4. associate-*l* 77.9%

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

      5. fmm-def 80.9%

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

      6. associate-*l* 80.9%

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

      7. *-commutative 80.9%

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

   6. Applied egg-rr 80.9%

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

      1. fmm-undef 77.9%

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

      2. *-commutative 77.9%

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

   8. Simplified 77.9%

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

   9. Taylor expanded in b around inf 63.8%

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

   if -1.40000000000000005e194 < (*.f64 b c) < -4.60000000000000017e-271

   1. Initial program 84.9%

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

   3. Simplified 87.4%

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

      1. associate-*r* 87.5%

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

      2. distribute-rgt-out-- 86.2%

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

      3. associate-+l- 86.2%

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

      4. associate-*l* 86.1%

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

      5. fmm-def 87.4%

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

      6. associate-*l* 87.4%

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

      7. *-commutative 87.4%

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

   6. Applied egg-rr 87.4%

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

      1. fmm-undef 86.1%

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

      2. *-commutative 86.1%

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

   8. Simplified 86.1%

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

   9. Taylor expanded in t around inf 56.6%

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

   10. Taylor expanded in x around inf 37.0%

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

   if -4.60000000000000017e-271 < (*.f64 b c) < 6.7999999999999996e-306 or 2.39999999999999982e31 < (*.f64 b c) < 6.30000000000000024e144

   1. Initial program 76.3%

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

   3. Simplified 77.8%

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

      1. associate-*r* 77.9%

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

      2. distribute-rgt-out-- 76.3%

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

      3. associate-+l- 76.3%

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

      4. associate-*l* 76.1%

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

      5. fmm-def 76.1%

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

      6. associate-*l* 76.1%

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

      7. *-commutative 76.1%

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

   6. Applied egg-rr 76.1%

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

      1. fmm-undef 76.1%

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

      2. *-commutative 76.1%

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

   8. Simplified 76.1%

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

      1. sub-neg 76.1%

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

      2. associate-*l* 82.6%

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

      3. *-commutative 82.6%

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

   10. Applied egg-rr 82.6%

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

       1. unsub-neg 82.6%

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

       2. associate-*r* 82.6%

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

   12. Simplified 82.6%

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

   13. Taylor expanded in i around inf 38.5%

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

       1. *-commutative 38.5%

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

   15. Simplified 38.5%

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

   if 6.7999999999999996e-306 < (*.f64 b c) < 2.39999999999999982e31

   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 87.5%

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

   5. Taylor expanded in j around inf 44.8%

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

Alternative 6: 87.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+215}:\\ \;\;\;\;y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - t \cdot \left(a \cdot 4 - x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

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
 (if (<= y -2.8e+215)
   (-
    (* y (+ (* -4.0 (/ (* t a) y)) (+ (* 18.0 (* t (* x z))) (/ (* b c) y))))
    (* 4.0 (* x i)))
   (-
    (- (- (* b c) (* (* x 4.0) i)) (* t (- (* a 4.0) (* x (* z (* 18.0 y))))))
    (* 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 tmp;
	if (y <= -2.8e+215) {
		tmp = (y * ((-4.0 * ((t * a) / y)) + ((18.0 * (t * (x * z))) + ((b * c) / y)))) - (4.0 * (x * i));
	} else {
		tmp = (((b * c) - ((x * 4.0) * i)) - (t * ((a * 4.0) - (x * (z * (18.0 * y)))))) - (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) :: tmp
    if (y <= (-2.8d+215)) then
        tmp = (y * (((-4.0d0) * ((t * a) / y)) + ((18.0d0 * (t * (x * z))) + ((b * c) / y)))) - (4.0d0 * (x * i))
    else
        tmp = (((b * c) - ((x * 4.0d0) * i)) - (t * ((a * 4.0d0) - (x * (z * (18.0d0 * y)))))) - (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 tmp;
	if (y <= -2.8e+215) {
		tmp = (y * ((-4.0 * ((t * a) / y)) + ((18.0 * (t * (x * z))) + ((b * c) / y)))) - (4.0 * (x * i));
	} else {
		tmp = (((b * c) - ((x * 4.0) * i)) - (t * ((a * 4.0) - (x * (z * (18.0 * y)))))) - (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):
	tmp = 0
	if y <= -2.8e+215:
		tmp = (y * ((-4.0 * ((t * a) / y)) + ((18.0 * (t * (x * z))) + ((b * c) / y)))) - (4.0 * (x * i))
	else:
		tmp = (((b * c) - ((x * 4.0) * i)) - (t * ((a * 4.0) - (x * (z * (18.0 * y)))))) - (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)
	tmp = 0.0
	if (y <= -2.8e+215)
		tmp = Float64(Float64(y * Float64(Float64(-4.0 * Float64(Float64(t * a) / y)) + Float64(Float64(18.0 * Float64(t * Float64(x * z))) + Float64(Float64(b * c) / y)))) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i)) - Float64(t * Float64(Float64(a * 4.0) - Float64(x * Float64(z * Float64(18.0 * y)))))) - 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)
	tmp = 0.0;
	if (y <= -2.8e+215)
		tmp = (y * ((-4.0 * ((t * a) / y)) + ((18.0 * (t * (x * z))) + ((b * c) / y)))) - (4.0 * (x * i));
	else
		tmp = (((b * c) - ((x * 4.0) * i)) - (t * ((a * 4.0) - (x * (z * (18.0 * y)))))) - (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_] := If[LessEqual[y, -2.8e+215], N[(N[(y * N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(18.0 * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e215

   1. Initial program 35.9%

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

   3. Simplified 45.5%

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

   5. Taylor expanded in j around 0 44.9%

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

   6. Taylor expanded in y around inf 74.6%

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

   if -2.8e215 < y

   1. Initial program 85.7%

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

      1. associate--l+ 85.7%

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

      2. distribute-rgt-out-- 87.4%

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

      3. associate-*r* 87.5%

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

      4. associate-*l* 87.5%

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

      5. associate-*r* 87.5%

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

      6. *-commutative 87.5%

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

   4. Applied egg-rr 87.5%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+215}:\\ \;\;\;\;y \cdot \left(-4 \cdot \frac{t \cdot a}{y} + \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right) + \frac{b \cdot c}{y}\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - t \cdot \left(a \cdot 4 - x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.5 \cdot 10^{+200}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{-235}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{+30}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 8.5 \cdot 10^{+144}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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) -2.5e+200)
   (* b c)
   (if (<= (* b c) 7.5e-235)
     (* t (* 18.0 (* z (* x y))))
     (if (<= (* b c) 3.2e+30)
       (* -27.0 (* j k))
       (if (<= (* b c) 8.5e+144) (* -4.0 (* x i)) (* 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) <= -2.5e+200) {
		tmp = b * c;
	} else if ((b * c) <= 7.5e-235) {
		tmp = t * (18.0 * (z * (x * y)));
	} else if ((b * c) <= 3.2e+30) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 8.5e+144) {
		tmp = -4.0 * (x * i);
	} 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) <= (-2.5d+200)) then
        tmp = b * c
    else if ((b * c) <= 7.5d-235) then
        tmp = t * (18.0d0 * (z * (x * y)))
    else if ((b * c) <= 3.2d+30) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 8.5d+144) then
        tmp = (-4.0d0) * (x * i)
    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) <= -2.5e+200) {
		tmp = b * c;
	} else if ((b * c) <= 7.5e-235) {
		tmp = t * (18.0 * (z * (x * y)));
	} else if ((b * c) <= 3.2e+30) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 8.5e+144) {
		tmp = -4.0 * (x * i);
	} 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) <= -2.5e+200:
		tmp = b * c
	elif (b * c) <= 7.5e-235:
		tmp = t * (18.0 * (z * (x * y)))
	elif (b * c) <= 3.2e+30:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 8.5e+144:
		tmp = -4.0 * (x * i)
	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) <= -2.5e+200)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 7.5e-235)
		tmp = Float64(t * Float64(18.0 * Float64(z * Float64(x * y))));
	elseif (Float64(b * c) <= 3.2e+30)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 8.5e+144)
		tmp = Float64(-4.0 * Float64(x * i));
	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) <= -2.5e+200)
		tmp = b * c;
	elseif ((b * c) <= 7.5e-235)
		tmp = t * (18.0 * (z * (x * y)));
	elseif ((b * c) <= 3.2e+30)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 8.5e+144)
		tmp = -4.0 * (x * i);
	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], -2.5e+200], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7.5e-235], N[(t * N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.2e+30], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 8.5e+144], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.50000000000000009e200 or 8.4999999999999998e144 < (*.f64 b c)

   1. Initial program 79.5%

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

   3. Simplified 84.0%

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

      1. associate-*r* 81.0%

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

      2. distribute-rgt-out-- 79.5%

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

      3. associate-+l- 79.5%

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

      4. associate-*l* 77.9%

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

      5. fmm-def 80.9%

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

      6. associate-*l* 80.9%

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

      7. *-commutative 80.9%

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

   6. Applied egg-rr 80.9%

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

      1. fmm-undef 77.9%

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

      2. *-commutative 77.9%

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

   8. Simplified 77.9%

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

   9. Taylor expanded in b around inf 63.8%

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

   if -2.50000000000000009e200 < (*.f64 b c) < 7.49999999999999968e-235

   1. Initial program 81.6%

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

   3. Simplified 83.2%

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

      1. associate-*r* 83.2%

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

      2. distribute-rgt-out-- 82.4%

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

      3. associate-+l- 82.4%

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

      4. associate-*l* 82.3%

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

      5. fmm-def 83.1%

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

      6. associate-*l* 83.1%

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

      7. *-commutative 83.1%

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

   6. Applied egg-rr 83.1%

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

      1. fmm-undef 82.3%

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

      2. *-commutative 82.3%

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

   8. Simplified 82.3%

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

   9. Taylor expanded in t around inf 53.4%

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

   10. Taylor expanded in x around inf 33.1%

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

       1. associate-*r* 35.5%

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

   12. Simplified 35.5%

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

   if 7.49999999999999968e-235 < (*.f64 b c) < 3.19999999999999973e30

   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 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 j around inf 44.3%

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

   if 3.19999999999999973e30 < (*.f64 b c) < 8.4999999999999998e144

   1. Initial program 76.9%

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

   3. Simplified 81.2%

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

      1. associate-*r* 81.6%

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

      2. distribute-rgt-out-- 76.9%

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

      3. associate-+l- 76.9%

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

      4. associate-*l* 76.6%

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

      5. fmm-def 76.6%

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

      6. associate-*l* 76.6%

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

      7. *-commutative 76.6%

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

   6. Applied egg-rr 76.6%

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

      1. fmm-undef 76.6%

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

      2. *-commutative 76.6%

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

   8. Simplified 76.6%

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

      1. sub-neg 76.6%

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

      2. associate-*l* 86.4%

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

      3. *-commutative 86.4%

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

   10. Applied egg-rr 86.4%

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

       1. unsub-neg 86.4%

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

       2. associate-*r* 86.4%

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

   12. Simplified 86.4%

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

   13. Taylor expanded in i around inf 44.1%

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

       1. *-commutative 44.1%

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

   15. Simplified 44.1%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.5 \cdot 10^{+200}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 7.5 \cdot 10^{-235}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{+30}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 8.5 \cdot 10^{+144}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 34.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -2.9 \cdot 10^{+232}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 8.2 \cdot 10^{-308}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 1.8 \cdot 10^{+31}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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 (* x i))))
   (if (<= (* b c) -2.9e+232)
     (* b c)
     (if (<= (* b c) 8.2e-308)
       t_1
       (if (<= (* b c) 1.8e+31)
         (* -27.0 (* j k))
         (if (<= (* b c) 3.8e+144) 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 * (x * i);
	double tmp;
	if ((b * c) <= -2.9e+232) {
		tmp = b * c;
	} else if ((b * c) <= 8.2e-308) {
		tmp = t_1;
	} else if ((b * c) <= 1.8e+31) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 3.8e+144) {
		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) * (x * i)
    if ((b * c) <= (-2.9d+232)) then
        tmp = b * c
    else if ((b * c) <= 8.2d-308) then
        tmp = t_1
    else if ((b * c) <= 1.8d+31) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 3.8d+144) 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 * (x * i);
	double tmp;
	if ((b * c) <= -2.9e+232) {
		tmp = b * c;
	} else if ((b * c) <= 8.2e-308) {
		tmp = t_1;
	} else if ((b * c) <= 1.8e+31) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 3.8e+144) {
		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 * (x * i)
	tmp = 0
	if (b * c) <= -2.9e+232:
		tmp = b * c
	elif (b * c) <= 8.2e-308:
		tmp = t_1
	elif (b * c) <= 1.8e+31:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 3.8e+144:
		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(x * i))
	tmp = 0.0
	if (Float64(b * c) <= -2.9e+232)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 8.2e-308)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.8e+31)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 3.8e+144)
		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 * (x * i);
	tmp = 0.0;
	if ((b * c) <= -2.9e+232)
		tmp = b * c;
	elseif ((b * c) <= 8.2e-308)
		tmp = t_1;
	elseif ((b * c) <= 1.8e+31)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 3.8e+144)
		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[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.9e+232], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 8.2e-308], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.8e+31], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.8e+144], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.90000000000000023e232 or 3.80000000000000026e144 < (*.f64 b c)

   1. Initial program 82.5%

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

   3. Simplified 85.7%

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

      1. associate-*r* 84.1%

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

      2. distribute-rgt-out-- 82.5%

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

      3. associate-+l- 82.5%

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

      4. associate-*l* 79.4%

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

      5. fmm-def 82.5%

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

      6. associate-*l* 82.5%

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

      7. *-commutative 82.5%

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

   6. Applied egg-rr 82.5%

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

      1. fmm-undef 79.4%

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

      2. *-commutative 79.4%

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

   8. Simplified 79.4%

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

   9. Taylor expanded in b around inf 66.9%

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

   if -2.90000000000000023e232 < (*.f64 b c) < 8.19999999999999965e-308 or 1.79999999999999998e31 < (*.f64 b c) < 3.80000000000000026e144

   1. Initial program 79.7%

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

   3. Simplified 82.4%

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

      1. associate-*r* 81.8%

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

      2. distribute-rgt-out-- 80.4%

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

      3. associate-+l- 80.4%

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

      4. associate-*l* 80.9%

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

      5. fmm-def 81.6%

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

      6. associate-*l* 81.6%

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

      7. *-commutative 81.6%

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

   6. Applied egg-rr 81.6%

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

      1. fmm-undef 80.9%

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

      2. *-commutative 80.9%

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

   8. Simplified 80.9%

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

      1. sub-neg 80.9%

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

      2. associate-*l* 84.4%

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

      3. *-commutative 84.4%

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

   10. Applied egg-rr 84.4%

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

       1. unsub-neg 84.4%

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

       2. associate-*r* 84.4%

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

   12. Simplified 84.4%

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

   13. Taylor expanded in i around inf 30.8%

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

       1. *-commutative 30.8%

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

   15. Simplified 30.8%

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

   if 8.19999999999999965e-308 < (*.f64 b c) < 1.79999999999999998e31

   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 87.5%

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

   5. Taylor expanded in j around inf 44.8%

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

Alternative 9: 79.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{-49} \lor \neg \left(t \leq 3 \cdot 10^{-40}\right):\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t\_1\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

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 (* 4.0 (* x i))))
   (if (or (<= t -5.8e-49) (not (<= t 3e-40)))
     (- (- (* b c) (* t (- (* a 4.0) (* 18.0 (* x (* y z)))))) t_1)
     (- (- (* b c) t_1) (* 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 = 4.0 * (x * i);
	double tmp;
	if ((t <= -5.8e-49) || !(t <= 3e-40)) {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - t_1;
	} else {
		tmp = ((b * c) - t_1) - (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) :: tmp
    t_1 = 4.0d0 * (x * i)
    if ((t <= (-5.8d-49)) .or. (.not. (t <= 3d-40))) then
        tmp = ((b * c) - (t * ((a * 4.0d0) - (18.0d0 * (x * (y * z)))))) - t_1
    else
        tmp = ((b * c) - t_1) - (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 = 4.0 * (x * i);
	double tmp;
	if ((t <= -5.8e-49) || !(t <= 3e-40)) {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - t_1;
	} else {
		tmp = ((b * c) - t_1) - (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 = 4.0 * (x * i)
	tmp = 0
	if (t <= -5.8e-49) or not (t <= 3e-40):
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - t_1
	else:
		tmp = ((b * c) - t_1) - (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(4.0 * Float64(x * i))
	tmp = 0.0
	if ((t <= -5.8e-49) || !(t <= 3e-40))
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(18.0 * Float64(x * Float64(y * z)))))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - t_1) - 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 = 4.0 * (x * i);
	tmp = 0.0;
	if ((t <= -5.8e-49) || ~((t <= 3e-40)))
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))) - t_1;
	else
		tmp = ((b * c) - t_1) - (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[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -5.8e-49], N[Not[LessEqual[t, 3e-40]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.8e-49 or 3.0000000000000002e-40 < t

   1. Initial program 86.5%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in j around 0 86.0%

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

   if -5.8e-49 < t < 3.0000000000000002e-40

   1. Initial program 76.7%

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

   3. Taylor expanded in t around 0 77.9%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-49} \lor \neg \left(t \leq 3 \cdot 10^{-40}\right):\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+128}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-198}:\\ \;\;\;\;t\_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+144}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= (* b c) -5e+128)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= (* b c) -5e-198)
       (+ t_1 (* -4.0 (* t a)))
       (if (<= (* b c) 5e+144)
         (+ (* i (* x -4.0)) t_1)
         (- (* 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 t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -5e+128) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -5e-198) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if ((b * c) <= 5e+144) {
		tmp = (i * (x * -4.0)) + t_1;
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if ((b * c) <= (-5d+128)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if ((b * c) <= (-5d-198)) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else if ((b * c) <= 5d+144) then
        tmp = (i * (x * (-4.0d0))) + t_1
    else
        tmp = (b * c) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -5e+128) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -5e-198) {
		tmp = t_1 + (-4.0 * (t * a));
	} else if ((b * c) <= 5e+144) {
		tmp = (i * (x * -4.0)) + t_1;
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if (b * c) <= -5e+128:
		tmp = (b * c) - (4.0 * (x * i))
	elif (b * c) <= -5e-198:
		tmp = t_1 + (-4.0 * (t * a))
	elif (b * c) <= 5e+144:
		tmp = (i * (x * -4.0)) + t_1
	else:
		tmp = (b * c) - (27.0 * (j * k))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -5e+128)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= -5e-198)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	elseif (Float64(b * c) <= 5e+144)
		tmp = Float64(Float64(i * Float64(x * -4.0)) + t_1);
	else
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if ((b * c) <= -5e+128)
		tmp = (b * c) - (4.0 * (x * i));
	elseif ((b * c) <= -5e-198)
		tmp = t_1 + (-4.0 * (t * a));
	elseif ((b * c) <= 5e+144)
		tmp = (i * (x * -4.0)) + t_1;
	else
		tmp = (b * c) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+128], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5e-198], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+144], N[(N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -5e128

   1. Initial program 82.9%

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

   3. Taylor expanded in t around 0 75.3%

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

   4. Taylor expanded in j around 0 73.1%

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

   if -5e128 < (*.f64 b c) < -4.9999999999999999e-198

   1. Initial program 83.9%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in a around inf 53.9%

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

      1. *-commutative 53.9%

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

   7. Simplified 53.9%

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

   if -4.9999999999999999e-198 < (*.f64 b c) < 4.9999999999999999e144

   1. Initial program 80.8%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in i around inf 53.6%

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

      1. metadata-eval 53.6%

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

      2. distribute-lft-neg-in 53.6%

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

      3. *-commutative 53.6%

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

      4. associate-*r* 53.6%

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

      5. distribute-rgt-neg-in 53.6%

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

      6. distribute-rgt-neg-in 53.6%

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

      7. metadata-eval 53.6%

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

      8. *-commutative 53.6%

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

   7. Simplified 53.6%

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

   if 4.9999999999999999e144 < (*.f64 b c)

   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 0 78.9%

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

   4. Taylor expanded in x around inf 58.6%

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

      1. cancel-sign-sub-inv 58.6%

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

      2. associate-/l* 63.3%

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

      3. metadata-eval 63.3%

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

   6. Simplified 63.3%

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

   7. Taylor expanded in x around 0 74.5%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+128}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-198}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+144}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;i \leq -2.9 \cdot 10^{+66}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.86 \cdot 10^{-230}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq 2.65 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \frac{c}{x} + i \cdot -4\right)\\ \end{array} \end{array} \]

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) (* -4.0 (* t a)))))
   (if (<= i -2.9e+66)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= i -2.8e-177)
       t_1
       (if (<= i 1.86e-230)
         (+ (* b c) (* j (* k -27.0)))
         (if (<= i 2.65e+57) t_1 (* x (+ (* b (/ c x)) (* i -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) + (-4.0 * (t * a));
	double tmp;
	if (i <= -2.9e+66) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (i <= -2.8e-177) {
		tmp = t_1;
	} else if (i <= 1.86e-230) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (i <= 2.65e+57) {
		tmp = t_1;
	} else {
		tmp = x * ((b * (c / x)) + (i * -4.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    if (i <= (-2.9d+66)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (i <= (-2.8d-177)) then
        tmp = t_1
    else if (i <= 1.86d-230) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (i <= 2.65d+57) then
        tmp = t_1
    else
        tmp = x * ((b * (c / x)) + (i * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if (i <= -2.9e+66) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (i <= -2.8e-177) {
		tmp = t_1;
	} else if (i <= 1.86e-230) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (i <= 2.65e+57) {
		tmp = t_1;
	} else {
		tmp = x * ((b * (c / x)) + (i * -4.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	tmp = 0
	if i <= -2.9e+66:
		tmp = (b * c) - (4.0 * (x * i))
	elif i <= -2.8e-177:
		tmp = t_1
	elif i <= 1.86e-230:
		tmp = (b * c) + (j * (k * -27.0))
	elif i <= 2.65e+57:
		tmp = t_1
	else:
		tmp = x * ((b * (c / x)) + (i * -4.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (i <= -2.9e+66)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (i <= -2.8e-177)
		tmp = t_1;
	elseif (i <= 1.86e-230)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (i <= 2.65e+57)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(b * Float64(c / x)) + Float64(i * -4.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	tmp = 0.0;
	if (i <= -2.9e+66)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (i <= -2.8e-177)
		tmp = t_1;
	elseif (i <= 1.86e-230)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (i <= 2.65e+57)
		tmp = t_1;
	else
		tmp = x * ((b * (c / x)) + (i * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.9e+66], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.8e-177], t$95$1, If[LessEqual[i, 1.86e-230], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.65e+57], t$95$1, N[(x * N[(N[(b * N[(c / x), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.89999999999999986e66

   1. Initial program 80.4%

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

   3. Taylor expanded in t around 0 75.8%

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

   4. Taylor expanded in j around 0 65.1%

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

   if -2.89999999999999986e66 < i < -2.79999999999999987e-177 or 1.86000000000000004e-230 < i < 2.64999999999999993e57

   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 87.0%

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

   5. Taylor expanded in j around 0 76.8%

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

   6. Taylor expanded in x around 0 50.6%

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

   if -2.79999999999999987e-177 < i < 1.86000000000000004e-230

   1. Initial program 92.9%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in b around inf 63.4%

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

   if 2.64999999999999993e57 < i

   1. Initial program 71.2%

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

   3. Taylor expanded in t around 0 75.2%

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

   4. Taylor expanded in j around 0 62.0%

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

   5. Taylor expanded in x around inf 58.3%

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

      1. cancel-sign-sub-inv 67.7%

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

      2. associate-/l* 69.7%

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

      3. metadata-eval 69.7%

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

   7. Simplified 60.2%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{+66}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-177}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.86 \cdot 10^{-230}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq 2.65 \cdot 10^{+57}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \frac{c}{x} + i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ t_2 := t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -9.6 \cdot 10^{+190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -47:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+19}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* t (+ (* 18.0 (* z (* x y))) (* a -4.0)))))
   (if (<= t -9.6e+190)
     t_2
     (if (<= t -47.0)
       (- (- (* b c) (* 4.0 (* t a))) t_1)
       (if (<= t 2.6e+19) (- (- (* 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 = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	double tmp;
	if (t <= -9.6e+190) {
		tmp = t_2;
	} else if (t <= -47.0) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= 2.6e+19) {
		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 = t * ((18.0d0 * (z * (x * y))) + (a * (-4.0d0)))
    if (t <= (-9.6d+190)) then
        tmp = t_2
    else if (t <= (-47.0d0)) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (t <= 2.6d+19) 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 = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	double tmp;
	if (t <= -9.6e+190) {
		tmp = t_2;
	} else if (t <= -47.0) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= 2.6e+19) {
		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 = t * ((18.0 * (z * (x * y))) + (a * -4.0))
	tmp = 0
	if t <= -9.6e+190:
		tmp = t_2
	elif t <= -47.0:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif t <= 2.6e+19:
		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(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) + Float64(a * -4.0)))
	tmp = 0.0
	if (t <= -9.6e+190)
		tmp = t_2;
	elseif (t <= -47.0)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (t <= 2.6e+19)
		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 = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	tmp = 0.0;
	if (t <= -9.6e+190)
		tmp = t_2;
	elseif (t <= -47.0)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (t <= 2.6e+19)
		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[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.6e+190], t$95$2, If[LessEqual[t, -47.0], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 2.6e+19], 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 3 regimes

2. if t < -9.5999999999999994e190 or 2.6e19 < t

   1. Initial program 83.7%

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

   3. Simplified 88.8%

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

      1. associate-*r* 89.9%

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

      2. distribute-rgt-out-- 84.9%

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

      3. associate-+l- 84.9%

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

      4. associate-*l* 80.0%

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

      5. fmm-def 81.3%

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

      6. associate-*l* 81.3%

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

      7. *-commutative 81.3%

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

   6. Applied egg-rr 81.3%

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

      1. fmm-undef 80.0%

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

      2. *-commutative 80.0%

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

   8. Simplified 80.0%

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

   9. Taylor expanded in t around inf 76.9%

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

       1. cancel-sign-sub-inv 76.9%

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

       2. associate-*r* 78.2%

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

       3. metadata-eval 78.2%

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

   11. Simplified 78.2%

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

   if -9.5999999999999994e190 < t < -47

   1. Initial program 92.0%

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

   3. Taylor expanded in x around 0 71.0%

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

   if -47 < t < 2.6e19

   1. Initial program 78.1%

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

   3. Taylor expanded in t around 0 75.6%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{+190}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -47:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+19}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;i \leq -5.2 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{-231}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq 4.7 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a)))) (t_2 (- (* b c) (* 4.0 (* x i)))))
   (if (<= i -5.2e+67)
     t_2
     (if (<= i -6e-179)
       t_1
       (if (<= i 8.2e-231)
         (+ (* b c) (* j (* k -27.0)))
         (if (<= i 4.7e+58) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = (b * c) - (4.0 * (x * i));
	double tmp;
	if (i <= -5.2e+67) {
		tmp = t_2;
	} else if (i <= -6e-179) {
		tmp = t_1;
	} else if (i <= 8.2e-231) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (i <= 4.7e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    t_2 = (b * c) - (4.0d0 * (x * i))
    if (i <= (-5.2d+67)) then
        tmp = t_2
    else if (i <= (-6d-179)) then
        tmp = t_1
    else if (i <= 8.2d-231) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (i <= 4.7d+58) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = (b * c) - (4.0 * (x * i));
	double tmp;
	if (i <= -5.2e+67) {
		tmp = t_2;
	} else if (i <= -6e-179) {
		tmp = t_1;
	} else if (i <= 8.2e-231) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (i <= 4.7e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	t_2 = (b * c) - (4.0 * (x * i))
	tmp = 0
	if i <= -5.2e+67:
		tmp = t_2
	elif i <= -6e-179:
		tmp = t_1
	elif i <= 8.2e-231:
		tmp = (b * c) + (j * (k * -27.0))
	elif i <= 4.7e+58:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	tmp = 0.0
	if (i <= -5.2e+67)
		tmp = t_2;
	elseif (i <= -6e-179)
		tmp = t_1;
	elseif (i <= 8.2e-231)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (i <= 4.7e+58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	t_2 = (b * c) - (4.0 * (x * i));
	tmp = 0.0;
	if (i <= -5.2e+67)
		tmp = t_2;
	elseif (i <= -6e-179)
		tmp = t_1;
	elseif (i <= 8.2e-231)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (i <= 4.7e+58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.2e+67], t$95$2, If[LessEqual[i, -6e-179], t$95$1, If[LessEqual[i, 8.2e-231], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.7e+58], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -5.2000000000000001e67 or 4.69999999999999972e58 < i

   1. Initial program 76.0%

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

   3. Taylor expanded in t around 0 75.5%

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

   4. Taylor expanded in j around 0 63.6%

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

   if -5.2000000000000001e67 < i < -6.00000000000000012e-179 or 8.2000000000000003e-231 < i < 4.69999999999999972e58

   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 87.0%

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

   5. Taylor expanded in j around 0 76.8%

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

   6. Taylor expanded in x around 0 50.6%

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

   if -6.00000000000000012e-179 < i < 8.2000000000000003e-231

   1. Initial program 92.9%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in b around inf 63.4%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{+67}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-179}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{-231}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq 4.7 \cdot 10^{+58}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -6.3 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-196}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+18}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= t -6.3e-49)
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
     (if (<= t 3.6e-196)
       (+ (* i (* x -4.0)) t_1)
       (if (<= t 3.8e+18)
         (+ (* b c) t_1)
         (* t (+ (* 18.0 (* z (* x y))) (* 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 = j * (k * -27.0);
	double tmp;
	if (t <= -6.3e-49) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= 3.6e-196) {
		tmp = (i * (x * -4.0)) + t_1;
	} else if (t <= 3.8e+18) {
		tmp = (b * c) + t_1;
	} else {
		tmp = t * ((18.0 * (z * (x * y))) + (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 = j * (k * (-27.0d0))
    if (t <= (-6.3d-49)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= 3.6d-196) then
        tmp = (i * (x * (-4.0d0))) + t_1
    else if (t <= 3.8d+18) then
        tmp = (b * c) + t_1
    else
        tmp = t * ((18.0d0 * (z * (x * y))) + (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 = j * (k * -27.0);
	double tmp;
	if (t <= -6.3e-49) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= 3.6e-196) {
		tmp = (i * (x * -4.0)) + t_1;
	} else if (t <= 3.8e+18) {
		tmp = (b * c) + t_1;
	} else {
		tmp = t * ((18.0 * (z * (x * y))) + (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 = j * (k * -27.0)
	tmp = 0
	if t <= -6.3e-49:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= 3.6e-196:
		tmp = (i * (x * -4.0)) + t_1
	elif t <= 3.8e+18:
		tmp = (b * c) + t_1
	else:
		tmp = t * ((18.0 * (z * (x * y))) + (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(j * Float64(k * -27.0))
	tmp = 0.0
	if (t <= -6.3e-49)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= 3.6e-196)
		tmp = Float64(Float64(i * Float64(x * -4.0)) + t_1);
	elseif (t <= 3.8e+18)
		tmp = Float64(Float64(b * c) + t_1);
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) + 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 = j * (k * -27.0);
	tmp = 0.0;
	if (t <= -6.3e-49)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= 3.6e-196)
		tmp = (i * (x * -4.0)) + t_1;
	elseif (t <= 3.8e+18)
		tmp = (b * c) + t_1;
	else
		tmp = t * ((18.0 * (z * (x * y))) + (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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.3e-49], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-196], N[(N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 3.8e+18], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.2999999999999997e-49

   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 94.5%

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

      1. associate-*r* 93.3%

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

      2. distribute-rgt-out-- 87.9%

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

      3. associate-+l- 87.9%

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

      4. associate-*l* 82.5%

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

      5. fmm-def 82.5%

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

      6. associate-*l* 82.5%

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

      7. *-commutative 82.5%

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

   6. Applied egg-rr 82.5%

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

      1. fmm-undef 82.5%

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

      2. *-commutative 82.5%

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

   8. Simplified 82.5%

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

   9. Taylor expanded in t around inf 68.8%

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

   if -6.2999999999999997e-49 < t < 3.6000000000000001e-196

   1. Initial program 72.6%

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

   3. Simplified 76.3%

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

   5. Taylor expanded in i around inf 65.8%

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

      1. metadata-eval 65.8%

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

      2. distribute-lft-neg-in 65.8%

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

      3. *-commutative 65.8%

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

      4. associate-*r* 65.8%

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

      5. distribute-rgt-neg-in 65.8%

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

      6. distribute-rgt-neg-in 65.8%

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

      7. metadata-eval 65.8%

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

      8. *-commutative 65.8%

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

   7. Simplified 65.8%

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

   if 3.6000000000000001e-196 < t < 3.8e18

   1. Initial program 85.7%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in b around inf 59.9%

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

   if 3.8e18 < t

   1. Initial program 84.2%

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

   3. Simplified 84.4%

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

      1. associate-*r* 86.2%

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

      2. distribute-rgt-out-- 86.2%

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

      3. associate-+l- 86.2%

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

      4. associate-*l* 78.5%

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

      5. fmm-def 80.5%

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

      6. associate-*l* 80.5%

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

      7. *-commutative 80.5%

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

   6. Applied egg-rr 80.5%

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

      1. fmm-undef 78.5%

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

      2. *-commutative 78.5%

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

   8. Simplified 78.5%

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

   9. Taylor expanded in t around inf 71.4%

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

       1. cancel-sign-sub-inv 71.4%

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

       2. associate-*r* 73.3%

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

       3. metadata-eval 73.3%

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

   11. Simplified 73.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-196}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+18}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{-49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-196}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + t\_1\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+21}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* j (* k -27.0)))
        (t_2 (* t (+ (* 18.0 (* z (* x y))) (* a -4.0)))))
   (if (<= t -7.2e-49)
     t_2
     (if (<= t 2.9e-196)
       (+ (* i (* x -4.0)) t_1)
       (if (<= t 1.06e+21) (+ (* b c) 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 = j * (k * -27.0);
	double t_2 = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	double tmp;
	if (t <= -7.2e-49) {
		tmp = t_2;
	} else if (t <= 2.9e-196) {
		tmp = (i * (x * -4.0)) + t_1;
	} else if (t <= 1.06e+21) {
		tmp = (b * c) + 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 = j * (k * (-27.0d0))
    t_2 = t * ((18.0d0 * (z * (x * y))) + (a * (-4.0d0)))
    if (t <= (-7.2d-49)) then
        tmp = t_2
    else if (t <= 2.9d-196) then
        tmp = (i * (x * (-4.0d0))) + t_1
    else if (t <= 1.06d+21) then
        tmp = (b * c) + 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 = j * (k * -27.0);
	double t_2 = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	double tmp;
	if (t <= -7.2e-49) {
		tmp = t_2;
	} else if (t <= 2.9e-196) {
		tmp = (i * (x * -4.0)) + t_1;
	} else if (t <= 1.06e+21) {
		tmp = (b * c) + 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 = j * (k * -27.0)
	t_2 = t * ((18.0 * (z * (x * y))) + (a * -4.0))
	tmp = 0
	if t <= -7.2e-49:
		tmp = t_2
	elif t <= 2.9e-196:
		tmp = (i * (x * -4.0)) + t_1
	elif t <= 1.06e+21:
		tmp = (b * c) + 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(j * Float64(k * -27.0))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) + Float64(a * -4.0)))
	tmp = 0.0
	if (t <= -7.2e-49)
		tmp = t_2;
	elseif (t <= 2.9e-196)
		tmp = Float64(Float64(i * Float64(x * -4.0)) + t_1);
	elseif (t <= 1.06e+21)
		tmp = Float64(Float64(b * c) + 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 = j * (k * -27.0);
	t_2 = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	tmp = 0.0;
	if (t <= -7.2e-49)
		tmp = t_2;
	elseif (t <= 2.9e-196)
		tmp = (i * (x * -4.0)) + t_1;
	elseif (t <= 1.06e+21)
		tmp = (b * c) + 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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e-49], t$95$2, If[LessEqual[t, 2.9e-196], N[(N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 1.06e+21], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.19999999999999939e-49 or 1.06e21 < t

   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 90.4%

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

      1. associate-*r* 90.4%

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

      2. distribute-rgt-out-- 87.2%

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

      3. associate-+l- 87.2%

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

      4. associate-*l* 80.9%

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

      5. fmm-def 81.7%

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

      6. associate-*l* 81.7%

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

      7. *-commutative 81.7%

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

   6. Applied egg-rr 81.7%

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

      1. fmm-undef 80.9%

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

      2. *-commutative 80.9%

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

   8. Simplified 80.9%

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

   9. Taylor expanded in t around inf 69.9%

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

       1. cancel-sign-sub-inv 69.9%

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

       2. associate-*r* 69.2%

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

       3. metadata-eval 69.2%

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

   11. Simplified 69.2%

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

   if -7.19999999999999939e-49 < t < 2.89999999999999987e-196

   1. Initial program 72.6%

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

   3. Simplified 76.3%

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

   5. Taylor expanded in i around inf 65.8%

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

      1. metadata-eval 65.8%

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

      2. distribute-lft-neg-in 65.8%

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

      3. *-commutative 65.8%

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

      4. associate-*r* 65.8%

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

      5. distribute-rgt-neg-in 65.8%

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

      6. distribute-rgt-neg-in 65.8%

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

      7. metadata-eval 65.8%

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

      8. *-commutative 65.8%

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

   7. Simplified 65.8%

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

   if 2.89999999999999987e-196 < t < 1.06e21

   1. Initial program 85.7%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in b around inf 59.9%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-196}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+21}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 75.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-49} \lor \neg \left(t \leq 4.2 \cdot 10^{-41}\right):\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

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
 (if (or (<= t -8.6e-49) (not (<= t 4.2e-41)))
   (- (* b c) (* t (- (* a 4.0) (* 18.0 (* x (* y z))))))
   (- (- (* b c) (* 4.0 (* x i))) (* 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 tmp;
	if ((t <= -8.6e-49) || !(t <= 4.2e-41)) {
		tmp = (b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (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) :: tmp
    if ((t <= (-8.6d-49)) .or. (.not. (t <= 4.2d-41))) then
        tmp = (b * c) - (t * ((a * 4.0d0) - (18.0d0 * (x * (y * z)))))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - (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 tmp;
	if ((t <= -8.6e-49) || !(t <= 4.2e-41)) {
		tmp = (b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (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):
	tmp = 0
	if (t <= -8.6e-49) or not (t <= 4.2e-41):
		tmp = (b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - (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)
	tmp = 0.0
	if ((t <= -8.6e-49) || !(t <= 4.2e-41))
		tmp = Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(18.0 * Float64(x * Float64(y * z))))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - 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)
	tmp = 0.0;
	if ((t <= -8.6e-49) || ~((t <= 4.2e-41)))
		tmp = (b * c) - (t * ((a * 4.0) - (18.0 * (x * (y * z)))));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - (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_] := If[Or[LessEqual[t, -8.6e-49], N[Not[LessEqual[t, 4.2e-41]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.60000000000000033e-49 or 4.20000000000000025e-41 < t

   1. Initial program 86.5%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in 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 81.1%

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

   if -8.60000000000000033e-49 < t < 4.20000000000000025e-41

   1. Initial program 76.7%

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

   3. Taylor expanded in t around 0 77.9%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-49} \lor \neg \left(t \leq 4.2 \cdot 10^{-41}\right):\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 72.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+114} \lor \neg \left(x \leq 15600000\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

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
 (if (or (<= x -2.05e+114) (not (<= x 15600000.0)))
   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
   (- (- (* b c) (* 4.0 (* t a))) (* 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 tmp;
	if ((x <= -2.05e+114) || !(x <= 15600000.0)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - (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) :: tmp
    if ((x <= (-2.05d+114)) .or. (.not. (x <= 15600000.0d0))) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - (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 tmp;
	if ((x <= -2.05e+114) || !(x <= 15600000.0)) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - (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):
	tmp = 0
	if (x <= -2.05e+114) or not (x <= 15600000.0):
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - (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)
	tmp = 0.0
	if ((x <= -2.05e+114) || !(x <= 15600000.0))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - 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)
	tmp = 0.0;
	if ((x <= -2.05e+114) || ~((x <= 15600000.0)))
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = ((b * c) - (4.0 * (t * a))) - (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_] := If[Or[LessEqual[x, -2.05e+114], N[Not[LessEqual[x, 15600000.0]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.05e114 or 1.56e7 < x

   1. Initial program 70.7%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in x around inf 71.2%

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

   if -2.05e114 < x < 1.56e7

   1. Initial program 90.7%

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

   3. Taylor expanded in x around 0 72.0%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+114} \lor \neg \left(x \leq 15600000\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 55.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+128} \lor \neg \left(b \cdot c \leq 10^{+30}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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+128) (not (<= (* b c) 1e+30)))
   (- (* b c) (* 4.0 (* x i)))
   (+ (* j (* k -27.0)) (* -4.0 (* t a)))))

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+128) || !((b * c) <= 1e+30)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a));
	}
	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+128)) .or. (.not. ((b * c) <= 1d+30))) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * (t * a))
    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+128) || !((b * c) <= 1e+30)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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+128) or not ((b * c) <= 1e+30):
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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+128) || !(Float64(b * c) <= 1e+30))
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(t * a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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+128) || ~(((b * c) <= 1e+30)))
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = (j * (k * -27.0)) + (-4.0 * (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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+128], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1e+30]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -5e128 or 1e30 < (*.f64 b c)

   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 0 73.0%

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

   4. Taylor expanded in j around 0 66.5%

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

   if -5e128 < (*.f64 b c) < 1e30

   1. Initial program 82.5%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in a around inf 51.3%

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

      1. *-commutative 51.3%

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

   7. Simplified 51.3%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+128} \lor \neg \left(b \cdot c \leq 10^{+30}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 49.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -2.35 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{-302}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (<= j -2.35e+140)
     t_1
     (if (<= j 2.9e-302)
       (+ (* b c) (* -4.0 (* t a)))
       (if (<= j 1.02e-112) (* t (* 18.0 (* z (* x y)))) 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 (j <= -2.35e+140) {
		tmp = t_1;
	} else if (j <= 2.9e-302) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (j <= 1.02e-112) {
		tmp = t * (18.0 * (z * (x * y)));
	} 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 (j <= (-2.35d+140)) then
        tmp = t_1
    else if (j <= 2.9d-302) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (j <= 1.02d-112) then
        tmp = t * (18.0d0 * (z * (x * y)))
    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 (j <= -2.35e+140) {
		tmp = t_1;
	} else if (j <= 2.9e-302) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (j <= 1.02e-112) {
		tmp = t * (18.0 * (z * (x * y)));
	} 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 j <= -2.35e+140:
		tmp = t_1
	elif j <= 2.9e-302:
		tmp = (b * c) + (-4.0 * (t * a))
	elif j <= 1.02e-112:
		tmp = t * (18.0 * (z * (x * y)))
	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 (j <= -2.35e+140)
		tmp = t_1;
	elseif (j <= 2.9e-302)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (j <= 1.02e-112)
		tmp = Float64(t * Float64(18.0 * Float64(z * Float64(x * y))));
	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 (j <= -2.35e+140)
		tmp = t_1;
	elseif (j <= 2.9e-302)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (j <= 1.02e-112)
		tmp = t * (18.0 * (z * (x * y)));
	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[j, -2.35e+140], t$95$1, If[LessEqual[j, 2.9e-302], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.02e-112], N[(t * N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.35000000000000015e140 or 1.01999999999999996e-112 < j

   1. Initial program 75.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in b around inf 50.9%

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

   if -2.35000000000000015e140 < j < 2.89999999999999994e-302

   1. Initial program 85.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in j around 0 77.5%

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

   6. Taylor expanded in x around 0 48.1%

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

   if 2.89999999999999994e-302 < j < 1.01999999999999996e-112

   1. Initial program 91.4%

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

   3. Simplified 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. Step-by-step derivation

      1. associate-*r* 93.6%

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

      2. distribute-rgt-out-- 91.4%

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

      3. associate-+l- 91.4%

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

      4. associate-*l* 91.5%

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

      5. fmm-def 91.5%

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

      6. associate-*l* 91.5%

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

      7. *-commutative 91.5%

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

   6. Applied egg-rr 91.5%

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

      1. fmm-undef 91.5%

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

      2. *-commutative 91.5%

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

   8. Simplified 91.5%

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

   9. Taylor expanded in t around inf 62.0%

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

   10. Taylor expanded in x around inf 42.7%

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

       1. associate-*r* 42.8%

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

   12. Simplified 42.8%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.35 \cdot 10^{+140}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{-302}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 45.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+79} \lor \neg \left(y \leq 8 \cdot 10^{-50}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (<= y -3.6e+79) (not (<= y 8e-50)))
   (* t (* 18.0 (* z (* x y))))
   (+ (* b c) (* -4.0 (* t a)))))

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 <= -3.6e+79) || !(y <= 8e-50)) {
		tmp = t * (18.0 * (z * (x * y)));
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	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 ((y <= (-3.6d+79)) .or. (.not. (y <= 8d-50))) then
        tmp = t * (18.0d0 * (z * (x * y)))
    else
        tmp = (b * c) + ((-4.0d0) * (t * a))
    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 ((y <= -3.6e+79) || !(y <= 8e-50)) {
		tmp = t * (18.0 * (z * (x * y)));
	} else {
		tmp = (b * c) + (-4.0 * (t * a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (y <= -3.6e+79) or not (y <= 8e-50):
		tmp = t * (18.0 * (z * (x * y)))
	else:
		tmp = (b * c) + (-4.0 * (t * a))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -3.6e+79) || !(y <= 8e-50))
		tmp = Float64(t * Float64(18.0 * Float64(z * Float64(x * y))));
	else
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((y <= -3.6e+79) || ~((y <= 8e-50)))
		tmp = t * (18.0 * (z * (x * y)));
	else
		tmp = (b * c) + (-4.0 * (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[y, -3.6e+79], N[Not[LessEqual[y, 8e-50]], $MachinePrecision]], N[(t * N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5999999999999999e79 or 8.00000000000000006e-50 < y

   1. Initial program 69.7%

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

   3. Simplified 74.6%

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

      1. associate-*r* 73.8%

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

      2. distribute-rgt-out-- 70.6%

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

      3. associate-+l- 70.6%

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

      4. associate-*l* 75.2%

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

      5. fmm-def 76.8%

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

      6. associate-*l* 76.8%

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

      7. *-commutative 76.8%

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

   6. Applied egg-rr 76.8%

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

      1. fmm-undef 75.2%

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

      2. *-commutative 75.2%

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

   8. Simplified 75.2%

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

   9. Taylor expanded in t around inf 52.6%

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

   10. Taylor expanded in x around inf 44.2%

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

       1. associate-*r* 46.6%

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

   12. Simplified 46.6%

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

   if -3.5999999999999999e79 < y < 8.00000000000000006e-50

   1. Initial program 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in j around 0 71.7%

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

   6. Taylor expanded in x around 0 47.0%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+79} \lor \neg \left(y \leq 8 \cdot 10^{-50}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 38.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.9 \cdot 10^{+124} \lor \neg \left(b \cdot c \leq 2.8 \cdot 10^{+160}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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) -1.9e+124) (not (<= (* b c) 2.8e+160)))
   (* 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) <= -1.9e+124) || !((b * c) <= 2.8e+160)) {
		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) <= (-1.9d+124)) .or. (.not. ((b * c) <= 2.8d+160))) 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) <= -1.9e+124) || !((b * c) <= 2.8e+160)) {
		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) <= -1.9e+124) or not ((b * c) <= 2.8e+160):
		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) <= -1.9e+124) || !(Float64(b * c) <= 2.8e+160))
		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) <= -1.9e+124) || ~(((b * c) <= 2.8e+160)))
		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], -1.9e+124], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2.8e+160]], $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) < -1.8999999999999999e124 or 2.8e160 < (*.f64 b c)

   1. Initial program 80.7%

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

   3. Simplified 85.8%

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

      1. associate-*r* 82.0%

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

      2. distribute-rgt-out-- 80.7%

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

      3. associate-+l- 80.7%

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

      4. associate-*l* 77.9%

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

      5. fmm-def 80.5%

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

      6. associate-*l* 80.5%

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

      7. *-commutative 80.5%

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

   6. Applied egg-rr 80.5%

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

      1. fmm-undef 77.9%

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

      2. *-commutative 77.9%

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

   8. Simplified 77.9%

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

   9. Taylor expanded in b around inf 59.6%

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

   if -1.8999999999999999e124 < (*.f64 b c) < 2.8e160

   1. Initial program 82.3%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in j around inf 28.0%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.9 \cdot 10^{+124} \lor \neg \left(b \cdot c \leq 2.8 \cdot 10^{+160}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 23.4% accurate, 10.3× speedup

Math

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

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 81.8%

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

3. Simplified 84.2%

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

   1. associate-*r* 83.8%

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

   2. distribute-rgt-out-- 82.2%

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

   3. associate-+l- 82.2%

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

   4. associate-*l* 82.1%

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

   5. fmm-def 83.3%

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

   6. associate-*l* 83.3%

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

   7. *-commutative 83.3%

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

6. Applied egg-rr 83.3%

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

   1. fmm-undef 82.1%

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

   2. *-commutative 82.1%

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

8. Simplified 82.1%

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

9. Taylor expanded in b around inf 21.8%

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

Developer Target 1: 90.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024157 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

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

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